From a8f228d5a18d20ad2dbded57e54ece6a864e3f5b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 10 Oct 2025 20:17:54 -0400
Subject: [PATCH 001/181] First commit of the "Get'EM Back" project! The code
 has the main infrastructures to include Aparallel effects by solving apardot
 and stepping Aparallel accordingly. Of course many bugs must reside and for
 now the EM effects are not included in the GK rhs. I checked that the 2x2v
 D3D regression test is behaving exactly the same if we activate EM or not. I
 want to see next if we get meaningful Apar and Apardot values as the
 diagnostics are included.

---
 core/zero/gkyl_eqn_type.h                     |   1 +
 gyrokinetic/apps/gk_field.c                   | 193 +++++++++++++++++-
 gyrokinetic/apps/gk_species.c                 |  84 +++++++-
 gyrokinetic/apps/gk_species_projection.c      |   2 +-
 gyrokinetic/apps/gkyl_gyrokinetic.h           |   8 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  91 ++++++++-
 gyrokinetic/apps/gyrokinetic.c                |  48 ++++-
 gyrokinetic/apps/gyrokinetic_lw.c             |   1 +
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c |   4 +-
 gyrokinetic/zero/fem_poisson_perp.c           |  80 ++++++--
 gyrokinetic/zero/gkyl_fem_poisson_perp.h      |  22 ++
 gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h |   5 +
 12 files changed, 490 insertions(+), 49 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 194cd5f906..4df59b2be7 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -42,6 +42,7 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
   GKYL_GK_FIELD_ES_IWL = 3, // Inner-wall limited ES.
   GKYL_GK_FIELD_EM = 4, // Electromagnetic GK
+  GKYL_GK_FIELD_EM_IWL = 5, // Inner-wall limited EM
 };
 
 // Identifiers for specific field object types
diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 4ab9a42651..aba66e062b 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -115,6 +115,91 @@ gk_field_enforce_zbc_none(const gkyl_gyrokinetic_app *app, const struct gk_field
 {
 }
 
+static void
+gk_field_accumulate_current_dens_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->currentDens, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+
+    gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
+
+    gkyl_array_accumulate_range(field->currentDens, s->info.charge, s->m1.marr, &app->local);
+  } 
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void
+gk_field_accumulate_current_dens_dot_none(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+}
+
+static void
+gk_field_accumulate_current_dens_dot_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->currentDensdot, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+
+    gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
+
+    gkyl_array_accumulate_range(field->currentDensdot, s->info.charge, s->m1.marr, &app->local);
+  } 
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void
+gk_field_accumulate_current_dens_none(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+}
+
+static void 
+gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
+  gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
+  gkyl_fem_poisson_perp_solve(field->fem_apardot,field->apardot);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void 
+gk_field_ohm_solve_none(struct gkyl_gyrokinetic_app *app, struct gk_field *field)
+{
+}
+
+static void 
+gk_field_ampere_solve(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
+  gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void 
+gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field)
+{
+}
+
+static void
+gk_field_step_apar_dyn(struct gk_field *field, struct gkyl_array* out, double dt,
+  const struct gkyl_array* inp)
+{
+  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
+}
+
+static void
+gk_field_step_apar_none(struct gk_field *field, struct gkyl_array* out, double dt,
+  const struct gkyl_array* inp)
+{
+  // do nothing
+}
+
 // initialize field object
 struct gk_field* 
 gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
@@ -125,6 +210,10 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD_ES;
 
+  f->is_clopen = f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL;
+
+  f->is_em = f->gkfield_id == GKYL_GK_FIELD_EM || f->gkfield_id == GKYL_GK_FIELD_EM_IWL;
+
   f->calc_init_field = !f->info.zero_init_field;
   f->update_field = !f->info.is_static;
   // The combination update_field=true, calc_init_field=false is not allowed.
@@ -141,11 +230,6 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   // local phi (assuming domain decomposition is *only* in z right now)
   f->phi_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  }
-
   f->init_phi_pol = false;
   if (f->info.polarization_potential) {
     // Project the initial potential onto a p+1 tensor basis and compute the polarization
@@ -271,7 +355,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
   // Potential smoothing (in z) updater
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->is_clopen) {
     enum gkyl_fem_parproj_bc_type fem_parproj_bc_core, fem_parproj_bc_sol;
     if (app->cdim == 2) {
       fem_parproj_bc_core = GKYL_FEM_PARPROJ_PERIODIC;
@@ -393,6 +477,51 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       gkyl_array_copy(f->phi_wall_up, f->phi_wall_up_host);
   }
 
+  // Electromagnetic GK structures to evolve Aparallel
+  f->ohm_solve = gk_field_ohm_solve_none;
+  f->ampere_solve = gk_field_ampere_solve_none;
+  f->accumulate_current = gk_field_accumulate_current_dens_none;
+  f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_none;
+  f->step_apar = gk_field_step_apar_none;
+  if (f->is_em) {
+    f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar_old = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    
+    f->apar_host = f->apar;
+    f->apardot_host = f->apardot;
+    if (app->use_gpu) {
+      f->apar_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+      f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+    }
+
+    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apardot_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->lapWeightAmpere = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+
+    // Compute the weights in front of the laplacian operator (metric x 1/mu0)
+    struct gkyl_array *Jgij[3] = {app->gk_geom->gxxj, app->gk_geom->gxyj, app->gk_geom->gyyj};
+    for (int i=0; i<app->cdim-2/app->cdim; i++) {
+      gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
+    }
+    // FEM solver for Ampere equation (solved at IC only).
+    f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+        &f->info.ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+    // FEM solver for Ohm's law (evolves d(Apart)/dt).
+    f->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+      &f->info.ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+
+    // Pointer to function that solves Ohm's law and Amperes equation.
+    f->ohm_solve = gk_field_ohm_solve;
+    f->ampere_solve = gk_field_ampere_solve;
+    f->accumulate_current = gk_field_accumulate_current_dens_dyn;
+    f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_dyn;
+    f->step_apar = gk_field_step_apar_dyn;
+  }
+
   // Create operator needed for FLR effects.
   f->use_flr = false;
   f->invert_flr = gk_field_invert_flr_none;
@@ -441,7 +570,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
     // twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL){
+  if (f->is_clopen){
     gk_field_add_TSBC_and_SSFG_updaters(app,f);
     f->enforce_zbc = gk_field_enforce_zbc;
   } else {
@@ -471,6 +600,8 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
   const struct gkyl_array *fin[])
 {
   struct timespec wst = gkyl_wall_clock();
+  if (field->is_em)
+    gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
   gkyl_array_clear(field->rho_c, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
@@ -501,11 +632,23 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
         double q_s = field->info.electron_charge;
         gkyl_array_shiftc_range(field->rho_c, q_s*n_s0*sqrt(2.0), 0, &app->local);
       }
+      if (field->is_em) {
+        // Use m0 to update also the kSq matrix of the Ohm's law solver.
+        double fac = s->info.charge*s->info.charge/s->info.mass;
+        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0.marr, &app->local);
+      }
     }
   } 
   app->stat.field_phi_rhs_tm += gkyl_time_diff_now_sec(wst);
 }
 
+void
+gk_field_accumulate_current_dens(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  field->accumulate_current(app, field, fin);
+}
+
 static void
 gk_field_calc_ambi_pot_sheath_vals(gkyl_gyrokinetic_app *app, struct gk_field *field)
 {
@@ -584,7 +727,7 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
       // Gather charge density into global array.
       // Smooth the charge density. Input is rho_c_global_dg, globally smoothed in z,
       // and then output should be in *local* phi_smooth.
-      if (field->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+      if (field->is_clopen) {
         gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->rho_c, field->rho_c_global_dg);
         gkyl_fem_parproj_set_rhs(field->fem_parproj_core, field->rho_c_global_dg, field->rho_c_global_dg);
         gkyl_fem_parproj_solve(field->fem_parproj_core, field->rho_c_global_smooth);
@@ -623,6 +766,23 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
   app->stat.field_phi_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
+void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field)
+{
+  field->ampere_solve(app, field);
+}
+
+void gk_field_step_apar (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp)
+{
+  field->step_apar(field, out, a, inp);
+}
+
+void
+gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *fin[]){
+  struct timespec wst = gkyl_wall_clock();
+  field->accumulate_current_dot(app, field, fin);
+  field->ohm_solve(app, field);
+}
+
 static struct gkyl_app_restart_status
 header_from_file(gkyl_gyrokinetic_app *app, const char *fname)
 {
@@ -738,9 +898,20 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   gkyl_array_release(f->phi_fem);
   gkyl_array_release(f->phi_smooth);
 
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
+  if (f->is_em) {
+    gkyl_array_release(f->apar);
+    gkyl_array_release(f->apar_old);
+    gkyl_array_release(f->apar_host);
+    gkyl_array_release(f->apardot);
+    gkyl_array_release(f->apardot_host);
     gkyl_array_release(f->apar_fem);
     gkyl_array_release(f->apardot_fem);
+    gkyl_array_release(f->currentDens);
+    gkyl_array_release(f->currentDensdot);
+    gkyl_array_release(f->lapWeightAmpere);
+    gkyl_array_release(f->dApartdtSlvr_kSq);
+    gkyl_fem_poisson_perp_release(f->fem_apar_solver);
+    gkyl_fem_poisson_perp_release(f->fem_apardot);
   }
 
   if (f->init_phi_pol) {
@@ -764,7 +935,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     }
   }
 
-  if (app->cdim > 1 && f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (app->cdim > 1 && f->is_clopen) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
   } else {
@@ -772,7 +943,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   }
 
   // Release TS BS and SSFG updater
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->is_clopen) {
     if(app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_T_LU_lo);
     }
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 875ecb07c1..3b52779611 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -75,6 +75,38 @@ gk_species_omegaH_dt(gkyl_gyrokinetic_app *app, struct gk_species *gks, const st
   }
 }
 
+static double
+gk_species_update_bflux_and_cfl(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  // Compute and store (in the ghost cell of rhs) the boundary fluxes.
+  gk_species_bflux_rhs(app, &species->bflux, fin, rhs);
+
+  // Compute diagnostic moments of the boundary fluxes.
+  gk_species_bflux_calc_moms(app, &species->bflux, rhs, bflux_moms);
+  
+  // Reduce the CFL frequency anc compute stable dt needed by this species.
+  app->stat.n_species_omega_cfl +=1;
+  struct timespec tm = gkyl_wall_clock();
+  gkyl_array_reduce_range(species->omega_cfl, species->cflrate, GKYL_MAX, &species->local);
+
+  double omega_cfl_ho[1];
+  if (app->use_gpu) {
+    gkyl_cu_memcpy(omega_cfl_ho, species->omega_cfl, sizeof(double), GKYL_CU_MEMCPY_D2H);
+  }
+  else {
+    omega_cfl_ho[0] = species->omega_cfl[0];
+  }
+  double dt_out = app->cfl/omega_cfl_ho[0];
+  
+  // Enforce the omega_H constraint on dt.
+  double dt_omegaH = gk_species_omegaH_dt(app, species, fin);
+  dt_out = fmin(dt_out, dt_omegaH);
+
+  app->stat.species_omega_cfl_tm += gkyl_time_diff_now_sec(tm);
+  return dt_out;
+}
+
 static void
 gk_species_collisionless_rhs_included(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs)
@@ -175,6 +207,35 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   return dt_out;
 }
 
+static double
+gk_species_em_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  struct timespec wst = gkyl_wall_clock();
+
+  // We want here to just add the EM contribution to the collisionless update.
+  // We do not clear the cflrate or rhs.
+  // 1. compute the gk vars from EM fields
+  // something like:
+  // gkyl_dg_calc_gyrokinetic_vars_alpha_surf_em(species->calc_gk_vars, 
+  //   &app->local, &species->local, &species->local_ext, 
+  //   app->field->apardot, species->alpha_surf, species->sgn_alpha_surf, species->const_sgn_alpha);
+
+  // 2. add this contribution to the rhs
+  // If I understood correctly, the step 1. will set the variables required in step 2. so I can just
+  // call the same updater as in the collisionless electrostatic case.
+  // I think I can assume that this will add to rhs and cflrate and not overwrite them.
+  // gkyl_dg_updater_gyrokinetic_advance(species->slvr, &species->local, 
+  //   fin, species->cflrate, rhs);
+
+  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
+
+  // 3. Update the bflux and its moments and compute cflrate as usual
+  // (this is the same as in the electrostatic case)
+  double dt_out = gk_species_update_bflux_and_cfl(app, species, fin, rhs, bflux_moms);
+  return dt_out;
+}
+
 static double
 gk_species_rhs_implicit_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, double dt)
@@ -519,7 +580,7 @@ static void
 gk_species_calc_int_mom_dt_active(gkyl_gyrokinetic_app* app, struct gk_species *gks, double dt, struct gkyl_array *fdot_int_mom)
 {
   struct timespec wst = gkyl_wall_clock();
-  // Compute moment of f_new to compute moment of df/dt.
+  // Compute integrated moment of f_new to compute moment of df/dt.
   // Need to do it after the fields are updated.
   gk_species_moment_calc(&gks->integ_moms, gks->local, app->local, gks->f); 
   gkyl_array_set(fdot_int_mom, 1.0/dt, gks->integ_moms.marr);
@@ -1166,6 +1227,7 @@ gk_species_new_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
 
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
+  gks->em_rhs_func = gk_species_em_rhs_dynamic;
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
   gks->bc_func = gk_species_apply_bc_dynamic;
   gks->release_func = gk_species_release_dynamic;
@@ -1204,6 +1266,7 @@ gk_species_new_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *a
   
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
+  gks->em_rhs_func = gk_species_rhs_static;
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
   gks->bc_func = gk_species_apply_bc_static;
   gks->release_func = gk_species_release_static;
@@ -1682,6 +1745,13 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   // Allocate data for density (for charge density or upar calculation).
   gk_species_moment_init(app, gks, &gks->m0, GKYL_F_MOMENT_M0, false);
 
+  if (app->field->is_em) {
+    // To compute current density for Ampere's law and current dot for Ohm's law.
+    gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
+    gks->apar = gkyl_array_acquire(app->field->apar);
+    gks->apardot = gkyl_array_acquire(app->field->apardot);
+  }
+
   // Allocate data for diagnostic moments.
   int ndm = gks->info.num_diag_moments;
   gks->moms = gkyl_malloc(sizeof(struct gk_species_moment[ndm]));
@@ -1918,8 +1988,6 @@ gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *gks_self
   }
 }
 
-// Compute the RHS for species update, returning maximum stable
-// time-step.
 double
 gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
@@ -1927,6 +1995,13 @@ gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   return species->rhs_func(app, species, fin, rhs, bflux_moms);
 }
 
+double
+gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  return species->em_rhs_func(app, species, fin, rhs, bflux_moms);
+}
+
 // Compute the implicit RHS for species update, returning maximum stable
 // time-step.
 double
@@ -2057,6 +2132,9 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
 
   // Release moment data.
   gk_species_moment_release(app, &s->m0);
+  if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+    gk_species_moment_release(app, &s->m1);
+  }
   for (int i=0; i<s->info.num_diag_moments; ++i) {
     gk_species_moment_release(app, &s->moms[i]);
   }
diff --git a/gyrokinetic/apps/gk_species_projection.c b/gyrokinetic/apps/gk_species_projection.c
index 8501732a86..e8baa2b57b 100644
--- a/gyrokinetic/apps/gk_species_projection.c
+++ b/gyrokinetic/apps/gk_species_projection.c
@@ -280,7 +280,7 @@ init_maxwellian_gaussian(struct gkyl_gyrokinetic_app *app, struct gk_species *s,
   // Set periodicity for last dim if we are in IWL, and all other directions defined by the user.
   for (int dir = 0; dir < GKYL_MAX_CDIM; ++dir)
     fg_ctx.is_dir_periodic[dir] = false;
-  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL;
+  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
   for (int i=0; i < app->num_periodic_dir; ++i)
     fg_ctx.is_dir_periodic[app->periodic_dirs[i]] = true;
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 618c05442f..ab727f65ff 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -371,6 +371,10 @@ struct gkyl_gyrokinetic_field {
 
   struct gkyl_poisson_bc poisson_bcs;
 
+  // parameters for EMGK
+  struct gkyl_poisson_bc ampere_bcs;
+  double mu0;
+
   bool time_rate_diagnostics; // Writes the time rate of change of field energy.
 
   // Initial potential used to compute the total polarization density.
@@ -482,7 +486,9 @@ struct gkyl_gyrokinetic_stat {
 
   double field_tm; // Time to compute fields.
   double field_phi_rhs_tm; // Time spent on poisson eqn RHS.
-  double field_phi_solve_tm;   // Time spent to solve poisson eqn.
+  double field_phi_solve_tm; // Time spent to solve poisson eqn.
+  double field_apar_rhs_tm; // Time spent on parallel Ampere eqn RHS.
+  double field_apar_solve_tm; // Time spent to solve parallel Ampere eqn.
 
   double bc_tm; // Time to compute BCs.
   double species_bc_tm; // Time to compute species BCs.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 4ad1f42bdd..c2110cfa56 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -660,6 +660,7 @@ struct gk_species {
   struct gkyl_dg_calc_gyrokinetic_vars *calc_gk_vars;
 
   struct gk_species_moment m0; // for computing charge density
+  struct gk_species_moment m1; // for computing current density
   struct gk_species_moment integ_moms; // integrated moments
   struct gk_species_moment *moms; // diagnostic moments
   double *red_integ_diag, *red_integ_diag_global; // for reduction of integrated moments
@@ -755,7 +756,9 @@ struct gk_species {
     const struct gkyl_array *fin, struct gkyl_array *rhs);
   double (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
-  double (*rhs_implicit_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  double (*em_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+    const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
+    double (*rhs_implicit_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, double dt);
   void (*bc_func)(gkyl_gyrokinetic_app *app, const struct gk_species *species,
     struct gkyl_array *f);
@@ -928,6 +931,8 @@ struct gk_field {
 
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
+  bool is_em; // Whether EM model.
+  bool is_clopen; // Whether we are in a closed + open field line geometry.
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density
@@ -952,8 +957,20 @@ struct gk_field {
     };
     // EM GK model
     struct {
-      struct gkyl_array *apar_fem; // array for A_parallel
-      struct gkyl_array *apardot_fem; // array for d/dt A_parallel
+      struct gkyl_array *apar; // array for A_parallel (solved only in ic)
+      struct gkyl_array *apar_old; // previous state of A_parallel (for update with apardot)
+      struct gkyl_array *apar_host; // host copy for use IO
+      struct gkyl_array *apardot; // array for d(A_parallel)/dt (solved through Ohm's law)
+      struct gkyl_array *apardot_host; // host copy for use IO
+      struct gkyl_array *currentDens; // current density
+      struct gkyl_array *currentDensdot; // time derivative of current density
+      struct gkyl_array *apar_fem; // auxiliary array for A_parallel
+      struct gkyl_array *apardot_fem; // auxiliary array for d/dt A_parallel
+      struct gkyl_array *dApartdtSlvr_kSq; // contains sum_s q_s^2/m_s n_s
+      struct gkyl_array *dApartdtSlvr_rhs; // contains sum_s q_s int dv vpar d/dt(F_s)*
+      struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0)
+      struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar
+      struct gkyl_fem_poisson_perp *fem_apardot; // Solver for d(Apar)/dt
     };
   };
 
@@ -1011,6 +1028,17 @@ struct gk_field {
   
   // Pointer to function for the twist-and-shift BCs.
   void (*enforce_zbc) (const gkyl_gyrokinetic_app *app, const struct gk_field *field, struct gkyl_array *finout);
+
+  // Pointer to function to accumulate charge and current density.
+  void (*accumulate_current) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
+    const struct gkyl_array *fin[]);
+  void (*accumulate_current_dot) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
+    const struct gkyl_array *fin[]);
+
+  // Pointer to function to solve the Ohm's law and Ampere equation.
+  void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
+  void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
+  void (*step_apar) (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
 };
 
 // Gyrokinetic object: used as opaque pointer in user code.
@@ -2211,6 +2239,20 @@ void gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *spe
 double gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
+/**
+ * Add the electromagnetic part of the RHS from species distribution function
+ *
+ * @param app gyrokinetic app object.
+ * @param species Pointer to species.
+ * @param fin Input distribution function.
+ * @param rhs On output, the RHS from the species object.
+ * @param bflux_moms Output boundary flux moments (for diagnostics, stepped in time).
+ * @return Maximum stable time-step.
+ */
+double gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
+
+
 /**
  * Compute the *implicit* RHS from species distribution function
  *
@@ -2934,14 +2976,55 @@ void gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field
   const struct gkyl_array *fin[]);
 
 /**
- * Compute EM field.
+ * Accumulate current density for Ampere solve.
  *
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
+ * @param fin[] Input distribution function (num_species size).
+ */
+void gk_field_accumulate_current_dens(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[]);
+
+/**
+ * Compute initial magnetic vector parallel component
+ * 
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
  * @param em Output field.
  */
+void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field);
+
+/**
+ * Step the parallel component of the magnetic vector potential, apar, forward in time.
+ * 
+ * @param field Pointer to field.
+ * @param out Output array. (apar)
+ * @param dt Timestep.
+ * @param inp Input array. (apardot from Ohm's law)
+ */
+void gk_field_step_apar(struct gk_field *field, struct gkyl_array* out, double dt,
+  const struct gkyl_array* inp);
+
+/**
+ * Compute electrostatic potential, phi, from charge density and
+ * time derivative of the parallel component of the vector potential, apardot,
+ * from the m1 moment of the GK rhs computed in the last gyrokinetic_rhs call,
+ * and from the kSq term computed in the last gk_field_accumulate_rho_c call.
+ *
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
+ */
 void gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field);
 
+/**
+ * Compute Apardot from fin m1 moment using the Ohm's law.
+ *
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
+ * @param fin[] Input distribution function (num_species size).
+ */
+void gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *fin[]);
+
 /**
  * Read the field from a file.
  *
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index be66a17b1d..9c5d291928 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -461,6 +461,7 @@ gyrokinetic_calc_field_update(gkyl_gyrokinetic_app* app, double tcurr, const str
 {
   struct timespec wtm = gkyl_wall_clock();
   // Compute electrostatic potential from gyrokinetic Poisson's equation.
+  // This calls also compute kSq = \sum_s q^2/m n for Ohm's law.
   gk_field_accumulate_rho_c(app, app->field, fin);
 
   // Compute biased wall potential if present and time-dependent.
@@ -822,12 +823,16 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
       }
     }
 
-    if (app->field->info.init_from_file.type == 0 && app->field->info.init_field_profile == 0)
+    if (app->field->info.init_from_file.type == 0 && app->field->info.init_field_profile == 0) {
       // Compute the field.
+      // for EM, compute the initial ampere field using the fem helmholtz solver.
+      gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
+      gk_field_calc_apar_ic(app, app->field);
+
       // MF 2024/09/27/: Need the cast here for consistency. Fixing
       // this may require removing 'const' from a lot of places.
       gyrokinetic_calc_field_update(app, t0, (const struct gkyl_array **) distf);
-    else {
+    } else {
       if (app->field->info.init_field_profile == 0)
         // Read the field.
         gk_field_file_import_init(app, app->field->info.init_from_file);
@@ -1031,10 +1036,6 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
 {
   if (app->field->update_field || frame == 0) {
     struct timespec wtm = gkyl_wall_clock();
-    // Copy data from device to host before writing it out.
-    if (app->use_gpu) {
-      gkyl_array_copy(app->field->phi_host, app->field->phi_smooth);
-    }
 
     struct gkyl_msgpack_data *mt = gk_array_meta_new( (struct gyrokinetic_output_meta) {
         .frame = frame,
@@ -1049,8 +1050,33 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     char fileNm[sz+1]; // ensures no buffer overflow
     snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
 
+    // Copy data from device to host before writing it out.
+    if (app->use_gpu) {
+      gkyl_array_copy(app->field->phi_host, app->field->phi_smooth);
+    }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
+    if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+      const char *fmt = "%s-apar_%d.gkyl";
+      int sz = gkyl_calc_strlen(fmt, app->name, frame);
+      char fileNm[sz+1]; // ensures no buffer overflow
+      snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+      if (app->use_gpu) {
+        gkyl_array_copy(app->field->apar_host, app->field->apar);
+      }
+      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
+    }
+    if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+      const char *fmt = "%s-dapardt_%d.gkyl";
+      int sz = gkyl_calc_strlen(fmt, app->name, frame);
+      char fileNm[sz+1]; // ensures no buffer overflow
+      snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+      if (app->use_gpu) {
+        gkyl_array_copy(app->field->apardot_host, app->field->apardot);
+      }
+      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm);
+    }
+
     gk_array_meta_release(mt);
 
     app->stat.field_io_tm += gkyl_time_diff_now_sec(wtm);
@@ -1665,6 +1691,16 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
+  gk_field_em_rhs(app, app->field, fin);
+
+  // Add electromagnetic contributions to the collisionless update of charged species.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    double dt1 = gk_species_em_rhs(app, s, fin[i], fout[i], bflux_out[i]);
+    dtmin = fmin(dtmin, dt1);
+  }
+
+
   struct timespec wtm = gkyl_wall_clock();
   double dt_max_rel_diff = 0.01;
   // Check if dtmin is slightly smaller than dt. Use dt if it is
diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 152f77deab..1222bb4bcc 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -61,6 +61,7 @@ static const struct gkyl_str_int_pair gk_field_type[] = {
   { "Adiabatic", GKYL_GK_FIELD_ADIABATIC },
   { "ElectrostaticIWL", GKYL_GK_FIELD_ES_IWL },
   { "Electromagnetic", GKYL_GK_FIELD_EM },
+  { "ElectromagneticIWL", GKYL_GK_FIELD_EM_IWL },
   { 0, 0 }
 };
 
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index cb123e1000..cb0762a1d1 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -33,6 +33,8 @@ gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_step_f(gkns, fout_neut[i], dta, fin_neut[i]);
     gk_neut_species_bflux_step_f(app, &gkns->bflux, bflux_out_neut[i], dta, bflux_in_neut[i]);
   }
+  gk_field_step_apar(app->field, app->field->apardot, dta, app->field->apar);
+
   app->stat.fwd_euler_step_f_tm += gkyl_time_diff_now_sec(wst);
   app->stat.fwd_euler_tm += gkyl_time_diff_now_sec(wst_fe);
 
@@ -130,7 +132,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
           // Recalculate the field.
           for (int i=0; i<app->num_species; ++i)
             fin[i] = app->species[i].f;
-          gyrokinetic_calc_field(app, tcurr, fin);
+          gyrokinetic_calc_field(app, tcurr, fin); // Why don't we apply BCs here?
 
           // Collect stats.
           double dt_rel_diff = (dt-st.dt_actual)/st.dt_actual;
diff --git a/gyrokinetic/zero/fem_poisson_perp.c b/gyrokinetic/zero/fem_poisson_perp.c
index 96085bb331..7dab8a515a 100644
--- a/gyrokinetic/zero/fem_poisson_perp.c
+++ b/gyrokinetic/zero/fem_poisson_perp.c
@@ -2,6 +2,8 @@
 #include <gkyl_fem_poisson_perp_priv.h>
 #include <gkyl_array_reduce.h>
 
+void gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up);
+
 struct gkyl_fem_poisson_perp*
 gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gkyl_rect_grid *grid,
   const struct gkyl_basis basis, struct gkyl_poisson_bc *bcs, struct gkyl_array *epsilon,
@@ -27,17 +29,17 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
 
   // We assume epsilon and kSq live on the device, and we create a host-side
   // copies temporarily to compute the LHS matrix. This also works for CPU solves.
-  struct gkyl_array *epsilon_ho = gkyl_array_new(GKYL_DOUBLE, up->epsilon->ncomp, up->epsilon->size);
-  gkyl_array_copy(epsilon_ho, up->epsilon);
-  struct gkyl_array *kSq_ho;
+  up->epsilon_ho = gkyl_array_new(GKYL_DOUBLE, up->epsilon->ncomp, up->epsilon->size);
+  gkyl_array_copy(up->epsilon_ho, up->epsilon);
   if (kSq) {
     up->ishelmholtz = true;
-    kSq_ho = gkyl_array_new(GKYL_DOUBLE, kSq->ncomp, kSq->size);
-    gkyl_array_copy(kSq_ho, kSq);
+    up->kSq = gkyl_array_acquire(kSq);
+    up->kSq_ho = gkyl_array_new(GKYL_DOUBLE, up->kSq->ncomp, up->kSq->size);
+    gkyl_array_copy(up->kSq_ho, up->kSq);
   } else {
     up->ishelmholtz = false;
-    kSq_ho = gkyl_array_new(GKYL_DOUBLE, up->num_basis, 1);
-    gkyl_array_clear(kSq_ho, 0.);
+    up->kSq_ho = gkyl_array_new(GKYL_DOUBLE, up->num_basis, 1);
+    gkyl_array_clear(up->kSq_ho, 0.);
   }
 
   up->globalidx = gkyl_malloc(sizeof(long[up->num_basis])); // global index, one for each basis in a cell.
@@ -177,14 +179,22 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
   up->prob = gkyl_superlu_prob_new(up->par_range.volume, up->numnodes_global, up->numnodes_global, 1);
 #endif
 
-  struct gkyl_mat_triples **tri = gkyl_malloc(up->par_range.volume*sizeof(struct gkyl_mat_triples *));
+  up->tri = gkyl_malloc(up->par_range.volume*sizeof(struct gkyl_mat_triples *));
   for (size_t i=0; i<up->par_range.volume; i++) {
-    tri[i] = gkyl_mat_triples_new(up->numnodes_global, up->numnodes_global);
+    up->tri[i] = gkyl_mat_triples_new(up->numnodes_global, up->numnodes_global);
 #ifdef GKYL_HAVE_CUDA
-    if (up->use_gpu) gkyl_mat_triples_set_rowmaj_order(tri[i]);
+    if (up->use_gpu) gkyl_mat_triples_set_rowmaj_order(up->tri[i]);
 #endif
   }
 
+  gkyl_fem_poisson_perp_build_stiffness_matrix(up);
+
+  return up;
+}
+
+void
+gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up)
+{
   // Assign non-zero elements in A.
   int idx0[GKYL_MAX_CDIM],  idx1[GKYL_MAX_CDIM];
   gkyl_range_iter_init(&up->par_iter1d, &up->par_range1d);
@@ -200,8 +210,8 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
 
       long linidx = gkyl_range_idx(up->solve_range, idx1);
 
-      double *eps_p = gkyl_array_fetch(epsilon_ho, linidx);
-      double *kSq_p = up->ishelmholtz? gkyl_array_fetch(kSq_ho, linidx) : gkyl_array_fetch(kSq_ho,0);
+      double *eps_p = gkyl_array_fetch(up->epsilon_ho, linidx);
+      double *kSq_p = up->ishelmholtz? gkyl_array_fetch(up->kSq_ho, linidx) : gkyl_array_fetch(up->kSq_ho,0);
 
       int keri = idx_to_inup_ker(up->ndim_perp, up->num_cells, up->perp_iter2d.idx);
       for (size_t d=0; d<up->ndim; d++) idx0[d] = idx1[d] - 1;
@@ -209,26 +219,40 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
 
       // Apply the -nabla . (epsilon*nabla_perp)-kSq stencil.
       keri = idx_to_inloup_ker(up->ndim_perp, up->num_cells, idx1);
-      up->kernels->lhsker[keri](eps_p, kSq_p, up->dx, up->bcvals, up->globalidx, tri[paridx]);
+      up->kernels->lhsker[keri](eps_p, kSq_p, up->dx, up->bcvals, up->globalidx, up->tri[paridx]);
     }
   }
 #ifdef GKYL_HAVE_CUDA
   if (up->use_gpu)
-    gkyl_culinsolver_amat_from_triples(up->prob_cu, tri);
+    gkyl_culinsolver_amat_from_triples(up->prob_cu, up->tri);
   else
-    gkyl_superlu_amat_from_triples(up->prob, tri);
+    gkyl_superlu_amat_from_triples(up->prob, up->tri);
 #else
-  gkyl_superlu_amat_from_triples(up->prob, tri);
+  gkyl_superlu_amat_from_triples(up->prob, up->tri);
 #endif
+  
+  up->make_stiff = false; // Reset the flag.
+}
 
-  for (size_t i=0; i<up->par_range.volume; i++)
-    gkyl_mat_triples_release(tri[i]);
-  gkyl_free(tri);
+void
+gkyl_fem_poisson_perp_update_epsilon(struct gkyl_fem_poisson_perp *up, struct gkyl_array *epsilon)
+{
+  gkyl_array_release(up->epsilon);
+  up->epsilon = gkyl_array_acquire(epsilon);
+  gkyl_array_copy(up->epsilon_ho, up->epsilon);
 
-  gkyl_array_release(epsilon_ho);
-  gkyl_array_release(kSq_ho);
+  up->make_stiff = true; // Need to remake the stiffness matrix.
+}
 
-  return up;
+void
+gkyl_fem_poisson_perp_update_kSq(struct gkyl_fem_poisson_perp *up, struct gkyl_array *kSq)
+{
+  assert(up->ishelmholtz);
+  gkyl_array_release(up->kSq);
+  up->kSq = gkyl_array_acquire(kSq);
+  gkyl_array_copy(up->kSq_ho, up->kSq);
+
+  up->make_stiff = true; // Need to remake the stiffness matrix.
 }
 
 void
@@ -310,6 +334,11 @@ gkyl_fem_poisson_perp_set_rhs(gkyl_fem_poisson_perp *up, struct gkyl_array *rhsi
 
 void
 gkyl_fem_poisson_perp_solve(gkyl_fem_poisson_perp *up, struct gkyl_array *phiout) {
+
+  // Check if we need to rebuild the stiffness matrix (if epsilon or kSq got updated).
+  if (up->make_stiff)
+    gkyl_fem_poisson_perp_build_stiffness_matrix(up);
+
 #ifdef GKYL_HAVE_CUDA
   if (up->use_gpu) {
     assert(gkyl_array_is_cu_dev(phiout));
@@ -376,5 +405,12 @@ void gkyl_fem_poisson_perp_release(struct gkyl_fem_poisson_perp *up)
   gkyl_free(up->perp_range);
   gkyl_free(up->globalidx);
   gkyl_array_release(up->epsilon);
+  gkyl_array_release(up->epsilon_ho);
+  if (up->ishelmholtz)
+    gkyl_array_release(up->kSq);
+  gkyl_array_release(up->kSq_ho);
+  for (size_t i=0; i<up->par_range.volume; i++)
+    gkyl_mat_triples_release(up->tri[i]);
+  gkyl_free(up->tri);
   gkyl_free(up);
 }
diff --git a/gyrokinetic/zero/gkyl_fem_poisson_perp.h b/gyrokinetic/zero/gkyl_fem_poisson_perp.h
index c5e7166836..9821be893f 100644
--- a/gyrokinetic/zero/gkyl_fem_poisson_perp.h
+++ b/gyrokinetic/zero/gkyl_fem_poisson_perp.h
@@ -40,6 +40,28 @@ struct gkyl_fem_poisson_perp* gkyl_fem_poisson_perp_new(
   const struct gkyl_basis basis, struct gkyl_poisson_bc *bcs, struct gkyl_array *epsilon,
   struct gkyl_array *kSq, bool use_gpu);
 
+/**
+ * Update the epsilon array and set the make_stiff flag to true to recompute stiffness
+ * matrix at the next solve call.
+ * 
+ * @param up updater to solver.
+ * @param epsilon new epsilon array.
+ */
+void
+gkyl_fem_poisson_perp_update_epsilon(struct gkyl_fem_poisson_perp *up, struct gkyl_array *epsilon);
+
+/**
+ * Update the kSq array and set the make_stiff flag to true to recompute stiffness
+ * matrix at the next solve call. The kSq must be passed as a non Null pointer to array
+ * in the gkyl_fem_poisson_perp_new call.
+ * 
+ * @param up updater to solver.
+ * @param kSq new kSq array.
+ */
+void
+gkyl_fem_poisson_perp_update_kSq(struct gkyl_fem_poisson_perp *up, struct gkyl_array *kSq);
+
+
 /**
  * Assign the right-side vector with the discontinuous (DG) source field.
  *
diff --git a/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h b/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
index 48d28084af..583df01f6f 100644
--- a/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
+++ b/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
@@ -461,7 +461,12 @@ struct gkyl_fem_poisson_perp {
   bool isdirperiodic[GKYL_MAX_DIM]; // =true if direction is periodic.
 
   struct gkyl_array *epsilon; // Permittivity.
+  struct gkyl_array *epsilon_ho; // Permittivity on host.
+  struct gkyl_array *kSq; // k squared (Helmholtz term).
+  struct gkyl_array *kSq_ho; // k square on host.
   bool ishelmholtz; // If solving Helmholtz equation (kSq is not zero/NULL).
+  bool make_stiff; // Flag to indicate if we need to remake the stiffness matrix.
+  struct gkyl_mat_triples **tri; // Matrix triples for building stiffness matrices.
 
   bool isdomperiodic; // =true if all directions are periodic.
   struct gkyl_array *rhs_cellavg;

From 1291837eceaa0f4dee1993a3fa7231f9bf00289a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 10 Oct 2025 20:38:25 -0400
Subject: [PATCH 002/181] fix merge conflicts

---
 gyrokinetic/apps/gk_field.c              |  2 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 11 ++++++++++-
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 78e672a3c2..082ca0ca69 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -550,7 +550,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
     // Compute the weights in front of the laplacian operator (metric x 1/mu0)
-    struct gkyl_array *Jgij[3] = {app->gk_geom->gxxj, app->gk_geom->gxyj, app->gk_geom->gyyj};
+    struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
     for (int i=0; i<app->cdim-2/app->cdim; i++) {
       gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
     }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e4befad9c0..e8f4545bd9 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1071,7 +1071,16 @@ struct gk_field {
   struct gkyl_skin_surf_from_ghost *ssfg_x_lo;
   
   // Pointer to functions for the twist-and-shift BCs.
-  void (*enforce_zbc) (const gkyl_gyrokinetic_app *app, const struct gk_field *field, struct gkyl_array *finout);
+  void (*enforce_zbc) (const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout);
+
+  // Pointer to function for electromagnetic field solve.
+  void (*accumulate_current) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
+    const struct gkyl_array *fin[]);
+  void (*accumulate_current_dot) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
+    const struct gkyl_array *fin[]);
+  void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
+  void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
+  void (*step_apar) (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
 };
 
 // Gyrokinetic object: used as opaque pointer in user code.

From 033255e0dd7cb011f3b388683b32e9cee56a0eb4 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 14 Oct 2025 11:50:37 -0400
Subject: [PATCH 003/181] rename apardot output file name from "dapartdt" to
 "apardot"

---
 gyrokinetic/apps/gyrokinetic.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 606f2b42e1..f5c91a7aba 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1166,7 +1166,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
       gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
     }
     if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
-      const char *fmt = "%s-dapardt_%d.gkyl";
+      const char *fmt = "%s-apardot_%d.gkyl";
       int sz = gkyl_calc_strlen(fmt, app->name, frame);
       char fileNm[sz+1]; // ensures no buffer overflow
       snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);

From 6cdedc086efaf74c4dfc309134d1372d2b12eefa Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 14 Oct 2025 13:45:32 -0700
Subject: [PATCH 004/181] add BC for ampere and ohm laws, fix the acquisition
 of apar and apardot in species. Mu0 needs to be set in the input file, other
 wise there will be a division by 0.

---
 gyrokinetic/apps/gk_field.c         | 32 ++++++++++++++++++++---------
 gyrokinetic/apps/gk_species.c       |  9 ++++----
 gyrokinetic/apps/gkyl_gyrokinetic.h |  4 ++--
 3 files changed, 28 insertions(+), 17 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 082ca0ca69..3daafa6721 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -176,7 +176,7 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
   gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
-  gkyl_fem_poisson_perp_solve(field->fem_apardot,field->apardot);
+  gkyl_fem_poisson_perp_solve(field->fem_apardot, field->apardot);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -554,12 +554,29 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     for (int i=0; i<app->cdim-2/app->cdim; i++) {
       gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
     }
+    // Translate input file BCs into Ampere BCs.
+    struct gkyl_poisson_bc ampere_bcs = { };
+    for (int d=0; d<app->cdim-1; d++) {
+      struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
+      if (bc_lo != 0) {
+        ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
+        for (int i=0; i<3; i++)
+          ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+      }
+
+      struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
+      if (bc_up != 0) {
+        ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
+        for (int i=0; i<3; i++)
+          ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+      }
+    }
     // FEM solver for Ampere equation (solved at IC only).
     f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-        &f->info.ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+        &ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
     // FEM solver for Ohm's law (evolves d(Apart)/dt).
     f->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-      &f->info.ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+      &ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
 
     // Pointer to function that solves Ohm's law and Amperes equation.
     f->ohm_solve = gk_field_ohm_solve;
@@ -687,14 +704,9 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
         gkyl_array_shiftc_range(field->rho_c, q_s*n_s0*dg_norm, 0, &app->local);
       }
       if (field->is_em) {
-        // Use m0 to update also the kSq matrix of the Ohm's law solver.
-        double fac = s->info.charge*s->info.charge/s->info.mass;
-        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0.marr, &app->local);
-      }
-      if (field->is_em) {
-        // Use m0 to update also the kSq matrix of the Ohm's law solver.
+        // Use m0 to update also update the kSq matrix for the Ohm's law solver.
         double fac = s->info.charge*s->info.charge/s->info.mass;
-        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0.marr, &app->local);
+        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg.marr, &app->local);
       }
     }
   } 
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 3f2128b277..5381d62ec4 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1650,9 +1650,10 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->flux_surf = mkarr(app->use_gpu, flux_surf_sz, gks->local_ext.volume);
   // 4. EM fields: phi and (if EM GK) Apar and d/dt Apar  
   gks->gyro_phi = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  gks->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  gks->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);    
-
+  if (app->field->is_em) {
+    gks->apar = gkyl_array_acquire(app->field->apar);
+    gks->apardot = gkyl_array_acquire(app->field->apardot);
+  }
   gks->calc_gk_vars = gkyl_dg_calc_gyrokinetic_vars_new(&gks->grid, &app->basis, &gks->basis, 
     gks->info.charge, gks->info.mass, gks->gkmodel_id, app->gk_geom, 
     app->dg_geom, app->gk_dg_geom, gks->vel_map, app->use_gpu);
@@ -1679,8 +1680,6 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   if (app->field->is_em) {
     // To compute current density for Ampere's law and current dot for Ohm's law.
     gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
-    gks->apar = gkyl_array_acquire(app->field->apar);
-    gks->apardot = gkyl_array_acquire(app->field->apardot);
   }
 
   // Allocate data for diagnostic moments.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 8bd0564f42..a70808f7b6 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -384,8 +384,8 @@ struct gkyl_gyrokinetic_field {
   struct gkyl_gyrokinetic_bc poisson_bcs[2*GKYL_MAX_CDIM];
 
   // parameters for EMGK
-  struct gkyl_poisson_bc ampere_bcs;
-  double mu0;
+  struct gkyl_gyrokinetic_bc ampere_bcs[2*GKYL_MAX_CDIM];
+  double mu0; // Magnetic permeability of free space.
 
   bool time_rate_diagnostics; // Writes the time rate of change of field energy.
 

From 0cf7fa4f5c296d12f376a81e1a0389bd20d49ad6 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 14 Oct 2025 13:47:12 -0700
Subject: [PATCH 005/181] typo in m0_gyroavg (.marr stayed)

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 3daafa6721..6863502b9c 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -706,7 +706,7 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
       if (field->is_em) {
         // Use m0 to update also update the kSq matrix for the Ohm's law solver.
         double fac = s->info.charge*s->info.charge/s->info.mass;
-        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg.marr, &app->local);
+        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
       }
     }
   } 

From 509c55b164658690500486329e6e0a5666410de0 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 14 Oct 2025 14:27:38 -0700
Subject: [PATCH 006/181] fix host array alloc and add a boolean to check if
 the field is em in the species struct.

---
 gyrokinetic/apps/gk_field.c              |  6 ++++--
 gyrokinetic/apps/gk_species.c            | 19 ++++++++++++-------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  1 +
 3 files changed, 17 insertions(+), 9 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 6863502b9c..fd64a55a2c 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -971,9 +971,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   if (f->is_em) {
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar_old);
-    gkyl_array_release(f->apar_host);
     gkyl_array_release(f->apardot);
-    gkyl_array_release(f->apardot_host);
     gkyl_array_release(f->apar_fem);
     gkyl_array_release(f->apardot_fem);
     gkyl_array_release(f->currentDens);
@@ -982,6 +980,10 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     gkyl_array_release(f->dApartdtSlvr_kSq);
     gkyl_fem_poisson_perp_release(f->fem_apar_solver);
     gkyl_fem_poisson_perp_release(f->fem_apardot);
+    if (app->use_gpu) {
+      gkyl_array_release(f->apar_host);
+      gkyl_array_release(f->apardot_host);
+    }
   }
 
   if (f->init_phi_pol) {
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 5381d62ec4..6a8b630736 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1605,6 +1605,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
 
   // Determine field-type.
   gks->gkfield_id = app->field->gkfield_id;
+  gks->gkfield_is_em = app->field->is_em;
   if (gks->info.no_by) {
     gks->gkmodel_id = GKYL_GK_MODEL_NO_BY;
   }
@@ -1650,10 +1651,14 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->flux_surf = mkarr(app->use_gpu, flux_surf_sz, gks->local_ext.volume);
   // 4. EM fields: phi and (if EM GK) Apar and d/dt Apar  
   gks->gyro_phi = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  if (app->field->is_em) {
+  if (gks->gkfield_is_em) {
     gks->apar = gkyl_array_acquire(app->field->apar);
     gks->apardot = gkyl_array_acquire(app->field->apardot);
   }
+  else {
+    gks->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    gks->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  }
   gks->calc_gk_vars = gkyl_dg_calc_gyrokinetic_vars_new(&gks->grid, &app->basis, &gks->basis, 
     gks->info.charge, gks->info.mass, gks->gkmodel_id, app->gk_geom, 
     app->dg_geom, app->gk_dg_geom, gks->vel_map, app->use_gpu);
@@ -1677,7 +1682,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   // Allocate data for density (for charge density or upar calculation).
   gk_species_moment_init(app, gks, &gks->m0, GKYL_F_MOMENT_M0, false);
 
-  if (app->field->is_em) {
+  if (gks->gkfield_is_em) {
     // To compute current density for Ampere's law and current dot for Ohm's law.
     gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
   }
@@ -1717,7 +1722,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gkyl_sub_range_intersect(&gks->global_upper_ghost[dir], &gks->local_ext, &gks->global_upper_ghost[dir]);
   }
 
-  if (gk_app_inp->geometry.has_LCFS) {
+  if (gk_app_inp->geometry.has_LCFS) { // I think we could use field->is_clopen instead. Or call has_LCFS, is_clopen?
     // IWL simulation. Create core and SOL global ranges.
     int idx_LCFS_lo = app->gk_geom->idx_LCFS_lo;
     int len_core = idx_LCFS_lo;
@@ -2069,12 +2074,12 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
 
   // Release moment data.
   gk_species_moment_release(app, &s->m0);
-  if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+  if (s->gkfield_is_em)
     gk_species_moment_release(app, &s->m1);
-  }
-  for (int i=0; i<s->info.num_diag_moments; ++i) {
+
+  for (int i=0; i<s->info.num_diag_moments; ++i)
     gk_species_moment_release(app, &s->moms[i]);
-  }
+
   gkyl_free(s->moms);
 
   gk_species_source_release(app, &s->src);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e8f4545bd9..454e01b576 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -661,6 +661,7 @@ struct gk_species {
 
   enum gkyl_gkmodel_id gkmodel_id; // Gyrokinetic species model.
   enum gkyl_gkfield_id gkfield_id; // Gyrokinetic field model.
+  bool gkfield_is_em; // To store whether the field is EM.
 
   struct gkyl_basis basis; // Phase-space basis.
 

From 355f6f9a7745edaf51000d111b4b733a45320043 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 15 Oct 2025 10:08:17 -0400
Subject: [PATCH 007/181] add diagnostic for integrated Apar energy.

---
 gyrokinetic/apps/gk_field.c              | 30 ++++++++++++++++++++++++
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  2 ++
 gyrokinetic/apps/gyrokinetic.c           | 13 ++++++++++
 3 files changed, 45 insertions(+)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 082ca0ca69..48a0ceb02a 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -462,6 +462,18 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       1, GKYL_ARRAY_INTEGRATE_OP_EPS_GRADPERP_SQ, app->use_gpu);
   }
 
+  f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+  // Factor for EM energy.
+  if (f->is_em) {
+    assert(f->info.mu0 > 0.0);
+    assert(app->cdim > 1); // EM is not implemented in 1x yet.
+    f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
+    struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
+    for (int i=0; i<app->cdim-2/app->cdim; i++) {
+      gkyl_array_set_offset(f->apar_energy_fac, -0.5/f->info.mu0, Jgij[i], i*app->basis.num_basis); // the -1 is to be consistent with ES energy.
+    }
+  }
+
   f->calc_energy_dt_func = gk_field_calc_energy_dt_none;
   if (f->info.time_rate_diagnostics) {
     f->calc_energy_dt_func = gk_field_calc_energy_dt_active;
@@ -943,6 +955,22 @@ gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_field
 
     gkyl_dynvec_append(field->integ_energy_dot, tm, energy_dot_global);
   }
+
+  if (field->is_em) {
+    gkyl_array_integrate_advance(field->calc_em_energy, field->apar, 
+      1.0, field->apar_energy_fac, &app->local, &app->local, field->em_energy_red);
+
+    gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->em_energy_red, field->em_energy_red_global);
+
+    double energy_global[1] = { 0.0 };
+    if (app->use_gpu)
+      gkyl_cu_memcpy(energy_global, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+    else
+      energy_global[0] = field->em_energy_red_global[0];
+
+    gkyl_dynvec_append(field->integ_apar_energy, tm, energy_global);
+  }
+
   app->stat.field_diag_calc_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -968,8 +996,10 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
     gkyl_array_release(f->dApartdtSlvr_kSq);
+    gkyl_array_release(f->apar_energy_fac);
     gkyl_fem_poisson_perp_release(f->fem_apar_solver);
     gkyl_fem_poisson_perp_release(f->fem_apardot);
+    gkyl_dynvec_release(f->integ_apar_energy);
   }
 
   if (f->init_phi_pol) {
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e8f4545bd9..53d21dab40 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1017,6 +1017,7 @@ struct gk_field {
 
   double es_energy_fac_1d; 
   struct gkyl_array *es_energy_fac; 
+  struct gkyl_array *apar_energy_fac; 
   bool is_dirichletvar; // Whether user provided spatially varying phi BCs.
   struct gkyl_array *phi_bc; // Spatially varying BC.
   struct gkyl_array *epsilon; // Polarization weight including geometric factors.
@@ -1041,6 +1042,7 @@ struct gk_field {
   struct gkyl_array_integrate *calc_em_energy;
   double *em_energy_red, *em_energy_red_global; // memory for use in GPU reduction of EM energy
   gkyl_dynvec integ_energy; // integrated energy components
+  gkyl_dynvec integ_apar_energy; // integrated EM energy components (separate from electrostatic energy for debugging purposes)
   bool is_first_energy_write_call; // flag for energy dynvec written first time
 
   double *em_energy_red_old, *em_energy_red_new; // memory for use in GPU reduction of old EM energy.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index f5c91a7aba..77e9cbd3bd 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1207,6 +1207,11 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     char fileNm0[sz0+1]; // ensures no buffer overflow
     snprintf(fileNm0, sizeof fileNm0, fmt0, app->name);
 
+    const char *fmt0_apar = "%s-apar_energy.gkyl";
+    int sz0_apar = gkyl_calc_strlen(fmt0_apar, app->name);
+    char fileNm0_apar[sz0_apar+1]; // ensures no buffer overflow
+    snprintf(fileNm0_apar, sizeof fileNm0_apar, fmt0_apar, app->name);
+
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
@@ -1214,15 +1219,23 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).
         gkyl_dynvec_write(app->field->integ_energy, fileNm0);
+
+        if (app->field->is_em)
+          gkyl_dynvec_write(app->field->integ_apar_energy, fileNm0_apar);
+
         app->field->is_first_energy_write_call = false;
       }
       else {
         // Append to existing file.
         gkyl_dynvec_awrite(app->field->integ_energy, fileNm0);
+        if (app->field->is_em)
+          gkyl_dynvec_awrite(app->field->integ_apar_energy, fileNm0_apar);
       }
       app->stat.n_field_diag_io += 1;
     }
     gkyl_dynvec_clear(app->field->integ_energy);
+    if (app->field->is_em)
+      gkyl_dynvec_clear(app->field->integ_apar_energy);
 
     if (app->field->info.time_rate_diagnostics) {
       // Write out the time rate of change of the field energy.

From d426e40427a4deaa59b4356b1b50190ba55057c6 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 15 Oct 2025 10:22:50 -0400
Subject: [PATCH 008/181] remove unused arrays

---
 gyrokinetic/apps/gk_field.c              | 4 ----
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 2 --
 2 files changed, 6 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index b5b177a7e0..c882603720 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -554,8 +554,6 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
     }
 
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->lapWeightAmpere = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
@@ -1000,8 +998,6 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar_old);
     gkyl_array_release(f->apardot);
-    gkyl_array_release(f->apar_fem);
-    gkyl_array_release(f->apardot_fem);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e3c50db09f..0e4beec09a 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1006,8 +1006,6 @@ struct gk_field {
       struct gkyl_array *apardot_host; // host copy for use IO
       struct gkyl_array *currentDens; // current density
       struct gkyl_array *currentDensdot; // time derivative of current density
-      struct gkyl_array *apar_fem; // auxiliary array for A_parallel
-      struct gkyl_array *apardot_fem; // auxiliary array for d/dt A_parallel
       struct gkyl_array *dApartdtSlvr_kSq; // contains sum_s q_s^2/m_s n_s
       struct gkyl_array *dApartdtSlvr_rhs; // contains sum_s q_s int dv vpar d/dt(F_s)*
       struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0)

From 255ac969ee77de565ddab76519fe141c09301999 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 15 Oct 2025 10:32:10 -0400
Subject: [PATCH 009/181] bufix: move the apar enery dynvec inside the if em
 statement.

---
 gyrokinetic/apps/gk_field.c | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index c882603720..fcb5c09c04 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -175,6 +175,7 @@ static void
 gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
+  // The update of kSq is causing issues with leaks and valgrind.
   gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
   gkyl_fem_poisson_perp_solve(field->fem_apardot, field->apardot);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
@@ -462,9 +463,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       1, GKYL_ARRAY_INTEGRATE_OP_EPS_GRADPERP_SQ, app->use_gpu);
   }
 
-  f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
   // Factor for EM energy.
   if (f->is_em) {
+    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
     assert(f->info.mu0 > 0.0);
     assert(app->cdim > 1); // EM is not implemented in 1x yet.
     f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);

From 3be111e868e8149facdaf44789513b9fde57f6c2 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 15 Oct 2025 11:55:25 -0400
Subject: [PATCH 010/181] kSq in the Ohm's law fem_poisson_perp solver is now
 updated by releasing and recreating a solver because just rebuilding the
 matrix introduces memory leaks.

---
 gyrokinetic/apps/gk_field.c | 24 +++++++++++++++---------
 1 file changed, 15 insertions(+), 9 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index fcb5c09c04..37946d8c56 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -174,9 +174,16 @@ gk_field_accumulate_current_dens_none(gkyl_gyrokinetic_app *app, struct gk_field
 static void 
 gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
-  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
+  
   // The update of kSq is causing issues with leaks and valgrind.
-  gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
+  // gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
+  
+  // Temporary solution to avoid superLU leak when updating kSq: we release and re-create the solver
+  gkyl_fem_poisson_perp_release(field->fem_apardot);
+  field->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+    &field->ampere_bcs, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
+
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
   gkyl_fem_poisson_perp_solve(field->fem_apardot, field->apardot);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -566,28 +573,27 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
     }
     // Translate input file BCs into Ampere BCs.
-    struct gkyl_poisson_bc ampere_bcs = { };
     for (int d=0; d<app->cdim-1; d++) {
       struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
       if (bc_lo != 0) {
-        ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
+        f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
         for (int i=0; i<3; i++)
-          ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+          f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
       }
 
       struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
       if (bc_up != 0) {
-        ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
+        f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
         for (int i=0; i<3; i++)
-          ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+          f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
       }
     }
     // FEM solver for Ampere equation (solved at IC only).
     f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-        &ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+        &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
     // FEM solver for Ohm's law (evolves d(Apart)/dt).
     f->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-      &ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+      &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
 
     // Pointer to function that solves Ohm's law and Amperes equation.
     f->ohm_solve = gk_field_ohm_solve;

From 5819a154ca33d75ac03cc7c4f82c8fc106de1cf8 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 15 Oct 2025 11:56:11 -0400
Subject: [PATCH 011/181] need to pass bc in the structure to do the release
 remake poisson perp solver

---
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 1 +
 1 file changed, 1 insertion(+)

diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 0e4beec09a..0cd2760c52 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1011,6 +1011,7 @@ struct gk_field {
       struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0)
       struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar
       struct gkyl_fem_poisson_perp *fem_apardot; // Solver for d(Apar)/dt
+      struct gkyl_poisson_bc ampere_bcs; // BCs for Apar and d(Apar)/dt
     };
   };
 

From 952e1eef2d3ddd0b786369c0d45321086ada5cc0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 10:51:56 -0400
Subject: [PATCH 012/181] Add 1x solvers for EM, refactor a few arrays, remove
 unused ones, add em computation in comp time, note a "TODO" for the next
 step, lso removed an unused variable in fem_poisson_perp

---
 gyrokinetic/apps/gk_field.c              | 187 ++++++++++++++++-------
 gyrokinetic/apps/gk_species.c            |   1 +
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  40 +++--
 gyrokinetic/apps/gyrokinetic.c           |   7 +-
 gyrokinetic/zero/fem_poisson_perp.c      |   5 +-
 5 files changed, 169 insertions(+), 71 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 37946d8c56..ba310185c6 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -145,20 +145,20 @@ gk_field_accumulate_current_dens_dyn(gkyl_gyrokinetic_app *app, struct gk_field
 
 static void
 gk_field_accumulate_current_dens_dot_none(gkyl_gyrokinetic_app *app, struct gk_field *field, 
-  const struct gkyl_array *fin[])
+  struct gkyl_array *rhs_in[])
 {
 }
 
 static void
 gk_field_accumulate_current_dens_dot_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, 
-  const struct gkyl_array *fin[])
+  struct gkyl_array *rhs_in[])
 {
   struct timespec wst = gkyl_wall_clock();
   gkyl_array_clear(field->currentDensdot, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
 
-    gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
+    gk_species_moment_calc(&s->m1, s->local, app->local, rhs_in[i]);
 
     gkyl_array_accumulate_range(field->currentDensdot, s->info.charge, s->m1.marr, &app->local);
   } 
@@ -176,15 +176,45 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
   
   // The update of kSq is causing issues with leaks and valgrind.
-  // gkyl_fem_poisson_perp_update_kSq(field->fem_apardot, field->dApartdtSlvr_kSq);
-  
+  // gkyl_fem_poisson_perp_update_kSq(field->fem_apardot_solver, field->dApartdtSlvr_kSq);
+
   // Temporary solution to avoid superLU leak when updating kSq: we release and re-create the solver
-  gkyl_fem_poisson_perp_release(field->fem_apardot);
-  field->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+  gkyl_fem_poisson_perp_release(field->fem_apardot_solver);
+  field->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
     &field->ampere_bcs, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
 
-  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot, field->currentDensdot);
-  gkyl_fem_poisson_perp_solve(field->fem_apardot, field->apardot);
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
+  gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+/**
+ * @brief Solve Ohm's law in the parallel direction, i.e.
+ * 
+ * (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) dApar/dt = sum_s q_s int dv vpar d/dt(F_s)
+ * 
+ * The first parenthesis is computed in dApartdtSlvr_lhs_factor_global. The right hand side is in currentDensdot_global.
+ */
+static void 
+gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+
+  // Compute the new dApartdtSlvr_kSq (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
+  gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
+  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
+  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->dApartdtSlvr_lhs_factor, field->dApartdtSlvr_lhs_factor_global);
+  
+  gkyl_fem_parproj_release(field->fem_apardot_parproj);
+  field->fem_apardot_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+    field->fem_parproj_ampere_bc, field->dApartdtSlvr_lhs_factor_global, 0, app->use_gpu);
+
+  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDensdot, field->currentDensdot_global);
+
+  gkyl_fem_parproj_set_rhs(field->fem_apardot_parproj, field->currentDensdot_global, field->currentDensdot_global);
+  gkyl_fem_parproj_solve(field->fem_apardot_parproj, field->phi_fem);
+
+  gkyl_array_copy_range_to_range(field->apardot, field->phi_fem, &app->local, &field->global_sub_range);
+
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -201,6 +231,21 @@ gk_field_ampere_solve(gkyl_gyrokinetic_app *app, struct gk_field *field){
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
+static void 
+gk_field_ampere_solve_1x(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+
+  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDens, field->currentDens_global);
+
+  gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->currentDens_global, field->currentDens_global);
+  gkyl_fem_parproj_solve(field->fem_apar_parproj, field->phi_fem);
+
+  gkyl_array_copy_range_to_range(field->apar, field->phi_fem, &app->local, &field->global_sub_range);
+
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+
 static void 
 gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field)
 {
@@ -470,18 +515,6 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       1, GKYL_ARRAY_INTEGRATE_OP_EPS_GRADPERP_SQ, app->use_gpu);
   }
 
-  // Factor for EM energy.
-  if (f->is_em) {
-    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
-    assert(f->info.mu0 > 0.0);
-    assert(app->cdim > 1); // EM is not implemented in 1x yet.
-    f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
-    struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
-    for (int i=0; i<app->cdim-2/app->cdim; i++) {
-      gkyl_array_set_offset(f->apar_energy_fac, -0.5/f->info.mu0, Jgij[i], i*app->basis.num_basis); // the -1 is to be consistent with ES energy.
-    }
-  }
-
   f->calc_energy_dt_func = gk_field_calc_energy_dt_none;
   if (f->info.time_rate_diagnostics) {
     f->calc_energy_dt_func = gk_field_calc_energy_dt_active;
@@ -567,40 +600,78 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->lapWeightAmpere = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
-    // Compute the weights in front of the laplacian operator (metric x 1/mu0)
-    struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
-    for (int i=0; i<app->cdim-2/app->cdim; i++) {
-      gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
+    if (app->cdim == 1) {
+      f->currentDens_global = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+      f->currentDensdot_global = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+      f->dApartdtSlvr_lhs_factor = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+      f->dApartdtSlvr_lhs_factor_global = mkarr(app->use_gpu, f->dApartdtSlvr_lhs_factor->ncomp, app->global_ext.volume);
+      
+      // Need to set weight to kperpsq*polarizationWeight for use in potential smoothing.
+      gkyl_array_copy(f->lapWeightAmpere, app->gk_geom->geo_int.jacobgeo);
+      gkyl_array_scale(f->lapWeightAmpere, f->info.kperpSq);
+
+      f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
+      for (int d=0; d<app->num_periodic_dir; ++d)
+        if (app->periodic_dirs[d] == app->cdim-1) f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_PERIODIC;
+
+      f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+        f->fem_parproj_ampere_bc, f->lapWeightAmpere, 0, app->use_gpu);
+
+      // Declare a dummy solver for d(Apar)/dt (will be updated at each time step).
+      f->fem_apardot_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+        f->fem_parproj_ampere_bc, f->dApartdtSlvr_kSq, 0, app->use_gpu);
+
+      f->ohm_solve = gk_field_ohm_solve_1x;
+      f->ampere_solve = gk_field_ampere_solve_1x;
     }
-    // Translate input file BCs into Ampere BCs.
-    for (int d=0; d<app->cdim-1; d++) {
-      struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
-      if (bc_lo != 0) {
-        f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
-        for (int i=0; i<3; i++)
-          f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+    else if (app->cdim > 1) {
+      // Compute the weights in front of the laplacian operator (metric x 1/mu0)
+      struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
+      for (int i=0; i<app->cdim-2/app->cdim; i++) {
+        gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
       }
+      // Translate input file BCs into Ampere BCs.
+      for (int d=0; d<app->cdim-1; d++) {
+        struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
+        if (bc_lo != 0) {
+          f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
+          for (int i=0; i<3; i++)
+            f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+        }
 
-      struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
-      if (bc_up != 0) {
-        f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
-        for (int i=0; i<3; i++)
-          f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+        struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
+        if (bc_up != 0) {
+          f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
+          for (int i=0; i<3; i++)
+            f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+        }
       }
+      // FEM solver for Ampere equation (solved at IC only).
+      f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+          &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+      // FEM solver for Ohm's law (evolves d(Apart)/dt).
+      f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+        &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+
+      f->ohm_solve = gk_field_ohm_solve;
+      f->ampere_solve = gk_field_ampere_solve;
     }
-    // FEM solver for Ampere equation (solved at IC only).
-    f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-        &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
-    // FEM solver for Ohm's law (evolves d(Apart)/dt).
-    f->fem_apardot = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-      &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
-
-    // Pointer to function that solves Ohm's law and Amperes equation.
-    f->ohm_solve = gk_field_ohm_solve;
-    f->ampere_solve = gk_field_ampere_solve;
     f->accumulate_current = gk_field_accumulate_current_dens_dyn;
     f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_dyn;
     f->step_apar = gk_field_step_apar_dyn;
+
+    // Factor for EM energy.
+    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+    f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
+    f->apar_energy_fac_1d = 0;
+    assert(f->info.mu0 > 0.0);
+    if (app->cdim == 1) {
+      f->apar_energy_fac_1d = 0.5/f->info.mu0 * f->info.kperpSq;
+      f->apar_energy_fac_1d *= -1.0; // the -1 is to be consistent with ES energy.
+    }
+    else if (app->cdim > 1) {
+      gkyl_array_set(f->apar_energy_fac, -0.5, f->lapWeightAmpere);
+    }
   }
 
   // Create operator needed for FLR effects.
@@ -864,10 +935,11 @@ void gk_field_step_apar (struct gk_field *field, struct gkyl_array* out, double
 }
 
 void
-gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *fin[]){
+gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[]){
   struct timespec wst = gkyl_wall_clock();
-  field->accumulate_current_dot(app, field, fin);
+  field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
+  app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 
 static struct gkyl_app_restart_status
@@ -985,6 +1057,9 @@ gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_field
     else
       energy_global[0] = field->em_energy_red_global[0];
 
+    if (app->cdim == 1)
+      energy_global[0] *= field->apar_energy_fac_1d; 
+
     gkyl_dynvec_append(field->integ_apar_energy, tm, energy_global);
   }
 
@@ -1010,8 +1085,18 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     gkyl_array_release(f->lapWeightAmpere);
     gkyl_array_release(f->dApartdtSlvr_kSq);
     gkyl_array_release(f->apar_energy_fac);
-    gkyl_fem_poisson_perp_release(f->fem_apar_solver);
-    gkyl_fem_poisson_perp_release(f->fem_apardot);
+    if (app->cdim > 1) {
+      gkyl_fem_poisson_perp_release(f->fem_apar_solver);
+      gkyl_fem_poisson_perp_release(f->fem_apardot_solver);  
+    }
+    else {
+      gkyl_array_release(f->currentDens_global);
+      gkyl_array_release(f->currentDensdot_global);
+      gkyl_array_release(f->dApartdtSlvr_lhs_factor);
+      gkyl_array_release(f->dApartdtSlvr_lhs_factor_global);
+      gkyl_fem_parproj_release(f->fem_apar_parproj);
+      gkyl_fem_parproj_release(f->fem_apardot_parproj);  
+    }
     if (app->use_gpu) {
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 6a8b630736..59f29655d0 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -205,6 +205,7 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   return dt_out;
 }
 
+// TODO: Make this function do something.
 static double
 gk_species_em_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 0cd2760c52..7d0e3511de 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -999,24 +999,32 @@ struct gk_field {
     };
     // EM GK model
     struct {
-      struct gkyl_array *apar; // array for A_parallel (solved only in ic)
-      struct gkyl_array *apar_old; // previous state of A_parallel (for update with apardot)
-      struct gkyl_array *apar_host; // host copy for use IO
-      struct gkyl_array *apardot; // array for d(A_parallel)/dt (solved through Ohm's law)
-      struct gkyl_array *apardot_host; // host copy for use IO
-      struct gkyl_array *currentDens; // current density
-      struct gkyl_array *currentDensdot; // time derivative of current density
-      struct gkyl_array *dApartdtSlvr_kSq; // contains sum_s q_s^2/m_s n_s
-      struct gkyl_array *dApartdtSlvr_rhs; // contains sum_s q_s int dv vpar d/dt(F_s)*
-      struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0)
-      struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar
-      struct gkyl_fem_poisson_perp *fem_apardot; // Solver for d(Apar)/dt
-      struct gkyl_poisson_bc ampere_bcs; // BCs for Apar and d(Apar)/dt
+      struct gkyl_array *apar; // Array for A_parallel (solved only in ic).
+      struct gkyl_array *apar_old; // Previous state of A_parallel (for update with apardot).
+      struct gkyl_array *apar_host; // Host copy for use IO.
+      struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
+      struct gkyl_array *apardot_host; // Host copy for use IO.
+      struct gkyl_array *currentDens; // Current density.
+      struct gkyl_array *currentDens_global; // Current density.
+      struct gkyl_array *currentDensdot; // Time derivative of current density.
+      struct gkyl_array *currentDensdot_global; // Time derivative of current density (accross all MPI ranks).
+      struct gkyl_array *dApartdtSlvr_kSq; // Contains sum_s q_s^2/m_s n_s.
+      struct gkyl_array *dApartdtSlvr_lhs_factor; // Contains kperp^2/mu_0 + sum_s q_s^2/m_s n_s for 1D Ohm solve.
+      struct gkyl_array *dApartdtSlvr_lhs_factor_global; // Contains kperp^2/mu_0 + sum_s q_s^2/m_s n_s for 1D Ohm solve.
+      struct gkyl_array *dApartdtSlvr_rhs; // Contains sum_s q_s int dv vpar d/dt(F_s)*.
+      struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0).
+      struct gkyl_fem_parproj *fem_apar_parproj; // FEM smoother for projecting Apar onto continuous FEM basis
+      struct gkyl_fem_parproj *fem_apardot_parproj; // FEM smoother for projecting d(Apar)/dt onto continuous FEM basis
+      struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar.
+      struct gkyl_fem_poisson_perp *fem_apardot_solver; // Solver for d(Apar)/dt.
+      struct gkyl_poisson_bc ampere_bcs; // BCs for Apar and d(Apar)/dt.
+      enum gkyl_fem_parproj_bc_type fem_parproj_ampere_bc; // Type of BC for projecting onto FEM basis.
     };
   };
 
   double es_energy_fac_1d; 
   struct gkyl_array *es_energy_fac; 
+  double apar_energy_fac_1d;
   struct gkyl_array *apar_energy_fac; 
   bool is_dirichletvar; // Whether user provided spatially varying phi BCs.
   struct gkyl_array *phi_bc; // Spatially varying BC.
@@ -1079,7 +1087,7 @@ struct gk_field {
   void (*accumulate_current) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
     const struct gkyl_array *fin[]);
   void (*accumulate_current_dot) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
-    const struct gkyl_array *fin[]);
+    struct gkyl_array *rhs_in[]);
   void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*step_apar) (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
@@ -3177,9 +3185,9 @@ void gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field);
  *
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
- * @param fin[] Input distribution function (num_species size).
+ * @param rhs_in[] right-hand side of the ES GK equation for each species.
  */
-void gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *fin[]);
+void gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[]);
 
 /**
  * Read the field from a file.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 77e9cbd3bd..47f6e330dc 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1816,7 +1816,8 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
-  gk_field_em_rhs(app, app->field, fin);
+  // Compute the electromagnetic field RHS (solves Ohm's law using RHS).
+  gk_field_em_rhs(app, app->field, fout);
 
   // Add electromagnetic contributions to the collisionless update of charged species.
   for (int i=0; i<app->num_species; ++i) {
@@ -1881,7 +1882,7 @@ gkyl_gyrokinetic_app_stat(gkyl_gyrokinetic_app* app)
     + stat->species_heat_tm
     + stat->neut_species_collisionless_tm + stat->neut_species_coll_tm + stat->neut_species_react_tm
     + stat->neut_species_omega_cfl_tm + stat->neut_species_src_tm + stat->dfdt_dt_reduce_tm + stat->fwd_euler_step_f_tm;
-  stat->field_sum_tm = stat->field_phi_rhs_tm  + stat->field_phi_solve_tm;
+  stat->field_sum_tm = stat->field_phi_rhs_tm  + stat->field_phi_solve_tm + stat->field_apar_rhs_tm + stat->field_apar_solve_tm;
   stat->bc_sum_tm = stat->species_bc_tm + stat->neut_species_bc_tm;
   stat->time_rate_diags_sum_tm = stat->fdot_tm + stat->phidot_tm;
   stat->pos_shift_sum_tm = stat->species_pos_shift_tm + stat->neut_species_pos_shift_tm + stat->pos_shift_quasineut_tm;
@@ -1937,6 +1938,8 @@ gkyl_gyrokinetic_app_print_timings(gkyl_gyrokinetic_app* app, FILE *iostream)
   gkyl_gyrokinetic_app_cout(app, iostream, "    * Field solves:                    %.4e sec. / %4.2f %%.\n", stat->field_tm, ratio_to_percent(stat->field_tm,stat->time_loop_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Phi eqn RHS:                   %.4e sec. / %4.2f %%.\n", stat->field_phi_rhs_tm  , ratio_to_percent(stat->field_phi_rhs_tm  ,stat->field_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Phi eqn solve:                 %.4e sec. / %4.2f %%.\n", stat->field_phi_solve_tm, ratio_to_percent(stat->field_phi_solve_tm,stat->field_tm, 0.0));
+  gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Apar eqn RHS:                  %.4e sec. / %4.2f %%.\n", stat->field_apar_rhs_tm , ratio_to_percent(stat->field_apar_rhs_tm ,stat->field_tm, 0.0));
+  gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Apar eqn solve:                %.4e sec. / %4.2f %%.\n", stat->field_apar_solve_tm, ratio_to_percent(stat->field_apar_solve_tm,stat->field_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Accounted for:                 %4.2f %%.\n", ratio_to_percent(stat->field_sum_tm, stat->field_tm, 100.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "    * Boundary conditions::            %.4e sec. / %4.2f %%.\n", stat->bc_tm, ratio_to_percent(stat->bc_tm,stat->time_loop_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Species (charged):             %.4e sec. / %4.2f %%.\n", stat->species_bc_tm     , ratio_to_percent(stat->species_bc_tm     ,stat->bc_tm, 0.0));
diff --git a/gyrokinetic/zero/fem_poisson_perp.c b/gyrokinetic/zero/fem_poisson_perp.c
index 7dab8a515a..dff3fd154a 100644
--- a/gyrokinetic/zero/fem_poisson_perp.c
+++ b/gyrokinetic/zero/fem_poisson_perp.c
@@ -203,7 +203,6 @@ gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up)
 
     gkyl_range_iter_init(&up->perp_iter2d, &up->perp_range2d);
     while (gkyl_range_iter_next(&up->perp_iter2d)) {
-      long perpidx = gkyl_range_idx(&up->perp_range2d, up->perp_iter2d.idx);
 
       for (size_t d=0; d<up->ndim_perp; d++) idx1[d] = up->perp_iter2d.idx[d];
       idx1[up->pardir] = up->par_iter1d.idx[0];
@@ -336,8 +335,10 @@ void
 gkyl_fem_poisson_perp_solve(gkyl_fem_poisson_perp *up, struct gkyl_array *phiout) {
 
   // Check if we need to rebuild the stiffness matrix (if epsilon or kSq got updated).
-  if (up->make_stiff)
+  if (up->make_stiff) {
+    assert(false); // AH Oct 15, 2025: This call is not valgrind clean. It seems that we cannot rebuild the matrix that easily.
     gkyl_fem_poisson_perp_build_stiffness_matrix(up);
+  }
 
 #ifdef GKYL_HAVE_CUDA
   if (up->use_gpu) {

From e2dfc0c6c366072b046e3288353928620b9ea70c Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 11:17:51 -0400
Subject: [PATCH 013/181] still unstable version but compiles.

---
 gyrokinetic/apps/gk_species.c            | 35 ------------------------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  2 ++
 2 files changed, 2 insertions(+), 35 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 6feeff74a1..8175777986 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -105,41 +105,6 @@ gk_species_update_bflux_and_cfl(gkyl_gyrokinetic_app *app, struct gk_species *sp
   return dt_out;
 }
 
-static void
-gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  const struct gkyl_array *fin, struct gkyl_array *rhs)
-{
-  struct timespec wst = gkyl_wall_clock();
-
-  // Compute the surface expansion of the phase space flux
-  // Note: Each cell stores the *lower* surface expansions of the 
-  // phase space flux, so local_ext range needed to index the output
-  // values of flux_surf even though we only loop over local ranges
-  // to avoid evaluating quantities such as geometry in ghost cells
-  // where they are not defined.
-  gkyl_dg_calc_gyrokinetic_vars_flux_surf(species->calc_gk_vars, 
-    &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, fin, species->flux_surf, species->cflrate);
-
-  gkyl_dg_updater_gyrokinetic_advance(species->slvr, &species->local, 
-    fin, species->cflrate, rhs);
-
-  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
-}
-
-static void
-gk_species_collisionless_rhs_disabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  const struct gkyl_array *fin, struct gkyl_array *rhs)
-{
-}
-
-static void
-gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  const struct gkyl_array *fin, struct gkyl_array *rhs)
-{
-  species->collisionless_rhs_func(app, species, fin, rhs);
-}
-
 static double
 gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 95129950e0..47aabbb241 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -707,6 +707,8 @@ struct gk_species {
   struct gkyl_array *f_host; // Host copy for IO and initialization.
 
   struct gkyl_array *gyro_phi; // Gyroaveraged electrostatic potential.
+  struct gkyl_array *apar; // Parallel component of vector potential (for EM simulations).
+  struct gkyl_array *apardot; // Time derivative of parallel component of vector potential.
   
   struct gk_species_moment m0; // Computes charge density.
   struct gk_species_moment m1; // Computes current density.

From 736260b303dfe117e92580e2f4c95b1bfb8a11c3 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 11:37:59 -0400
Subject: [PATCH 014/181] remove em from species and put it in the
 collisionless structure. Note: We cannot use GKYL_GK_COLLISIONLESS_EM because
 this will remove the kernels for surf and volume terms... I want EM to keep
 them and just call new ones that will only add the EM contributions,
 especially because I need the ES RHS to compute current dot. We'll have to
 think about how to do that in a good way

---
 gyrokinetic/apps/gk_species.c               | 13 ++-----------
 gyrokinetic/apps/gk_species_collisionless.c |  3 ++-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h    |  6 ++----
 3 files changed, 6 insertions(+), 16 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 8175777986..ce8d100dac 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1557,7 +1557,6 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     else
       gks->upper_bc[d].type = GKYL_BC_GK_SKIP;
   }
-gks->gkfield_is_em = app->field->is_em;
  
   // Allocate distribution function arrays.
   gks->f = mkarr(app->use_gpu, gks->basis.num_basis, gks->local_ext.volume);
@@ -1628,14 +1627,6 @@ gks->gkfield_is_em = app->field->is_em;
   gks->collisionless = (struct gk_collisionless) { };
   gk_species_collisionless_init(app, gks, &gks->collisionless);
 
-  if (gks->gkfield_is_em) {
-    gks->apar = gkyl_array_acquire(app->field->apar);
-    gks->apardot = gkyl_array_acquire(app->field->apardot);
-  }
-  else {
-    gks->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    gks->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  }
   // Initialize an anomalous diffusion term.
   gks->anom_diff = (struct gk_anomalous_diff) { };
   gk_species_anomalous_diff_init(app, gks, &gks->anom_diff);
@@ -1643,7 +1634,7 @@ gks->gkfield_is_em = app->field->is_em;
   // Allocate data for density (for charge density or upar calculation).
   gk_species_moment_init(app, gks, &gks->m0, GKYL_F_MOMENT_M0, false);
 
-  if (gks->gkfield_is_em) {
+  if (gks->collisionless.is_em) {
     // To compute current density for Ampere's law and current dot for Ohm's law.
     gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
   }
@@ -1979,7 +1970,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
 
   // Release moment data.
   gk_species_moment_release(app, &s->m0);
-  if (s->gkfield_is_em)
+  if (s->collisionless.is_em)
     gk_species_moment_release(app, &s->m1);
 
   for (int i=0; i<s->info.num_diag_moments; ++i)
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 8b995903b9..90a0b18578 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -63,6 +63,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   struct gk_collisionless *gkcls)
 {
   gkcls->collisionless_id = gks->info.collisionless.type;
+  gkcls->is_em = app->field->is_em;
   gkcls->write_diagnostics = gks->info.collisionless.write_diagnostics;
 
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
@@ -105,7 +106,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Allocate arrays to store surface phase space flux.
     gkcls->flux_surf = mkarr(app->use_gpu, flux_surf_sz, gks->local_ext.volume);
 
-    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+    if (gkcls->is_em) {
       // Parallel component of magnetic vector potential.
       gkcls->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
       gkcls->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);    
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 47aabbb241..a8cc2d5eca 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -214,6 +214,7 @@ struct gk_species;
 struct gk_collisionless {
   enum gkyl_gk_collisionless_type collisionless_id; // Type of collisionless terms.
   bool write_diagnostics; // Whether to write diagnostics out.
+  bool is_em; // To store whether we have EM effects.
 
   // Organization of the different equation objects and the required data and solvers
   struct gkyl_array *flux_surf; // Array for surface phase space flux
@@ -679,7 +680,6 @@ struct gk_heating {
 // Species data.
 struct gk_species {
   struct gkyl_gyrokinetic_species info; // Input data.
-  bool gkfield_is_em; // To store whether the field is EM.
   struct gkyl_basis basis; // Phase-space basis.
 
   // Basis on device (points to host basis if running w/o GPU).
@@ -707,9 +707,7 @@ struct gk_species {
   struct gkyl_array *f_host; // Host copy for IO and initialization.
 
   struct gkyl_array *gyro_phi; // Gyroaveraged electrostatic potential.
-  struct gkyl_array *apar; // Parallel component of vector potential (for EM simulations).
-  struct gkyl_array *apardot; // Time derivative of parallel component of vector potential.
-  
+
   struct gk_species_moment m0; // Computes charge density.
   struct gk_species_moment m1; // Computes current density.
   struct gk_species_moment integ_moms; // Integrated moments.

From 1a6cce3767f21f7950564af86dc65e50548cc589 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 14:42:13 -0400
Subject: [PATCH 015/181] Separation of the "NO_BY" and ES/EM options.
 collisionless_id sets now if we are evolving ES, EM_BPAR, EM_BPERP, or EM
 without mentioning NO_BY anymore. Instead a new boolean `no_by` is introduced
 in the collisionless public and private tables. The kernel selections is now
 done according to the value of no_by and not according to the
 collisionless_id anymore. This makes the code cleaner and avoid introducing
 three other enums for EM+NO_BY.

---
 core/zero/gkyl_eqn_type.h                     |  1 -
 gyrokinetic/apps/gk_species_collisionless.c   |  5 ++--
 gyrokinetic/apps/gkyl_gyrokinetic.h           |  1 +
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  3 +-
 gyrokinetic/apps/gyrokinetic_lw.c             |  1 -
 gyrokinetic/zero/dg_gyrokinetic.c             | 12 ++++----
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         | 14 ++++-----
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |  4 +--
 gyrokinetic/zero/gk_collisionless_flux.c      | 25 ++++++++--------
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  | 29 +++++++++----------
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |  4 +--
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  2 +-
 .../zero/gkyl_dg_updater_gyrokinetic.h        |  4 +--
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h |  4 +--
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  2 +-
 15 files changed, 55 insertions(+), 56 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 0cd1a98c56..4b354c546a 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -177,7 +177,6 @@ enum gkyl_gk_anomalous_diff_id {
 enum gkyl_gk_collisionless_type {
   GKYL_GK_COLLISIONLESS_NONE = 0, // Turns off collisionless terms.
   GKYL_GK_COLLISIONLESS_ES, // Electrostatic.
-  GKYL_GK_COLLISIONLESS_ES_NO_BY, // Electrostatic, w/o toroidal field (b_y=0).
   GKYL_GK_COLLISIONLESS_EM_BPERP, // Electromagnetic with B_perp fluctuations.
   GKYL_GK_COLLISIONLESS_EM_BPAR, // Electromagnetic with B_par fluctuations.
   GKYL_GK_COLLISIONLESS_EM, // Electromagnetic with B_perp and B_par fluctuations.
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 90a0b18578..7eebd357e1 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -63,6 +63,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   struct gk_collisionless *gkcls)
 {
   gkcls->collisionless_id = gks->info.collisionless.type;
+  gkcls->no_by = gks->info.collisionless.no_by;
   gkcls->is_em = app->field->is_em;
   gkcls->write_diagnostics = gks->info.collisionless.write_diagnostics;
 
@@ -123,7 +124,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     }
 
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->collisionless_id, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->no_by, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -131,7 +132,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->collisionless_id, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->no_by, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     // Methods chosen at runtime.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index ac97e1eb3c..8a2040b470 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -70,6 +70,7 @@ struct gkyl_phase_diagnostics_inp {
 // Parameters for collisionless terms.
 struct gkyl_gyrokinetic_collisionless {
   enum gkyl_gk_collisionless_type type; // Type of collisionless terms.
+  bool no_by; // Whether to neglect the toroidal field (b_y=0)
   bool write_diagnostics; // Whether to output diagnostics.
 };
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index a8cc2d5eca..024b0fe5b4 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -213,8 +213,9 @@ struct gk_species;
 
 struct gk_collisionless {
   enum gkyl_gk_collisionless_type collisionless_id; // Type of collisionless terms.
+  bool no_by; // Whether to neglect the toroidal field (b_y=0).
+  bool is_em; // Whether we have EM effects.
   bool write_diagnostics; // Whether to write diagnostics out.
-  bool is_em; // To store whether we have EM effects.
 
   // Organization of the different equation objects and the required data and solvers
   struct gkyl_array *flux_surf; // Array for surface phase space flux
diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 6cd165b810..7549463faa 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -58,7 +58,6 @@ static const struct gkyl_str_int_pair position_map_type[] = {
 static const struct gkyl_str_int_pair gk_collisionless_type[] = {
   { "None", GKYL_GK_COLLISIONLESS_NONE },
   { "GKCollisionlessES", GKYL_GK_COLLISIONLESS_ES },
-  { "GKCollisionlessES_no_by", GKYL_GK_COLLISIONLESS_ES_NO_BY },
   { "GKCollisionlessEM_Bperp", GKYL_GK_COLLISIONLESS_EM_BPERP },
   { "GKCollisionlessEM_Bpar", GKYL_GK_COLLISIONLESS_EM_BPAR },
   { "GKCollisionlessEM", GKYL_GK_COLLISIONLESS_EM },
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 4a6a884e0f..40fe241260 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -46,13 +46,13 @@ gkyl_gyrokinetic_set_auxfields(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_gyr
 struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
+  const double charge, const double mass, double skip_cell_threshold, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
-      charge, mass, skip_cell_threshold, collless_type, gk_geom, vel_map);
+      charge, mass, skip_cell_threshold, no_by, gk_geom, vel_map);
 #endif
 
   struct dg_gyrokinetic *gyrokinetic = gkyl_malloc(sizeof(struct dg_gyrokinetic));
@@ -106,12 +106,12 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       break;
   }
 
-  if (collless_type == GKYL_GK_COLLISIONLESS_ES) {
-    gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
-  }
-  else if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+  if (no_by) {
     gyrokinetic->eqn.vol_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
+  else {
+    gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
+  }
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
   if (cdim>1)
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 4f8de2ac59..2aa30eac05 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -37,7 +37,7 @@ gkyl_gyrokinetic_set_auxfields_cu(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_basis_type b_type,
-  int cv_index, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type collless_type)
+  int cv_index, int cdim, int vdim, int poly_order, const bool no_by)
 {
   gyrokinetic->auxfields.flux_surf = 0; 
   gyrokinetic->auxfields.phi = 0; 
@@ -79,12 +79,12 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       break;    
   }  
 
-  if (collless_type == GKYL_GK_COLLISIONLESS_ES) {
-    gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
-  }
-  else if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+  if (no_by) {
     gyrokinetic->eqn.vol_term = vol_no_by_kernels[cv_index].kernels[poly_order];
   }
+  else {
+    gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
+  }
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
   if (cdim>1)
@@ -105,7 +105,7 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
 struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
+  const double charge, const double mass, double skip_cell_threshold, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
 {
   struct dg_gyrokinetic *gyrokinetic = (struct dg_gyrokinetic*) gkyl_malloc(sizeof(*gyrokinetic));
@@ -144,7 +144,7 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gkyl_cu_memcpy(gyrokinetic_cu, gyrokinetic, sizeof(struct dg_gyrokinetic), GKYL_CU_MEMCPY_H2D);
 
   dg_gyrokinetic_set_cu_dev_ptrs<<<1,1>>>(gyrokinetic_cu, cbasis->b_type, cv_index[cdim].vdim[vdim],
-    cdim, vdim, poly_order, collless_type);
+    cdim, vdim, poly_order, no_by);
 
   // set parent on_dev pointer
   gyrokinetic->eqn.on_dev = &gyrokinetic_cu->eqn;
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 5dc875fd80..98724d5c10 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -20,7 +20,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const struct gk_geometry *gk_geom, 
+  const bool no_by, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -28,7 +28,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, collless_type, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, no_by, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 6ea95a5e3e..f07c78a61a 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -12,7 +12,7 @@
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, enum gkyl_gk_collisionless_type type,
+  const double charge, const double mass, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
@@ -20,7 +20,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis, 
-      charge, mass, type, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, no_by, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
@@ -40,27 +40,26 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
-  if (type == GKYL_GK_COLLISIONLESS_ES) {
+  if (no_by) {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
-  }
-  else if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+  } else {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
   }
 
   up->flags = 0;
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 2d95e67072..21a88add72 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -199,10 +199,20 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
-  int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type,
+  int cdim, int vdim, int poly_order, const bool no_by,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
-  if (type == GKYL_GK_COLLISIONLESS_ES) {
+  if (no_by) {
+    for (int d=0; d<cdim; ++d) {
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+        }
+        up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+  } else {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
       up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
@@ -213,23 +223,12 @@ gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up,
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
   }
-  else if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
-    for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-    }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
-  }
 }
 
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, enum gkyl_gk_collisionless_type type,
+  const double charge, const double mass, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
@@ -267,7 +266,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   struct gkyl_gk_collisionless_flux *up_cu = (struct gkyl_gk_collisionless_flux*) gkyl_cu_malloc(sizeof(*up_cu));
   gkyl_cu_memcpy(up_cu, up, sizeof(gkyl_gk_collisionless_flux), GKYL_CU_MEMCPY_H2D);
 
-  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, cdim, vdim, poly_order, type, bctype_conf_dev);
+  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, cdim, vdim, poly_order, no_by, bctype_conf_dev);
 
   gkyl_cu_free(bctype_conf_dev);
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index f4ada736a3..650accf811 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -27,7 +27,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param charge Species charge
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
- * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (b_y=0)
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -36,7 +36,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const struct gk_geometry *gk_geom,
+  const bool no_by, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index e556f3ae55..2a1083be5f 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -469,7 +469,7 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
  */
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_if_smaller_than, enum gkyl_gk_collisionless_type collless_type,
+  const double charge, const double mass, double skip_if_smaller_than, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index c1dfa9793b..722919a2fd 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -29,7 +29,7 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param charge Species charge
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
- * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (b_y=0)
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -40,7 +40,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  enum gkyl_gk_collisionless_type collless_type, const struct gk_geometry *gk_geom,
+  const bool no_by, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index e5717c0922..76380470f9 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -22,7 +22,7 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * @param phase_basis Phase space basis functions
  * @param charge Species charge
  * @param mass Species mass
- * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (b_y=0)
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
@@ -33,7 +33,7 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
+  const double charge, const double mass, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 45ac4a7559..29ba71a250 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -432,7 +432,7 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_o
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  double charge, double mass, enum gkyl_gk_collisionless_type collless_type,
+  double charge, double mass, const bool no_by,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf);

From b0a64aae34a6ca9371db7d5c2be45a291ce40de9 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 14:46:28 -0400
Subject: [PATCH 016/181] adapt the regression tests that were using
 GKYL_GK_COLLISIONLESS_ES_NO_BY

---
 gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c    | 6 ++++--
 gyrokinetic/creg/rt_gk_bgk_im_cross_relax_1x2v_p1.c | 6 ++++--
 gyrokinetic/creg/rt_gk_lapd_cart_3x2v_p1.c          | 6 ++++--
 gyrokinetic/creg/rt_gk_lbo_cross_relax_1x2v_p1.c    | 6 ++++--
 gyrokinetic/creg/rt_gk_mdpx_cart_3x2v_p1.c          | 6 ++++--
 gyrokinetic/creg/rt_gk_multib_asdex_2x2v_p1.c       | 6 ++++--
 gyrokinetic/creg/rt_gk_multib_slab_2x2v_p1.c        | 6 ++++--
 gyrokinetic/creg/rt_gk_multib_step_2x2v_p1.c        | 6 ++++--
 gyrokinetic/creg/rt_gk_multib_step_sol_1x2v_p1.c    | 6 ++++--
 gyrokinetic/creg/rt_gk_multib_step_sol_2x2v_p1.c    | 6 ++++--
 gyrokinetic/creg/rt_gk_sheath_cx_2x2v_p1.c          | 6 ++++--
 gyrokinetic/creg/rt_gk_sheath_flr_2x2v_p1.c         | 6 ++++--
 gyrokinetic/creg/rt_gk_sheath_nonuniformx_2x2v_p1.c | 6 ++++--
 gyrokinetic/creg/rt_gk_slab_2x2v_p1.c               | 6 ++++--
 gyrokinetic/creg/rt_gk_step_2x2v_p1_cons.c          | 6 ++++--
 gyrokinetic/creg/rt_gk_step_out_2x2v_p1.c           | 6 ++++--
 16 files changed, 64 insertions(+), 32 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c b/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
index 827c3e6286..a6443fb656 100644
--- a/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
@@ -400,7 +400,8 @@ main(int argc, char **argv)
     },   
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -448,7 +449,8 @@ main(int argc, char **argv)
     },      
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES_NO,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_bgk_im_cross_relax_1x2v_p1.c b/gyrokinetic/creg/rt_gk_bgk_im_cross_relax_1x2v_p1.c
index 57c2de256c..6555a35f5b 100644
--- a/gyrokinetic/creg/rt_gk_bgk_im_cross_relax_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_bgk_im_cross_relax_1x2v_p1.c
@@ -400,7 +400,8 @@ main(int argc, char **argv)
     },   
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -449,7 +450,8 @@ main(int argc, char **argv)
     },       
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_lapd_cart_3x2v_p1.c b/gyrokinetic/creg/rt_gk_lapd_cart_3x2v_p1.c
index 23579385ae..0ad200f91e 100644
--- a/gyrokinetic/creg/rt_gk_lapd_cart_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_lapd_cart_3x2v_p1.c
@@ -436,7 +436,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -494,7 +495,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_lbo_cross_relax_1x2v_p1.c b/gyrokinetic/creg/rt_gk_lbo_cross_relax_1x2v_p1.c
index b6f9354149..f14bfb465d 100644
--- a/gyrokinetic/creg/rt_gk_lbo_cross_relax_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_lbo_cross_relax_1x2v_p1.c
@@ -393,7 +393,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -434,7 +435,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_mdpx_cart_3x2v_p1.c b/gyrokinetic/creg/rt_gk_mdpx_cart_3x2v_p1.c
index e5e06211cc..e406a54518 100644
--- a/gyrokinetic/creg/rt_gk_mdpx_cart_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_mdpx_cart_3x2v_p1.c
@@ -350,7 +350,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -423,7 +424,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_multib_asdex_2x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_asdex_2x2v_p1.c
index 4f40060622..cf676db43b 100644
--- a/gyrokinetic/creg/rt_gk_multib_asdex_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_asdex_2x2v_p1.c
@@ -1233,7 +1233,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -1367,7 +1368,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_multib_slab_2x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_slab_2x2v_p1.c
index 669714fdf7..87b48104dc 100644
--- a/gyrokinetic/creg/rt_gk_multib_slab_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_slab_2x2v_p1.c
@@ -543,7 +543,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -631,7 +632,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_multib_step_2x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_step_2x2v_p1.c
index d88d1d56a5..36c1a2da81 100644
--- a/gyrokinetic/creg/rt_gk_multib_step_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_step_2x2v_p1.c
@@ -1278,7 +1278,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -1626,7 +1627,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_multib_step_sol_1x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_step_sol_1x2v_p1.c
index 3d2e16e335..99855e6ec5 100644
--- a/gyrokinetic/creg/rt_gk_multib_step_sol_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_step_sol_1x2v_p1.c
@@ -513,7 +513,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -588,7 +589,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_multib_step_sol_2x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_step_sol_2x2v_p1.c
index d1261ce2aa..5fa23521e0 100644
--- a/gyrokinetic/creg/rt_gk_multib_step_sol_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_step_sol_2x2v_p1.c
@@ -537,7 +537,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -640,7 +641,8 @@ main(int argc, char **argv)
     .cells = { cells_v[0], cells_v[1] },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_sheath_cx_2x2v_p1.c b/gyrokinetic/creg/rt_gk_sheath_cx_2x2v_p1.c
index 2aa140d8da..f9b5e30ce8 100644
--- a/gyrokinetic/creg/rt_gk_sheath_cx_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_sheath_cx_2x2v_p1.c
@@ -514,7 +514,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -570,7 +571,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_sheath_flr_2x2v_p1.c b/gyrokinetic/creg/rt_gk_sheath_flr_2x2v_p1.c
index 53d758d0ec..cdcf63ce11 100644
--- a/gyrokinetic/creg/rt_gk_sheath_flr_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_sheath_flr_2x2v_p1.c
@@ -512,7 +512,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -573,7 +574,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_sheath_nonuniformx_2x2v_p1.c b/gyrokinetic/creg/rt_gk_sheath_nonuniformx_2x2v_p1.c
index ca9043d1f5..d94c496f92 100644
--- a/gyrokinetic/creg/rt_gk_sheath_nonuniformx_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_sheath_nonuniformx_2x2v_p1.c
@@ -628,7 +628,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -685,7 +686,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c b/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
index 2124f223f8..0dd76b882e 100644
--- a/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
@@ -392,7 +392,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -459,7 +460,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_step_2x2v_p1_cons.c b/gyrokinetic/creg/rt_gk_step_2x2v_p1_cons.c
index 975aad39e6..1342424db6 100644
--- a/gyrokinetic/creg/rt_gk_step_2x2v_p1_cons.c
+++ b/gyrokinetic/creg/rt_gk_step_2x2v_p1_cons.c
@@ -398,7 +398,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -507,7 +508,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
diff --git a/gyrokinetic/creg/rt_gk_step_out_2x2v_p1.c b/gyrokinetic/creg/rt_gk_step_out_2x2v_p1.c
index 575401b5e6..7d6d4cb930 100644
--- a/gyrokinetic/creg/rt_gk_step_out_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_step_out_2x2v_p1.c
@@ -396,7 +396,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {
@@ -479,7 +480,8 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
 
     .collisions =  {

From 6edf384c063e873728cbb9dd199a0d5c6780b2ee Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Oct 2025 14:50:37 -0400
Subject: [PATCH 017/181] reduction of t_end of this rt to make it much faster
 to run (4sec against 40sec).

---
 gyrokinetic/creg/rt_gk_slab_2x2v_p1.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c b/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
index 0dd76b882e..b44cd0a489 100644
--- a/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_slab_2x2v_p1.c
@@ -124,7 +124,7 @@ create_ctx(void)
   double vpar_max_ion = 6.0 * vti; // Domain boundary (ion velocity space: parallel velocity direction).
   double mu_max_ion = (3.0 / 2.0) * 0.5 * mass_ion * pow(4.0 * vti,2) / (2.0 * B0); // Domain boundary (ion velocity space: magnetic moment direction).
 
-  double t_end = 5.0e-6; // Final simulation time.
+  double t_end = 0.5e-6; // Final simulation time.
   int num_frames = 1; // Number of output frames.
   double write_phase_freq = 0.2; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
   int int_diag_calc_num = num_frames*100;

From c955dc8972047944100f60a6f2703011dd857844 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 21 Oct 2025 13:34:09 -0400
Subject: [PATCH 018/181] dummy commit to connect with DR #867

---
 gyrokinetic/apps/gk_field.c | 2 --
 1 file changed, 2 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index ba310185c6..508093d48b 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -135,9 +135,7 @@ gk_field_accumulate_current_dens_dyn(gkyl_gyrokinetic_app *app, struct gk_field
   gkyl_array_clear(field->currentDens, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-
     gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
-
     gkyl_array_accumulate_range(field->currentDens, s->info.charge, s->m1.marr, &app->local);
   } 
   app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);

From cae1c9bc5e8f7a84f02baf56f2d3aa283c7f8b0f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Oct 2025 16:53:17 -0400
Subject: [PATCH 019/181] add smoothing of apardot add also gyro_apardot (to
 pass it to the species struct, I don't think we will add FLR to EM soon). We
 also add an option to the gkyl_dg_gyrokinetic updater to get an EM adder only
 or ES. And also add many empty kernels for the code to compile and checking
 the workflow. This branch is related to the gkylcas branch
 https://github.com/ammarhakim/gkylcas/pull/89

---
 gyrokinetic/apps/gk_field.c                   |  5 ++
 gyrokinetic/apps/gk_species.c                 | 28 +++++------
 gyrokinetic/apps/gk_species_collisionless.c   | 47 ++++++++++++++++++-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      | 26 +++++++++-
 gyrokinetic/apps/gyrokinetic.c                |  4 +-
 gyrokinetic/zero/dg_gyrokinetic.c             |  2 +-
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |  4 +-
 gyrokinetic/zero/gk_collisionless_flux.c      | 13 ++++-
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |  3 +-
 .../zero/gkyl_dg_updater_gyrokinetic.h        |  3 +-
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h | 17 +++----
 11 files changed, 116 insertions(+), 36 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 508093d48b..c15d7f46f8 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -585,6 +585,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_old = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apardot_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
@@ -937,6 +938,9 @@ gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_a
   struct timespec wst = gkyl_wall_clock();
   field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
+  
+  gk_field_fem_projection_par(app, field, field->apardot_smooth, field->apardot_smooth);
+
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -1078,6 +1082,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar_old);
     gkyl_array_release(f->apardot);
+    gkyl_array_release(f->apardot_smooth);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index ce8d100dac..7ed12921f5 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -176,25 +176,11 @@ gk_species_em_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 {
   struct timespec wst = gkyl_wall_clock();
 
-  // We want here to just add the EM contribution to the collisionless update.
-  // We do not clear the cflrate or rhs.
-  // 1. compute the gk vars from EM fields
-  // something like:
-  // gkyl_dg_calc_gyrokinetic_vars_alpha_surf_em(species->calc_gk_vars, 
-  //   &app->local, &species->local, &species->local_ext, 
-  //   app->field->apardot, species->alpha_surf, species->sgn_alpha_surf, species->const_sgn_alpha);
-
-  // 2. add this contribution to the rhs
-  // If I understood correctly, the step 1. will set the variables required in step 2. so I can just
-  // call the same updater as in the collisionless electrostatic case.
-  // I think I can assume that this will add to rhs and cflrate and not overwrite them.
-  // gkyl_dg_updater_gyrokinetic_advance(species->slvr, &species->local, 
-  //   fin, species->cflrate, rhs);
+  gk_species_collisionless_add_em_rhs(app, species, &species->collisionless, fin, rhs);
 
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 
-  // 3. Update the bflux and its moments and compute cflrate as usual
-  // (this is the same as in the electrostatic case)
+  // Update the bflux and its moments and compute cflrate as usual
   double dt_out = gk_species_update_bflux_and_cfl(app, species, fin, rhs, bflux_moms);
   return dt_out;
 }
@@ -1623,6 +1609,12 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gks->gyro_phi = gkyl_array_acquire(app->field->phi_smooth);
   }
 
+  gks->is_em = app->field->is_em;
+  if (gks->is_em) {
+    // We do not have FLR effects for EM yet.
+    gks->gyro_apardot = gkyl_array_acquire(app->field->apardot_smooth);
+  }
+
   // Initialize the collisionless solver.
   gks->collisionless = (struct gk_collisionless) { };
   gk_species_collisionless_init(app, gks, &gks->collisionless);
@@ -1995,5 +1987,9 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
     gkyl_deflated_fem_poisson_release(s->flr_op);
   }
 
+  if (s->is_em) {
+    gkyl_array_release(s->gyro_apardot);
+  }
+
   s->release_func(app, s);
 }
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 7eebd357e1..483dc94334 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -23,6 +23,15 @@ gk_species_collisionless_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_speci
     species->gyro_phi, fin, gkcls->flux_surf, species->cflrate);
 }
 
+static void
+gk_species_collisionless_add_em_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin)
+{
+  gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_op_add_em, 
+    &app->local, &species->local, &app->local_ext, &species->local_ext, 
+    species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
+}
+
 static void
 gk_species_collisionless_rhs_disabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
@@ -43,6 +52,20 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
+static void
+gk_species_collisionless_add_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
+{
+  struct timespec wst = gkyl_wall_clock();
+
+  gkcls->add_em_flux(app, species, gkcls, fin);
+
+  gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_add_em, &species->local, 
+    fin, species->cflrate, rhs);
+
+  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
+}
+
 static void
 gk_species_collisionless_write_diags_disabled(gkyl_gyrokinetic_app* app, struct gk_species *gks,
   struct gk_collisionless *gkcls, double tm, int frame)
@@ -70,6 +93,8 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
+  gkcls->add_em_flux = gk_species_collisionless_flux_disabled;
+  gkcls->add_em_rhs = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -124,7 +149,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     }
 
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->no_by, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->no_by, false, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -132,12 +157,16 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->no_by, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->no_by, false, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     // Methods chosen at runtime.
     gkcls->flux_func = gk_species_collisionless_flux_enabled;
     gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
+    if (gkcls->is_em) {
+      gkcls->add_em_flux = gk_species_collisionless_add_em_flux_enabled;
+      gkcls->add_em_rhs = gk_species_collisionless_add_em_rhs_enabled;
+    }
     if (gkcls->write_diagnostics) {
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
     }
@@ -158,6 +187,20 @@ gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *speci
   gkcls->rhs_func(app, species, gkcls, fin, rhs);
 }
 
+void
+gk_species_collisionless_add_em_flux(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin)
+{
+  gkcls->add_em_flux(app, species, gkcls, fin);
+}
+
+void
+gk_species_collisionless_add_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
+{
+  gkcls->add_em_rhs(app, species, gkcls, fin, rhs);
+}
+
 void
 gk_species_collisionless_write_diags(gkyl_gyrokinetic_app* app, struct gk_species *gks,
   struct gk_collisionless *gkcls, double tm, int frame)
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 024b0fe5b4..a109ab3386 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -224,12 +224,19 @@ struct gk_collisionless {
 
   struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
   gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.
- 
+
+  struct gkyl_gk_collisionless_flux *surf_flux_op_add_em; // To add EM collisionless fluxes.
+  gkyl_dg_updater_gyrokinetic *slvr_add_em; // To add EM collisionless rhs.
+
   // Methods chosen at runtime.
   void (*flux_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin);
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
+  void (*add_em_flux)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+    struct gk_collisionless *gkcls, const struct gkyl_array *fin);
+  void (*add_em_rhs)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+    struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
   void (*write_diags_func)(gkyl_gyrokinetic_app* app, struct gk_species *gks,
     struct gk_collisionless *gkcls, double tm, int frame);
 };
@@ -708,6 +715,8 @@ struct gk_species {
   struct gkyl_array *f_host; // Host copy for IO and initialization.
 
   struct gkyl_array *gyro_phi; // Gyroaveraged electrostatic potential.
+  struct gkyl_array *gyro_apardot; // Gyroaveraged parallel vector potential time derivative.
+  bool is_em; // Whether electromagnetic terms are present.
 
   struct gk_species_moment m0; // Computes charge density.
   struct gk_species_moment m1; // Computes current density.
@@ -1007,6 +1016,7 @@ struct gk_field {
       struct gkyl_array *apar_old; // Previous state of A_parallel (for update with apardot).
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
+      struct gkyl_array *apardot_smooth; // Smoothed d(A_parallel)/dt.
       struct gkyl_array *apardot_host; // Host copy for use IO.
       struct gkyl_array *currentDens; // Current density.
       struct gkyl_array *currentDens_global; // Current density.
@@ -1362,6 +1372,18 @@ void gk_species_collisionless_flux(gkyl_gyrokinetic_app *app, struct gk_species
 void gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *gks,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
+/**
+ * @brief Add electromagnetic contribution to the collisionless RHS.
+ * 
+ * @param app Gyrokinetic app object.
+ * @param gks Pointer to species.
+ * @param gkcls Species collisionless object.
+ * @param fin Input distribution function.
+ * @param rhs On output, the RHS from collisionless terms including EM contribution.
+ */
+void gk_species_collisionless_add_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
+
 /**
  * Write out diagnostics from the collisionless terms.
  *
@@ -3240,7 +3262,7 @@ void gk_field_step_apar(struct gk_field *field, struct gkyl_array* out, double d
 void gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field);
 
 /**
- * Compute Apardot from fin m1 moment using the Ohm's law.
+ * Compute Apardot from Ohm's law using the m1 moment of the GK electrostatic RHS.
  *
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 2b0c256d22..fb5d188ef9 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1812,17 +1812,17 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
-  // Compute the electromagnetic field RHS (solves Ohm's law using RHS).
+  // Compute the electromagnetic field RHS (solves Ohm's law using the full ES RHS).
   gk_field_em_rhs(app, app->field, fout);
 
   // Add electromagnetic contributions to the collisionless update of charged species.
+  // This is done after all ES terms since we need to compute M1 of fdot.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
     double dt1 = gk_species_em_rhs(app, s, fin[i], fout[i], bflux_out[i]);
     dtmin = fmin(dtmin, dt1);
   }
 
-
   struct timespec wtm = gkyl_wall_clock();
   double dt_max_rel_diff = 0.01;
   // Check if dtmin is slightly smaller than dt. Use dt if it is
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 40fe241260..5d8aac4631 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -46,7 +46,7 @@ gkyl_gyrokinetic_set_auxfields(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_gyr
 struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_cell_threshold, const bool no_by,
+  const double charge, const double mass, double skip_cell_threshold, const bool no_by, const bool add_em,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 #ifdef GKYL_HAVE_CUDA
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 98724d5c10..ecf3b34003 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -20,7 +20,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  const bool no_by, const struct gk_geometry *gk_geom, 
+  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -28,7 +28,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, no_by, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, no_by, add_em, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index f07c78a61a..f0de89b26b 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -12,7 +12,7 @@
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by,
+  const double charge, const double mass, const bool no_by, const bool add_em,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
@@ -35,6 +35,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
+  up->add_em = add_em;
   up->gk_geom = gkyl_gk_geometry_acquire(gk_geom);
   up->dg_geom = gkyl_dg_geom_acquire(dg_geom);
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
@@ -50,6 +51,16 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+  } else if (add_em) {
+    for (int d=0; d<cdim; ++d) {
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_add_em_flux_surf_conf_kern(d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(d, cdim, vdim,
+        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+    }
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_add_em_vpar_kern(cdim, vdim, poly_order);
   } else {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index 650accf811..4699b69acf 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -28,6 +28,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param no_by Whether to neglect the toroidal field (b_y=0)
+ * @param add_em Whether the updater only adds EM terms.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -36,7 +37,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  const bool no_by, const struct gk_geometry *gk_geom,
+  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 722919a2fd..6a3168695f 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -30,6 +30,7 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param no_by Whether to neglect the toroidal field (b_y=0)
+ * @param add_em Whether to add electromagnetic terms
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -40,7 +41,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  const bool no_by, const struct gk_geometry *gk_geom,
+  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index 76380470f9..47fdbb6918 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -17,23 +17,24 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * Create new updater to compute the surface expansion of phase space
  * flux due to the collisionless gyrokinetic terms.
  * 
- * @param phase_grid Phase space grid (for getting cell spacing and cell center)
- * @param conf_basis Configuration space basis functions
- * @param phase_basis Phase space basis functions
- * @param charge Species charge
- * @param mass Species mass
- * @param no_by Whether to neglect the toroidal field (b_y=0)
+ * @param phase_grid Phase space grid (for getting cell spacing and cell center).
+ * @param conf_basis Configuration space basis functions.
+ * @param phase_basis Phase space basis functions.
+ * @param charge Species charge.
+ * @param mass Species mass.
+ * @param no_by Whether to neglect the toroidal field (b_y=0).
+ * @param add_em Whether this updater is meant to add EM terms only.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
  * @param bctype_conf Type of conf-space BCs.
- * @param use_gpu bool to determine if on GPU
+ * @param use_gpu Whether to use GPU.
  * @return New updater pointer.
  */
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by,
+  const double charge, const double mass, const bool no_by, const bool add_em,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);

From b469f26ed05d0a9de6721aaaf617ae96789b3415 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Oct 2025 16:53:37 -0400
Subject: [PATCH 020/181] add all the empty kernels.

---
 .../gkyl_dg_gyrokinetic_kernels.h             | 222 ++++++
 ...nless_flux_add_em_edge_surfx_1x1v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfx_1x2v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfx_2x2v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfx_3x2v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfy_2x2v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfy_3x2v_ser_p1.c |  26 +
 ...nless_flux_add_em_edge_surfz_3x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c |  26 +
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfx_1x1v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfx_1x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfx_2x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfx_3x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfy_2x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfy_3x2v_ser_p1.c |  26 +
 ...add_em_multib_boundary_surfz_3x2v_ser_p1.c |  26 +
 ...flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c |  26 +
 ...flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c |  26 +
 ...flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c |  26 +
 ...flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c |  26 +
 ...flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c |  26 +
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  26 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  26 +
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  26 +
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  26 +
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  26 +
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  26 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  26 +
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  26 +
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  26 +
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  26 +
 ...s_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c |  26 +
 ...s_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c |  26 +
 ...less_flux_add_em_no_by_surfx_2x2v_ser_p1.c |  26 +
 ...less_flux_add_em_no_by_surfx_3x2v_ser_p1.c |  26 +
 ...less_flux_add_em_no_by_surfy_2x2v_ser_p1.c |  26 +
 ...less_flux_add_em_no_by_surfy_3x2v_ser_p1.c |  26 +
 ...less_flux_add_em_no_by_surfz_3x2v_ser_p1.c |  26 +
 ...ionless_flux_add_em_surfvpar_1x1v_ser_p1.c |  26 +
 ...ionless_flux_add_em_surfvpar_1x2v_ser_p1.c |  26 +
 ...ionless_flux_add_em_surfvpar_2x2v_ser_p1.c |  26 +
 ...ionless_flux_add_em_surfvpar_3x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfx_1x1v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfx_1x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfx_2x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfx_3x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfy_2x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfy_3x2v_ser_p1.c |  26 +
 ...lisionless_flux_add_em_surfz_3x2v_ser_p1.c |  26 +
 .../gkyl_gk_collisionless_flux_kernels.h      | 654 ++++++++++++++++++
 gyrokinetic/zero/gk_collisionless_flux.c      |   4 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   | 232 +++++++
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 186 ++++-
 59 files changed, 2699 insertions(+), 3 deletions(-)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c

diff --git a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
index 61117ef1c3..0bbbaf61e6 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
+++ b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
@@ -229,4 +229,226 @@ GKYL_CU_DH double dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1(const double *w,
               const int edge, double* GKYL_RESTRICT out); 
 
 
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x1v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x1v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x1v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x1v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x2v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p2(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p2(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(const double *w, const double *dxv,
+            const double *vmap, const double *vmapSq, const double q_, const double m_,
+            const double *bmag, const double *phi,
+            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *fin, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfz_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfz_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
+              const double *flux_surf_l, const double *flux_surf_r, 
+              double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
+              const double *vmap_prime_edge, const double *vmap_prime_skin, 
+              const double *flux_surf_edge, const double *flux_surf_skin, 
+              const int edge, double* GKYL_RESTRICT out); 
+
+
 EXTERN_C_END
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..02aed87ff6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..985bf5ff5b
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..58032fe55a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..366399870d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..9ee1465433
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..0d7b7b5a25
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..fb4e3657d6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..a1e3efe0f1
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..22417fa638
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..085ae07617
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..2edce2b85a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..d3be656a7e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..ba50f2ddbe
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..f456e80f01
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..4fe40b27ef
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..1d32b32127
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..461dac1bf7
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..11ea44c05a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..08d186e133
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..856155d7b3
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..8f3f6f1ea1
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..dc927940a8
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..47f50f2516
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..a87c9b3ef1
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..686d3fae37
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..bf8b075f11
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..2b39f7d630
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..2cf8ffecdd
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..5837b618aa
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..16282609e6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..35655d48b5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..f39f17c36a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..e3046b01f8
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..77014e76cc
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..4e4fb4bb6e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..6a56f51740
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..3977e7acc0
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..0b5dbee65d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..414ef9f8d4
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..89aad8d3fe
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..f8b28d3d49
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..9504159d0d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..d0cde6b276
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..9897d3b63f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..0f82c703ea
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..62c373ef5d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..7a22e7c4be
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..1fccf45fb9
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..7b7ec7808a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..6984c52216
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..d701443e15
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..70ca233a21
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..60fc96ea32
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..0ec404bc74
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c
@@ -0,0 +1,26 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index 364f4f88b5..5b20c9ed63 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -661,4 +661,658 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
               double* GKYL_RESTRICT flux_surf); 
 
 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p2(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p2(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p2(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p2(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1(
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
+
+
 EXTERN_C_END
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index f0de89b26b..a96b7533fc 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -55,12 +55,12 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
       up->flux_surf[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_add_em_flux_surf_conf_kern(d, cdim, vdim,
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
       up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_add_em_vpar_kern(cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 2a1083be5f..d8cae748f0 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -359,6 +359,238 @@ static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_vpar_
   { NULL, dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
+//
+// Serendipity volume kernels general geometry for adding EM terms.
+// Need to be separated like this for GPU build.
+//
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_add_em_vol_1x1v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_add_em_vol_1x2v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_add_em_vol_2x2v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_add_em_vol_3x2v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+// Volume kernel list.
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_vol_kernels[] = {
+  // 1x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1, NULL }, // 3
+};
+
+// Kernel list that add EM terms.
+// Surface kernel list: x-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_x_kernels[] = {
+  // 1x kernels
+  { NULL, dg_gyrokinetic_add_em_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_em_surfx_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_surfx_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Surface kernel list: y-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_y_kernels[] = {
+  // 1x kernels
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_surfy_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Surface kernel list: z-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_z_kernels[] = {
+  // 1x kernels
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  // 2x kernels
+  { NULL, NULL, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Acceleration surface kernel list: vpar-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_vpar_kernels[] = {
+  // 1x kernels
+  { NULL, dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1, NULL }, // 3
+};
+
+// Boundary surface kernel (zero-flux BCs) to add EM terms.
+// Conf-space advection boundary surface kernel list: x-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_x_kernels[] = {
+  // 1x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Conf-space advection boundary surface kernel list: y-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_y_kernels[] = {
+  // 1x kernels
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Conf-space advection boundary surface kernel list: z-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_z_kernels[] = {
+  // 1x kernels
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  // 2x kernels
+  { NULL, NULL, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Acceleration boundary surface kernel (zero-flux BCs) list: vpar-direction
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_vpar_kernels[] = {
+  // 1x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1, NULL }, // 3
+};
+
 // "Choose Kernel" based on cdim, vdim and polyorder
 #define CK(lst,cdim,vd,poly_order) lst[cv_index[cdim].vdim[vd]].kernels[poly_order]
 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 29ba71a250..9ebca86cd7 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -47,6 +47,7 @@ struct gkyl_gk_collisionless_flux {
                                                         // at upper configuration space edge
   gk_collisionless_flux_surfvpar_t flux_surfvpar[1]; // kernel for computing surface expansion of phase space flux alpha
   double charge, mass;
+  bool add_em; // wheter it is meant to only add electromagnetic terms.
   const struct gk_geometry *gk_geom; // Pointer to geometry struct.
   const struct gkyl_dg_geom *dg_geom; // Pointer to vol dg geometry struct.
   const struct gkyl_gk_dg_geom *gk_dg_geom; // Pointer to vol gk dg geometry struct.
@@ -57,7 +58,7 @@ struct gkyl_gk_collisionless_flux {
 };
 
 //
-// Serendipity surface kernels.
+// Electrostatic serendipity surface kernels.
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
@@ -305,6 +306,130 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
+//
+// Serendipity surface kernels to add electromagnetic effects.
+//
+// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_em_surfvpar_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1, NULL }, // 3
+};
+
+//
+// Kernels used at multiblock boundaries.
+//
+
+// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
@@ -424,6 +549,65 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_o
   return ser_gk_collisionless_flux_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_add_em_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)                                       
+      return ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)                                       
+      return ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surfvpar_t
+choose_gk_collisionless_flux_add_em_surf_vpar_kern(int cdim, int vdim, int poly_order)
+{
+  return ser_gk_collisionless_flux_add_em_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+}
+
 #ifdef GKYL_HAVE_CUDA
 /**
  * Create new updater to compute gyrokinetic variables on

From 8631c32e51adbf0de995dede0346223cd03ebef4 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Oct 2025 17:15:41 -0400
Subject: [PATCH 021/181] =?UTF-8?q?I=20think=20we=20have=20every=20declara?=
 =?UTF-8?q?tion=20of=20every=20add=5Fem=20+=20no=5Fby=20now=20=F0=9F=A4=AA?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/zero/gk_collisionless_flux.c      |  66 ++++---
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  75 +++++++
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 184 ++++++++++++++++++
 3 files changed, 299 insertions(+), 26 deletions(-)

diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index a96b7533fc..a3183db174 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -42,35 +42,49 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
   if (no_by) {
-    for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-    }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
-  } else if (add_em) {
-    for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+    if (add_em) {
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_no_by_edge_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+    } else {
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
-    for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+    if (add_em) {
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_surf_vpar_kern(cdim, vdim, poly_order);
+    } else {
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
   }
 
   up->flags = 0;
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index d8cae748f0..799848105a 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -493,6 +493,81 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_vol_kernels[] = {
   { NULL, kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1, NULL }, // 3
 };
 
+//
+// Serendipity volume kernels to add EM, no toroidal field (by=0)
+// Need to be separated like this for GPU build
+//
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_no_by_vol_2x2v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
+  return dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
+
+// Volume kernel list.
+GKYL_CU_D
+static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_no_by_vol_kernels[] = {
+  // 1x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1, NULL }, // 1
+  // 2x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1, NULL }, // 2
+  // 3x kernels
+  { NULL, kernel_dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1, NULL }, // 3
+};
+
 // Kernel list that add EM terms.
 // Surface kernel list: x-direction
 GKYL_CU_D
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 9ebca86cd7..3fddffa4a3 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -430,6 +430,130 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
+//
+// Serendipity surface kernels without toroidal field (by=0)
+//
+// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_em_no_by_surfvpar_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+};
+
+//
+// Kernels used at multiblock boundaries.
+//
+
+// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
+// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+GKYL_CU_D
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+};
+
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
@@ -608,6 +732,66 @@ choose_gk_collisionless_flux_add_em_surf_vpar_kern(int cdim, int vdim, int poly_
   return ser_gk_collisionless_flux_add_em_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_add_em_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_add_em_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_add_em_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_add_em_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surfvpar_t
+choose_gk_collisionless_flux_add_em_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
+{
+  return ser_gk_collisionless_flux_add_em_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+}
+
 #ifdef GKYL_HAVE_CUDA
 /**
  * Create new updater to compute gyrokinetic variables on

From 06a2b8880ad315c29742a16ef10ea56e928920f8 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 24 Oct 2025 14:14:13 -0400
Subject: [PATCH 022/181] reorganize how the kernel are declared, first all the
 electrostatic stuff, then all the EM.

---
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 266 +++++++++---------
 1 file changed, 133 insertions(+), 133 deletions(-)

diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 3fddffa4a3..bc01805ce9 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -306,8 +306,127 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surfvpar_t
+choose_gk_collisionless_flux_surf_vpar_kern(int cdim, int vdim, int poly_order)
+{
+  return ser_gk_collisionless_flux_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)                                       
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)                                       
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surf_t
+choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+{
+  if (bc == GKYL_BC_GK_SKIP) {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+  else {
+    if (dir == 0)
+      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 1)
+      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else if (dir == 2)
+      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+    else
+      return NULL;
+  }
+}
+
+GKYL_CU_D
+static gk_collisionless_flux_surfvpar_t
+choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
+{
+  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+}
+
+
 //
-// Serendipity surface kernels to add electromagnetic effects.
+// Electromagnetic serendipity surface kernels.
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
@@ -327,7 +446,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+// Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfy_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -336,7 +455,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+// Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfy_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -345,7 +464,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+// Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfz_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -354,7 +473,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+// Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfz_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -394,7 +513,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
+// Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -403,7 +522,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
+// Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfy_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -412,7 +531,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
+// Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -421,7 +540,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
+// Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfz_kernels[] = {
   { NULL, NULL, NULL }, // 0
@@ -430,6 +549,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
+
 //
 // Serendipity surface kernels without toroidal field (by=0)
 //
@@ -554,125 +674,6 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
   { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_surf_vpar_kern(int cdim, int vdim, int poly_order)
-{
-  return ser_gk_collisionless_flux_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
-{
-  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-}
-
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
 choose_gk_collisionless_flux_add_em_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
@@ -680,9 +681,9 @@ choose_gk_collisionless_flux_add_em_surf_conf_kern(int dir, int cdim, int vdim,
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
       return ser_gk_collisionless_flux_add_em_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)                                       
+    else if (dir == 1)
       return ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)                                       
+    else if (dir == 2)
       return ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
@@ -732,7 +733,6 @@ choose_gk_collisionless_flux_add_em_surf_vpar_kern(int cdim, int vdim, int poly_
   return ser_gk_collisionless_flux_add_em_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
-
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
 choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
@@ -740,9 +740,9 @@ choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(int dir, int cdim, int
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
       return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
+    else if (dir == 1)                                       
       return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
+    else if (dir == 2)                                       
       return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;

From 66f0ff3d632452f369355fd17915a46b3b35dca1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 24 Oct 2025 15:47:31 -0400
Subject: [PATCH 023/181] the empty kernels to add EM are now connected to the
 GK updater. The code is able to run without apparent issue with EM option
 turned on. need to check how clean it is in valgrind.

---
 gyrokinetic/apps/gk_field.c                   | 45 +++++++++-----
 gyrokinetic/apps/gk_species.c                 |  4 +-
 gyrokinetic/apps/gk_species_collisionless.c   | 61 ++++++++++++-------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      | 12 ++--
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c |  2 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   | 21 ++++---
 6 files changed, 90 insertions(+), 55 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index c15d7f46f8..0c89959f59 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -250,14 +250,20 @@ gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field)
 }
 
 static void
-gk_field_step_apar_dyn(struct gk_field *field, struct gkyl_array* out, double dt,
+gk_field_step_apar_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
-  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
+  gkyl_array_accumulate(out, dt, inp);
+
+  // Update the smooth version of Apar (out).
+  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
+  gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
+  gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
+  gkyl_array_copy_range_to_range(field->apar_smooth, field->apar_fem, &app->local, &field->global_sub_range);
 }
 
 static void
-gk_field_step_apar_none(struct gk_field *field, struct gkyl_array* out, double dt,
+gk_field_step_apar_none(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
   // do nothing
@@ -584,8 +590,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   if (f->is_em) {
     f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_old = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+    f->apar_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
@@ -622,13 +629,14 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
       f->ohm_solve = gk_field_ohm_solve_1x;
       f->ampere_solve = gk_field_ampere_solve_1x;
-    }
-    else if (app->cdim > 1) {
+    } else if (app->cdim > 1) {
+
       // Compute the weights in front of the laplacian operator (metric x 1/mu0)
       struct gkyl_array *Jgij[3] = {app->gk_geom->geo_int.gxxj, app->gk_geom->geo_int.gxyj, app->gk_geom->geo_int.gyyj};
       for (int i=0; i<app->cdim-2/app->cdim; i++) {
         gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
       }
+
       // Translate input file BCs into Ampere BCs.
       for (int d=0; d<app->cdim-1; d++) {
         struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
@@ -645,12 +653,17 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
             f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
         }
       }
+
       // FEM solver for Ampere equation (solved at IC only).
       f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
           &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
       // FEM solver for Ohm's law (evolves d(Apart)/dt).
       f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
         &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+      // FEM smoother for Aparallel.
+      f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
+      f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+        f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
 
       f->ohm_solve = gk_field_ohm_solve;
       f->ampere_solve = gk_field_ampere_solve;
@@ -658,9 +671,8 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->accumulate_current = gk_field_accumulate_current_dens_dyn;
     f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_dyn;
     f->step_apar = gk_field_step_apar_dyn;
-
+    
     // Factor for EM energy.
-    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
     f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
     f->apar_energy_fac_1d = 0;
     assert(f->info.mu0 > 0.0);
@@ -671,6 +683,8 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     else if (app->cdim > 1) {
       gkyl_array_set(f->apar_energy_fac, -0.5, f->lapWeightAmpere);
     }
+    // Diagnostic for integrated Aparallel energy.
+    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
   }
 
   // Create operator needed for FLR effects.
@@ -928,19 +942,17 @@ void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field)
   field->ampere_solve(app, field);
 }
 
-void gk_field_step_apar (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp)
+void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp)
 {
-  field->step_apar(field, out, a, inp);
+  field->step_apar(app, field, out, a, inp);
 }
 
 void
-gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[]){
+gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[])
+{
   struct timespec wst = gkyl_wall_clock();
   field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
-  
-  gk_field_fem_projection_par(app, field, field->apardot_smooth, field->apardot_smooth);
-
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -1081,8 +1093,9 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   if (f->is_em) {
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar_old);
+    gkyl_array_release(f->apar_fem);
+    gkyl_array_release(f->apar_smooth);
     gkyl_array_release(f->apardot);
-    gkyl_array_release(f->apardot_smooth);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
@@ -1097,9 +1110,9 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
       gkyl_array_release(f->currentDensdot_global);
       gkyl_array_release(f->dApartdtSlvr_lhs_factor);
       gkyl_array_release(f->dApartdtSlvr_lhs_factor_global);
-      gkyl_fem_parproj_release(f->fem_apar_parproj);
       gkyl_fem_parproj_release(f->fem_apardot_parproj);  
     }
+    gkyl_fem_parproj_release(f->fem_apar_parproj);
     if (app->use_gpu) {
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 7ed12921f5..f5cbf73523 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1612,7 +1612,8 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->is_em = app->field->is_em;
   if (gks->is_em) {
     // We do not have FLR effects for EM yet.
-    gks->gyro_apardot = gkyl_array_acquire(app->field->apardot_smooth);
+    gks->gyro_apar = gkyl_array_acquire(app->field->apar_smooth);
+    gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
   }
 
   // Initialize the collisionless solver.
@@ -1988,6 +1989,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
   }
 
   if (s->is_em) {
+    gkyl_array_release(s->gyro_apar);
     gkyl_array_release(s->gyro_apardot);
   }
 
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 483dc94334..1386995f8b 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -132,16 +132,6 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Allocate arrays to store surface phase space flux.
     gkcls->flux_surf = mkarr(app->use_gpu, flux_surf_sz, gks->local_ext.volume);
 
-    if (gkcls->is_em) {
-      // Parallel component of magnetic vector potential.
-      gkcls->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-      gkcls->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);    
-    }
-    else {
-      gkcls->apar    = gkyl_array_acquire(app->field->phi_smooth); // Not used.
-      gkcls->apardot = gkyl_array_acquire(app->field->phi_smooth); // Not used.
-    }
-
     enum gkyl_gyrokinetic_bc_type bctype_conf[2*GKYL_MAX_CDIM];
     for (int d=0; d<app->cdim; d++) {
       bctype_conf[d] = gks->lower_bc[d].type;
@@ -152,21 +142,44 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       gks->info.charge, gks->info.mass, gkcls->no_by, false, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
+    if (gkcls->is_em) {
+    }
+    
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
       .phi = gks->gyro_phi, .apar = gkcls->apar, .apardot = gkcls->apardot };
-    // Create solver.
-    gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
-      &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->no_by, false, app->gk_geom, gks->vel_map, 
-      &aux_inp, app->use_gpu);
-
-    // Methods chosen at runtime.
-    gkcls->flux_func = gk_species_collisionless_flux_enabled;
-    gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
-    if (gkcls->is_em) {
-      gkcls->add_em_flux = gk_species_collisionless_add_em_flux_enabled;
-      gkcls->add_em_rhs = gk_species_collisionless_add_em_rhs_enabled;
+      // Create solver.
+      gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+        &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+        gks->info.skip_cell_threshold, gkcls->no_by, false, app->gk_geom, gks->vel_map, 
+        &aux_inp, app->use_gpu);
+        
+        // Methods chosen at runtime.
+        gkcls->flux_func = gk_species_collisionless_flux_enabled;
+        gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
+
+      // Electromagnetic additional setup
+      if (gkcls->is_em) {
+
+        gkcls->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+        gkcls->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);  
+
+        // Create solvers to add EM contributions.
+        gkcls->surf_flux_op_add_em = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+          gks->info.charge, gks->info.mass, gkcls->no_by, true, app->gk_geom, 
+          app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
+        gkcls->slvr_add_em = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+          &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+          gks->info.skip_cell_threshold, gkcls->no_by, true, app->gk_geom, gks->vel_map, 
+          &aux_inp, app->use_gpu);
+        
+        // Runtime methods for EM contributions.  
+        gkcls->add_em_flux = gk_species_collisionless_add_em_flux_enabled;
+        gkcls->add_em_rhs = gk_species_collisionless_add_em_rhs_enabled;
+    } else {
+      gkcls->apar    = gkyl_array_acquire(app->field->phi_smooth); // Not used.
+      gkcls->apardot = gkyl_array_acquire(app->field->phi_smooth); // Not used.
     }
+
     if (gkcls->write_diagnostics) {
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
     }
@@ -220,7 +233,9 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
-    if (gkcls->write_diagnostics) {
+    if (gkcls->is_em) {
+      gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op_add_em);
+      gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_add_em);
     }
   }
 }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index a109ab3386..a46109ee1d 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -715,6 +715,7 @@ struct gk_species {
   struct gkyl_array *f_host; // Host copy for IO and initialization.
 
   struct gkyl_array *gyro_phi; // Gyroaveraged electrostatic potential.
+  struct gkyl_array *gyro_apar; // Gyroaveraged parallel vector potential.
   struct gkyl_array *gyro_apardot; // Gyroaveraged parallel vector potential time derivative.
   bool is_em; // Whether electromagnetic terms are present.
 
@@ -992,7 +993,7 @@ struct gk_field {
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density
   struct gkyl_array *rho_c;
-  struct gkyl_array *rho_c_global_dg;
+  struct gkyl_array *rho_c_global_dg; // Auxiliary array for global charge density but also used in smoothing.
   struct gkyl_array *rho_c_global_smooth; 
   struct gkyl_array *phi_fem, *phi_smooth; // arrays for updates
 
@@ -1014,9 +1015,10 @@ struct gk_field {
     struct {
       struct gkyl_array *apar; // Array for A_parallel (solved only in ic).
       struct gkyl_array *apar_old; // Previous state of A_parallel (for update with apardot).
+      struct gkyl_array *apar_fem; // FEM A_parallel. 
+      struct gkyl_array *apar_smooth; // Smoothed A_parallel.
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
-      struct gkyl_array *apardot_smooth; // Smoothed d(A_parallel)/dt.
       struct gkyl_array *apardot_host; // Host copy for use IO.
       struct gkyl_array *currentDens; // Current density.
       struct gkyl_array *currentDens_global; // Current density.
@@ -1104,7 +1106,7 @@ struct gk_field {
     struct gkyl_array *rhs_in[]);
   void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
-  void (*step_apar) (struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
+  void (*step_apar) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
 };
 
 // Gyrokinetic object: used as opaque pointer in user code.
@@ -3241,13 +3243,15 @@ void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field);
 
 /**
  * Step the parallel component of the magnetic vector potential, apar, forward in time.
+ * Also update apar_smooth used in the GK characteristics.
  * 
+ * @param app gyrokinetic app object.
  * @param field Pointer to field.
  * @param out Output array. (apar)
  * @param dt Timestep.
  * @param inp Input array. (apardot from Ohm's law)
  */
-void gk_field_step_apar(struct gk_field *field, struct gkyl_array* out, double dt,
+void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp);
 
 /**
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index cb0762a1d1..29bc693f9a 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -33,7 +33,7 @@ gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_step_f(gkns, fout_neut[i], dta, fin_neut[i]);
     gk_neut_species_bflux_step_f(app, &gkns->bflux, bflux_out_neut[i], dta, bflux_in_neut[i]);
   }
-  gk_field_step_apar(app->field, app->field->apardot, dta, app->field->apar);
+  gk_field_step_apar(app, app->field, app->field->apar, dta, app->field->apardot);
 
   app->stat.fwd_euler_step_f_tm += gkyl_time_diff_now_sec(wst);
   app->stat.fwd_euler_tm += gkyl_time_diff_now_sec(wst_fe);
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 799848105a..33bf5f7e6f 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -360,8 +360,8 @@ static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_vpar_
 };
 
 //
-// Serendipity volume kernels general geometry for adding EM terms.
-// Need to be separated like this for GPU build.
+// Serendipity volume kernels general geometry
+// Need to be separated like this for GPU build
 //
 
 GKYL_CU_DH
@@ -387,7 +387,7 @@ kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
@@ -416,7 +416,7 @@ kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
@@ -445,7 +445,7 @@ kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
@@ -474,7 +474,7 @@ kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
@@ -494,7 +494,7 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_vol_kernels[] = {
 };
 
 //
-// Serendipity volume kernels to add EM, no toroidal field (by=0)
+// Serendipity volume kernels general geometry, no toroidal field (by=0)
 // Need to be separated like this for GPU build
 //
 
@@ -515,7 +515,7 @@ kernel_dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_no_by_vol_2x2v_ser_p1(xc, dx,
+  return dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -568,7 +568,9 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_no_by_vol_kernels[] =
   { NULL, kernel_dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-// Kernel list that add EM terms.
+//
+// Serendipity surface kernels general geometry
+//
 // Surface kernel list: x-direction
 GKYL_CU_D
 static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_x_kernels[] = {
@@ -617,7 +619,6 @@ static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_vpar_kernels[] =
   { NULL, dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
-// Boundary surface kernel (zero-flux BCs) to add EM terms.
 // Conf-space advection boundary surface kernel list: x-direction
 GKYL_CU_D
 static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_x_kernels[] = {

From 3504b479bdffcab9d156b0802e051138bd8c552e Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 24 Oct 2025 16:25:08 -0400
Subject: [PATCH 024/181] fix a bug introduced by the merge

---
 gyrokinetic/apps/gk_species.c | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 879da7b9d5..6e2acc6185 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1841,13 +1841,6 @@ gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   return species->em_rhs_func(app, species, fin, rhs, bflux_moms);
 }
 
-double
-gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
-{
-  return species->em_rhs_func(app, species, fin, rhs, bflux_moms);
-}
-
 double
 gk_species_rhs_implicit(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, double dt)

From 4f6805fd103bf8730b660ff0db571b63690e1d93 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 24 Oct 2025 17:00:47 -0400
Subject: [PATCH 025/181] bugfix: m0 moment of species was allocated twice

---
 gyrokinetic/apps/gk_species.c | 8 ++------
 1 file changed, 2 insertions(+), 6 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 6e2acc6185..dff434c7bb 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1615,9 +1615,6 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->anom_diff = (struct gk_anomalous_diff) { };
   gk_species_anomalous_diff_init(app, gks, &gks->anom_diff);
 
-  // Allocate data for density (for charge density or upar calculation).
-  gk_species_moment_init(app, gks, &gks->m0, GKYL_F_MOMENT_M0, false);
-
   if (gks->collisionless.is_em) {
     // To compute current density for Ampere's law and current dot for Ohm's law.
     gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
@@ -1956,9 +1953,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
   gk_species_anomalous_diff_release(app, &s->anom_diff);
 
   // Release moment data.
-  gk_species_moment_release(app, &s->m0);
-  if (s->collisionless.is_em)
-    gk_species_moment_release(app, &s->m1);
+  gk_species_moment_release(app, &s->m0);    
 
   for (int i=0; i<s->info.num_diag_moments; ++i)
     gk_species_moment_release(app, &s->moms[i]);
@@ -1987,6 +1982,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
   }
 
   if (s->is_em) {
+    gk_species_moment_release(app, &s->m1);
     gkyl_array_release(s->gyro_apar);
     gkyl_array_release(s->gyro_apardot);
   }

From 26e1383384e9620b5fcf0388fafd86c5bca802c5 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 27 Oct 2025 09:29:20 -0400
Subject: [PATCH 026/181] add empty dg_gk em kernels

---
 ...tic_add_em_boundary_surfvpar_1x1v_ser_p1.c | 18 ++++++++++++++++++
 ...tic_add_em_boundary_surfvpar_1x2v_ser_p1.c | 18 ++++++++++++++++++
 ...tic_add_em_boundary_surfvpar_2x2v_ser_p1.c | 18 ++++++++++++++++++
 ...tic_add_em_boundary_surfvpar_3x2v_ser_p1.c | 18 ++++++++++++++++++
 ..._gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c | 17 +++++++++++++++++
 ..._gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c | 17 +++++++++++++++++
 ..._gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c | 17 +++++++++++++++++
 ..._gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c | 17 +++++++++++++++++
 .../dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c   | 19 +++++++++++++++++++
 .../dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c   | 19 +++++++++++++++++++
 .../dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c   | 19 +++++++++++++++++++
 .../dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c   | 19 +++++++++++++++++++
 12 files changed, 216 insertions(+)
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..0d0ee1dcb7
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,18 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_1x1v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_edge, const double *vmap_prime_skin,
+    const double *flux_surf_edge, const double *flux_surf_skin, 
+    const int edge, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
+  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
+  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
+  // edge: determines if the update is for the left edge (-1) or right edge (+1).
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..640fa5f1d1
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,18 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_1x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_edge, const double *vmap_prime_skin,
+    const double *flux_surf_edge, const double *flux_surf_skin, 
+    const int edge, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
+  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
+  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
+  // edge: determines if the update is for the left edge (-1) or right edge (+1).
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..363c18ba47
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,18 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_2x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_edge, const double *vmap_prime_skin,
+    const double *flux_surf_edge, const double *flux_surf_skin, 
+    const int edge, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
+  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
+  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
+  // edge: determines if the update is for the left edge (-1) or right edge (+1).
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..912a590a66
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,18 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_3x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_edge, const double *vmap_prime_skin,
+    const double *flux_surf_edge, const double *flux_surf_skin, 
+    const int edge, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
+  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
+  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
+  // edge: determines if the update is for the left edge (-1) or right edge (+1).
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..98e85d2209
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,17 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_1x1v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
+    const double *flux_surf_l, const double *flux_surf_r, 
+    double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
+  // flux_surf_l: Surface expansion of phase space flux on the left.
+  // flux_surf_r: Surface expansion of phase space flux on the right.
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..7abe4f702f
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,17 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_1x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
+    const double *flux_surf_l, const double *flux_surf_r, 
+    double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
+  // flux_surf_l: Surface expansion of phase space flux on the left.
+  // flux_surf_r: Surface expansion of phase space flux on the right.
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..daeebb1c56
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,17 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_2x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
+    const double *flux_surf_l, const double *flux_surf_r, 
+    double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
+  // flux_surf_l: Surface expansion of phase space flux on the left.
+  // flux_surf_r: Surface expansion of phase space flux on the right.
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..5e3a3a38e7
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,17 @@
+#include <gkyl_dg_gyrokinetic_kernels.h>
+#include <gkyl_basis_gkhyb_3x2v_p1_upwind_quad_to_modal.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
+    const double *flux_surf_l, const double *flux_surf_r, 
+    double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
+  // flux_surf_l: Surface expansion of phase space flux on the left.
+  // flux_surf_r: Surface expansion of phase space flux on the right.
+  // out: output increment in center cell.
+
+  return 0.0; 
+
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
new file mode 100644
index 0000000000..8a43c662e6
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
@@ -0,0 +1,19 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *phi,
+    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential .
+  // apar: parallel component of vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
new file mode 100644
index 0000000000..97230754e5
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
@@ -0,0 +1,19 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *phi,
+    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential .
+  // apar: parallel component of vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
new file mode 100644
index 0000000000..9236339f5d
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
@@ -0,0 +1,19 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *phi,
+    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential .
+  // apar: parallel component of vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
new file mode 100644
index 0000000000..219e2e35ae
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
@@ -0,0 +1,19 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *phi,
+    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential .
+  // apar: parallel component of vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  return 0.; 
+} 

From bf31f29c1405c3515f3ce6eac12af56613611125 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 27 Oct 2025 10:27:37 -0400
Subject: [PATCH 027/181] replace phi and dualcurlbhatoverB by apar and apardot

---
 .../dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c   |   4 +-
 .../dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c   |   4 +-
 .../dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c   |   4 +-
 .../dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c   |   4 +-
 .../gkyl_dg_gyrokinetic_kernels.h             | 124 +++---------------
 5 files changed, 25 insertions(+), 115 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
index 8a43c662e6..3eb7e85c0e 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
@@ -1,7 +1,7 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *phi,
-    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double q_, const double m_, const double *bmag, const double *apar,
+    const double *apardot, const double *rtg33inv, const double *bioverJB,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
index 97230754e5..971767445c 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
@@ -1,7 +1,7 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *phi,
-    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double q_, const double m_, const double *bmag, const double *apar,
+    const double *apardot, const double *rtg33inv, const double *bioverJB,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
index 9236339f5d..273c7fcf79 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
@@ -1,7 +1,7 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *phi,
-    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double q_, const double m_, const double *bmag, const double *apar,
+    const double *apardot, const double *rtg33inv, const double *bioverJB,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
index 219e2e35ae..cfb0840e3d 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
@@ -1,7 +1,7 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *phi,
-    const double *apar, const double *rtg33inv, const double *bioverJB,
+    const double q_, const double m_, const double *bmag, const double *apar,
+    const double *apardot, const double *rtg33inv, const double *bioverJB,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
diff --git a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
index 0bbbaf61e6..830cf6a25e 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
+++ b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
@@ -228,16 +228,15 @@ GKYL_CU_DH double dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1(const double *w,
               const double *flux_surf_edge, const double *flux_surf_skin, 
               const int edge, double* GKYL_RESTRICT out); 
 
-
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv,
+              GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x1v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x1v_ser_p1(const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
@@ -256,42 +255,15 @@ GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1(const doub
               const double *flux_surf_edge, const double *flux_surf_skin, 
               const int edge, double* GKYL_RESTRICT out); 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x1v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x1v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x2v_ser_p1(const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
@@ -310,42 +282,15 @@ GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1(const doub
               const double *flux_surf_edge, const double *flux_surf_skin, 
               const int edge, double* GKYL_RESTRICT out); 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x2v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_2x2v_ser_p1(const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
@@ -372,50 +317,15 @@ GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1(const doub
               const double *flux_surf_edge, const double *flux_surf_skin, 
               const int edge, double* GKYL_RESTRICT out); 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p2(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p2(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-
 GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(const double *w, const double *dxv,
             const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *phi,
-            const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+            const double *bmag, const double *apar, const double *apardot,
+            const double *rtg33inv, const double* bioverJB,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_3x2v_ser_p1(const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 

From 3fe8d4ed0b1c1cb0f23220ce0d473a2a461e84dc Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 5 Nov 2025 17:47:44 -0500
Subject: [PATCH 028/181] this is a chunky commit but it looks like it works in
 the electrostatic limit ! Changelog: - gk app level -- The bflux and cfl
 handling is now done outside of gk_species_rhs because it is clearer and it
 allows to avoid the bflux computation before having the RHS completed. --
 gyrokinetic_rhs now has the full flow for EM simulation, i.e. computes the
 ES+Apar RHS, get apardot from Ohm's law, add apardot to the rhs.

- GK zero level
--Volume kernels, the GK volume kernels now call the the aparallel contribution right after the electrostatic one.
--Surface kernels, the aparallel term is now included in the surface kernel computation and a lot of addition with Apar=0 are performed in the ES limit. We could create ES kernels instead to avoid it.
--The apardot term is added by using new gyrokinetic solver updater with kernels that do nothing except adding the apardot to the volume and surface terms. This allows to reuse a lot of the coding and do not touch other app.

Improvement: The flags are a bit messy (is_em, add_apardot). I will improve this after a mergin main into this branch.

GPU: Nothing is ready yet.
---
 gyrokinetic/apps/gk_field.c                   |    9 +-
 gyrokinetic/apps/gk_species.c                 |  111 +-
 gyrokinetic/apps/gk_species_collisionless.c   |  105 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |   58 +-
 gyrokinetic/apps/gyrokinetic.c                |   11 +-
 .../dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c |   50 +
 .../dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c |   53 +
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c |  126 ++
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c |  239 ++++
 ..._gyrokinetic_add_apardot_vol_1x1v_ser_p1.c |   25 +
 ..._gyrokinetic_add_apardot_vol_1x2v_ser_p1.c |   35 +
 ..._gyrokinetic_add_apardot_vol_2x2v_ser_p1.c |   55 +
 ..._gyrokinetic_add_apardot_vol_3x2v_ser_p1.c |   95 ++
 ...tic_add_em_boundary_surfvpar_1x1v_ser_p1.c |   18 -
 ...tic_add_em_boundary_surfvpar_1x2v_ser_p1.c |   18 -
 ...tic_add_em_boundary_surfvpar_2x2v_ser_p1.c |   18 -
 ...tic_add_em_boundary_surfvpar_3x2v_ser_p1.c |   18 -
 ..._gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c |   17 -
 ..._gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c |   17 -
 ..._gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c |   17 -
 ..._gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c |   17 -
 .../dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c   |   19 -
 .../dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c   |   19 -
 .../dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c   |   19 -
 .../dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c   |   19 -
 .../gkyl_dg_gyrokinetic_kernels.h             |  166 +--
 ...ss_flux_add_apardot_surfvpar_1x1v_ser_p1.c |   65 ++
 ...ss_flux_add_apardot_surfvpar_1x2v_ser_p1.c |   83 ++
 ...ss_flux_add_apardot_surfvpar_2x2v_ser_p1.c |  124 ++
 ...ss_flux_add_apardot_surfvpar_3x2v_ser_p1.c |  205 ++++
 ...nless_flux_add_em_edge_surfx_1x1v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfx_1x2v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfx_2x2v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfx_3x2v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfy_2x2v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfy_3x2v_ser_p1.c |   26 -
 ...nless_flux_add_em_edge_surfz_3x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c |   26 -
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfx_1x1v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfx_1x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfx_2x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfx_3x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfy_2x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfy_3x2v_ser_p1.c |   26 -
 ...add_em_multib_boundary_surfz_3x2v_ser_p1.c |   26 -
 ...flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c |   26 -
 ...flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c |   26 -
 ...flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c |   26 -
 ...flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c |   26 -
 ...flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c |   26 -
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |   26 -
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |   26 -
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |   26 -
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |   26 -
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |   26 -
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |   26 -
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |   26 -
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |   26 -
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |   26 -
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |   26 -
 ...s_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c |   26 -
 ...s_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c |   26 -
 ...less_flux_add_em_no_by_surfx_2x2v_ser_p1.c |   26 -
 ...less_flux_add_em_no_by_surfx_3x2v_ser_p1.c |   26 -
 ...less_flux_add_em_no_by_surfy_2x2v_ser_p1.c |   26 -
 ...less_flux_add_em_no_by_surfy_3x2v_ser_p1.c |   26 -
 ...less_flux_add_em_no_by_surfz_3x2v_ser_p1.c |   26 -
 ...ionless_flux_add_em_surfvpar_1x1v_ser_p1.c |   26 -
 ...ionless_flux_add_em_surfvpar_1x2v_ser_p1.c |   26 -
 ...ionless_flux_add_em_surfvpar_2x2v_ser_p1.c |   26 -
 ...ionless_flux_add_em_surfvpar_3x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfx_1x1v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfx_1x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfx_2x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfx_3x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfy_2x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfy_3x2v_ser_p1.c |   26 -
 ...lisionless_flux_add_em_surfz_3x2v_ser_p1.c |   26 -
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |    4 +-
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |    4 +-
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |   28 +-
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |   52 +-
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |   28 +-
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |   52 +-
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |   52 +-
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |    4 +-
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |    4 +-
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |   28 +-
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c |   52 +-
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |   28 +-
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c |   52 +-
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c |   52 +-
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |    4 +-
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |    4 +-
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |   28 +-
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c |   52 +-
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |   28 +-
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c |   52 +-
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c |   52 +-
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |    4 +-
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |    4 +-
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |    4 +-
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |    4 +-
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |    4 +-
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |    4 +-
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |    4 +-
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |    4 +-
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |    4 +-
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |    4 +-
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |    4 +-
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |    4 +-
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |    4 +-
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |    4 +-
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |    4 +-
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |   42 +-
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |   74 +-
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |    4 +-
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |    4 +-
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |    4 +-
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |    4 +-
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |    4 +-
 .../gk_collisionless_flux_surf_return_zero.c  |   11 +
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |   26 +-
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |   30 +-
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |   66 +-
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  170 ++-
 ..._collisionless_flux_surfvpar_return_zero.c |   11 +
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |    4 +-
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |    4 +-
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c |   28 +-
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |   52 +-
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c |   28 +-
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |   52 +-
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |   52 +-
 .../gkyl_gk_collisionless_flux_kernels.h      | 1023 ++---------------
 gyrokinetic/zero/dg_gyrokinetic.c             |   21 +-
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |    6 +-
 gyrokinetic/zero/gk_collisionless_flux.c      |   66 +-
 gyrokinetic/zero/gk_dg_geom.c                 |   10 +
 gyrokinetic/zero/gk_geometry.c                |    1 +
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |    5 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  400 +++----
 .../zero/gkyl_dg_updater_gyrokinetic.h        |   18 +-
 .../zero/gkyl_dg_updater_gyrokinetic_priv.h   |   11 +-
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h |   11 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  370 +-----
 gyrokinetic/zero/gkyl_gk_dg_geom.h            |    4 +
 153 files changed, 3000 insertions(+), 3571 deletions(-)
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index add7f4d31f..78aa5feee7 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -598,12 +598,12 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->accumulate_current = gk_field_accumulate_current_dens_none;
   f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_none;
   f->step_apar = gk_field_step_apar_none;
+  f->apar_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   if (f->is_em) {
     f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_old = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
-    f->apar_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
@@ -1099,12 +1099,13 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   gkyl_array_release(f->phi_fem);
   gkyl_array_release(f->phi_smooth);
 
+  // We need at least these two arrays even in ES case (kept 0).
+  gkyl_array_release(f->apar_smooth);
+  gkyl_array_release(f->apardot);
   if (f->is_em) {
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar_old);
     gkyl_array_release(f->apar_fem);
-    gkyl_array_release(f->apar_smooth);
-    gkyl_array_release(f->apardot);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index dff434c7bb..3254f0f5f9 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -73,8 +73,8 @@ gk_species_omegaH_dt(gkyl_gyrokinetic_app *app, struct gk_species *gks, const st
   }
 }
 
-static double
-gk_species_update_bflux_and_cfl(gkyl_gyrokinetic_app *app, struct gk_species *species,
+static void
+gk_species_update_bflux_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
   // Compute and store (in the ghost cell of rhs) the boundary fluxes.
@@ -82,7 +82,12 @@ gk_species_update_bflux_and_cfl(gkyl_gyrokinetic_app *app, struct gk_species *sp
 
   // Compute diagnostic moments of the boundary fluxes.
   gk_species_bflux_calc_moms(app, &species->bflux, rhs, bflux_moms);
-  
+}
+
+static double
+gk_species_get_cfl_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
   // Reduce the CFL frequency anc compute stable dt needed by this species.
   app->stat.n_species_omega_cfl +=1;
   struct timespec tm = gkyl_wall_clock();
@@ -106,6 +111,14 @@ gk_species_update_bflux_and_cfl(gkyl_gyrokinetic_app *app, struct gk_species *sp
 }
 
 static double
+gk_species_get_cfl_static(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  double omega_cfl = 1/DBL_MAX;
+  return app->cfl/omega_cfl;
+}
+
+static void
 gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
@@ -115,7 +128,7 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   gkyl_array_clear(species->cflrate, 0.0);
   gkyl_array_clear(rhs, 0.0);
 
-  // Collisionless terms.
+  // Collisionless terms (without Apardot).
   gk_species_collisionless_rhs(app, species, &species->collisionless, fin, rhs);
 
   // LBO Collisions.
@@ -140,49 +153,17 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 
   // Heating source.
   gk_species_heating_rhs(app, species, &species->heat_src, fin, rhs);
-
-  // Compute and store (in the ghost cell of rhs) the boundary fluxes.
-  gk_species_bflux_rhs(app, &species->bflux, fin, rhs);
-
-  // Compute diagnostic moments of the boundary fluxes.
-  gk_species_bflux_calc_moms(app, &species->bflux, rhs, bflux_moms);
-  
-  // Reduce the CFL frequency anc compute stable dt needed by this species.
-  app->stat.n_species_omega_cfl +=1;
-  struct timespec tm = gkyl_wall_clock();
-  gkyl_array_reduce_range(species->omega_cfl, species->cflrate, GKYL_MAX, &species->local);
-
-  double omega_cfl_ho[1];
-  if (app->use_gpu) {
-    gkyl_cu_memcpy(omega_cfl_ho, species->omega_cfl, sizeof(double), GKYL_CU_MEMCPY_D2H);
-  }
-  else {
-    omega_cfl_ho[0] = species->omega_cfl[0];
-  }
-  double dt_out = app->cfl/omega_cfl_ho[0];
-  
-  // Enforce the omega_H constraint on dt.
-  double dt_omegaH = gk_species_omegaH_dt(app, species, fin);
-  dt_out = fmin(dt_out, dt_omegaH);
-
-  app->stat.species_omega_cfl_tm += gkyl_time_diff_now_sec(tm);
-  return dt_out;
 }
 
-// TODO: Make this function do something.
-static double
-gk_species_em_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+static void
+gk_species_add_apardot_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
   struct timespec wst = gkyl_wall_clock();
 
-  gk_species_collisionless_add_em_rhs(app, species, &species->collisionless, fin, rhs);
+  gk_species_collisionless_add_apardot_rhs(app, species, &species->collisionless, fin, rhs);
 
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
-
-  // Update the bflux and its moments and compute cflrate as usual
-  double dt_out = gk_species_update_bflux_and_cfl(app, species, fin, rhs, bflux_moms);
-  return dt_out;
 }
 
 static double
@@ -215,12 +196,11 @@ gk_species_rhs_implicit_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *sp
   return app->cfl/omega_cfl;
 }
 
-static double
+static void
 gk_species_rhs_static(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  double omega_cfl = 1/DBL_MAX;
-  return app->cfl/omega_cfl;
+  // Do nothing.
 }
 
 static double
@@ -1104,7 +1084,9 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
 
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
-  gks->em_rhs_func = gk_species_em_rhs_dynamic;
+  gks->add_apardot_rhs_func = gks->is_em ? gk_species_add_apardot_dynamic : gk_species_rhs_static;
+  gks->bflux_update = gk_species_update_bflux_dynamic;
+  gks->get_cfl = gk_species_get_cfl_dynamic;
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
   gks->bc_func = gk_species_apply_bc_dynamic;
   gks->release_func = gk_species_release_dynamic;
@@ -1143,7 +1125,9 @@ gk_species_init_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
   
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
-  gks->em_rhs_func = gk_species_rhs_static;
+  gks->add_apardot_rhs_func = gk_species_rhs_static;
+  gks->bflux_update = gk_species_rhs_static;
+  gks->get_cfl = gk_species_get_cfl_static;  
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
   gks->bc_func = gk_species_apply_bc_static;
   gks->release_func = gk_species_release_static;
@@ -1601,11 +1585,9 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   }
 
   gks->is_em = app->field->is_em;
-  if (gks->is_em) {
-    // We do not have FLR effects for EM yet.
-    gks->gyro_apar = gkyl_array_acquire(app->field->apar_smooth);
-    gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
-  }
+  // We do not have FLR effects for EM yet.
+  gks->gyro_apar = gkyl_array_acquire(app->field->apar_smooth);
+  gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
 
   // Initialize the collisionless solver.
   gks->collisionless = (struct gk_collisionless) { };
@@ -1824,18 +1806,32 @@ gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *gks_self
   }
 }
 
-double
+void
 gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  return species->rhs_func(app, species, fin, rhs, bflux_moms);
+  species->rhs_func(app, species, fin, rhs, bflux_moms);
 }
 
-double
-gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void
+gk_species_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  species->add_apardot_rhs_func(app, species, fin, rhs, bflux_moms);
+}
+
+void 
+gk_species_update_bflux(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  species->bflux_update(app, species, fin, rhs, bflux_moms);
+}
+
+double 
+gk_species_get_cfl(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  return species->em_rhs_func(app, species, fin, rhs, bflux_moms);
+  return species->get_cfl(app, species, fin, rhs, bflux_moms);
 }
 
 double
@@ -1981,11 +1977,10 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
     gkyl_deflated_fem_poisson_release(s->flr_op);
   }
 
-  if (s->is_em) {
+  gkyl_array_release(s->gyro_apar);
+  gkyl_array_release(s->gyro_apardot);
+  if (s->is_em)
     gk_species_moment_release(app, &s->m1);
-    gkyl_array_release(s->gyro_apar);
-    gkyl_array_release(s->gyro_apardot);
-  }
 
   s->release_func(app, s);
 }
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 1386995f8b..649ee81075 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -20,17 +20,9 @@ gk_species_collisionless_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_speci
   // where they are not defined.
   gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, fin, gkcls->flux_surf, species->cflrate);
+    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
 }
 
-static void
-gk_species_collisionless_add_em_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  struct gk_collisionless *gkcls, const struct gkyl_array *fin)
-{
-  gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_op_add_em, 
-    &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
-}
 
 static void
 gk_species_collisionless_rhs_disabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
@@ -52,15 +44,18 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
-static void
-gk_species_collisionless_add_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+static void gk_species_collisionless_add_apardot_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
   struct timespec wst = gkyl_wall_clock();
 
-  gkcls->add_em_flux(app, species, gkcls, fin);
+  // Add Apardot surface flux contribution to RHS
+  gkyl_gk_collisionless_flux_surf(gkcls->add_apardot_surf_flux_op, 
+    &app->local, &species->local, &app->local_ext, &species->local_ext, 
+    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
 
-  gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_add_em, &species->local, 
+  // Advance the rhs adding only the Apardot volume contribution
+  gkyl_dg_updater_gyrokinetic_advance(gkcls->add_apardot_slvr, &species->local,
     fin, species->cflrate, rhs);
 
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
@@ -93,8 +88,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
-  gkcls->add_em_flux = gk_species_collisionless_flux_disabled;
-  gkcls->add_em_rhs = gk_species_collisionless_rhs_disabled;
+  gkcls->add_apardot_rhs_func = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -138,51 +132,39 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       bctype_conf[GKYL_MAX_CDIM+d] = gks->upper_bc[d].type;
     }
 
+    bool add_apardot = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->no_by, false, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
-    if (gkcls->is_em) {
-    }
-    
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
-      .phi = gks->gyro_phi, .apar = gkcls->apar, .apardot = gkcls->apardot };
-      // Create solver.
-      gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+      .phi = gks->gyro_phi, .apar = gks->gyro_apar, .apardot = gks->gyro_apardot };
+    // Create solver.
+    gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+      &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+      gks->info.skip_cell_threshold, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, gks->vel_map, 
+      &aux_inp, app->use_gpu);
+    
+    if (gkcls->is_em) {
+      add_apardot = true;
+      // Create a special flux operator that only adds the AparDot contribution.
+      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis,
+        gks->info.charge, gks->info.mass, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom,
+        app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
+      // Create solver that only adds AparDot terms.
+      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis,
         &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gks->info.skip_cell_threshold, gkcls->no_by, false, app->gk_geom, gks->vel_map, 
+        gks->info.skip_cell_threshold, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, gks->vel_map,
         &aux_inp, app->use_gpu);
-        
-        // Methods chosen at runtime.
-        gkcls->flux_func = gk_species_collisionless_flux_enabled;
-        gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
-
-      // Electromagnetic additional setup
-      if (gkcls->is_em) {
-
-        gkcls->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-        gkcls->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);  
-
-        // Create solvers to add EM contributions.
-        gkcls->surf_flux_op_add_em = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-          gks->info.charge, gks->info.mass, gkcls->no_by, true, app->gk_geom, 
-          app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
-        gkcls->slvr_add_em = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
-          &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-          gks->info.skip_cell_threshold, gkcls->no_by, true, app->gk_geom, gks->vel_map, 
-          &aux_inp, app->use_gpu);
-        
-        // Runtime methods for EM contributions.  
-        gkcls->add_em_flux = gk_species_collisionless_add_em_flux_enabled;
-        gkcls->add_em_rhs = gk_species_collisionless_add_em_rhs_enabled;
-    } else {
-      gkcls->apar    = gkyl_array_acquire(app->field->phi_smooth); // Not used.
-      gkcls->apardot = gkyl_array_acquire(app->field->phi_smooth); // Not used.
     }
-
-    if (gkcls->write_diagnostics) {
+          
+    // Methods chosen at runtime.
+    gkcls->flux_func = gk_species_collisionless_flux_enabled;
+    gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
+    if (gkcls->is_em)
+      gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
+    if (gkcls->write_diagnostics) 
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
-    }
   }
 }
 
@@ -200,18 +182,11 @@ gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *speci
   gkcls->rhs_func(app, species, gkcls, fin, rhs);
 }
 
-void
-gk_species_collisionless_add_em_flux(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  struct gk_collisionless *gkcls, const struct gkyl_array *fin)
-{
-  gkcls->add_em_flux(app, species, gkcls, fin);
-}
-
-void
-gk_species_collisionless_add_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void 
+gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
-  gkcls->add_em_rhs(app, species, gkcls, fin, rhs);
+  gkcls->add_apardot_rhs_func(app, species, gkcls, fin, rhs);
 }
 
 void
@@ -227,15 +202,13 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
   if (gkcls->collisionless_id) {
 
     gkyl_array_release(gkcls->flux_surf);
-    gkyl_array_release(gkcls->apar);
-    gkyl_array_release(gkcls->apardot);
   
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
     if (gkcls->is_em) {
-      gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op_add_em);
-      gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_add_em);
+      gkyl_gk_collisionless_flux_release(gkcls->add_apardot_surf_flux_op);
+      gkyl_dg_updater_gyrokinetic_release(gkcls->add_apardot_slvr);
     }
   }
 }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index cb00b3420a..738017ae3d 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -244,23 +244,18 @@ struct gk_collisionless {
 
   // Organization of the different equation objects and the required data and solvers
   struct gkyl_array *flux_surf; // Array for surface phase space flux
-  struct gkyl_array *apar; // A_parallel.
-  struct gkyl_array *apardot; // d/dt A_parallel.
 
   struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
+  struct gkyl_gk_collisionless_flux *add_apardot_surf_flux_op; // Updater to add Apardot terms to fluxes.
   gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.
-
-  struct gkyl_gk_collisionless_flux *surf_flux_op_add_em; // To add EM collisionless fluxes.
-  gkyl_dg_updater_gyrokinetic *slvr_add_em; // To add EM collisionless rhs.
+  gkyl_dg_updater_gyrokinetic *add_apardot_slvr; // Solver to add Apardot terms to RHS.
 
   // Methods chosen at runtime.
   void (*flux_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin);
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
-  void (*add_em_flux)(gkyl_gyrokinetic_app *app, struct gk_species *species,
-    struct gk_collisionless *gkcls, const struct gkyl_array *fin);
-  void (*add_em_rhs)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*add_apardot_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
   void (*write_diags_func)(gkyl_gyrokinetic_app* app, struct gk_species *gks,
     struct gk_collisionless *gkcls, double tm, int frame);
@@ -828,11 +823,15 @@ struct gk_species {
   bool is_first_ps_integ_write_call; // Flag first time writing ps_integ_diag.
 
   // Pointer to various functions selected at runtime.
-  double (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+    const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
+  void (*add_apardot_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
-  double (*em_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*bflux_update)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
-    double (*rhs_implicit_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  double (*get_cfl)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+    const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
+  double (*rhs_implicit_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, double dt);
   void (*bc_func)(gkyl_gyrokinetic_app *app, const struct gk_species *species,
     struct gkyl_array *f);
@@ -1441,15 +1440,15 @@ void gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
- * @brief Add electromagnetic contribution to the collisionless RHS.
+ * @brief Add Apardot electromagnetic contribution to the collisionless RHS.
  * 
  * @param app Gyrokinetic app object.
- * @param gks Pointer to species.
+ * @param species Pointer to species.
  * @param gkcls Species collisionless object.
  * @param fin Input distribution function.
  * @param rhs On output, the RHS from collisionless terms including EM contribution.
  */
-void gk_species_collisionless_add_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+void gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
@@ -2494,13 +2493,12 @@ void gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *spe
  * @param fin Input distribution function.
  * @param rhs On output, the RHS from the species object.
  * @param bflux_moms Output boundary flux moments (for diagnostics, stepped in time).
- * @return Maximum stable time-step.
  */
-double gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
- * Add the electromagnetic part of the RHS from species distribution function
+ * Add the Apardot electromagnetic part of the RHS from species distribution function
  *
  * @param app gyrokinetic app object.
  * @param species Pointer to species.
@@ -2509,9 +2507,33 @@ double gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
  * @param bflux_moms Output boundary flux moments (for diagnostics, stepped in time).
  * @return Maximum stable time-step.
  */
-double gk_species_em_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
+
+/**
+ * Update the boundary flux moments from species distribution function
+ *
+ * @param app gyrokinetic app object.
+ * @param species Pointer to species.
+ * @param fin Input distribution function.
+ * @param rhs On output, the RHS from the species object.
+ * @param bflux_moms Output boundary flux moments (for diagnostics, stepped in time).
+ */
+void gk_species_update_bflux(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
+/**
+ * Reduce and return the CFL condition from species distribution function
+ *
+ * @param app gyrokinetic app object.
+ * @param species Pointer to species.
+ * @param fin Input distribution function.
+ * @param rhs On output, the RHS from the species object.
+ * @param bflux_moms Output boundary flux moments (for diagnostics, stepped in time).
+ * @return Maximum stable time-step.
+ */
+double gk_species_get_cfl(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
  * Compute the *implicit* RHS from species distribution function
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index cef84c37fb..2b496b24c4 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1738,11 +1738,10 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     }
   }
 
-  // Compute collisionless terms of charged species.
+  // Compute collisionless terms of charged species. (Electrostatic + Apar)
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-    double dt1 = gk_species_rhs(app, s, fin[i], fout[i], bflux_out[i]);
-    dtmin = fmin(dtmin, dt1);
+    gk_species_rhs(app, s, fin[i], fout[i], bflux_out[i]);
   }
 
   // Compute collisionless terms of neutrals.
@@ -1772,10 +1771,12 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   gk_field_em_rhs(app, app->field, fout);
 
   // Add electromagnetic contributions to the collisionless update of charged species.
-  // This is done after all ES terms since we need to compute M1 of fdot.
+  // This is done after all ES+Apar terms since we need to compute M1 of fdot.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-    double dt1 = gk_species_em_rhs(app, s, fin[i], fout[i], bflux_out[i]);
+    gk_species_add_apardot_rhs(app, s, fin[i], fout[i], bflux_out[i]);
+    gk_species_update_bflux(app, s, fin[i], fout[i], bflux_out[i]);
+    double dt1 = gk_species_get_cfl(app, s, fin[i], fout[i], bflux_out[i]);
     dtmin = fmin(dtmin, dt1);
   }
 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
new file mode 100644
index 0000000000..16e90e0188
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
@@ -0,0 +1,50 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // b_i: covariant components of the field aligned unit vector.
+  // apar: parallel component of magnetic vector potential.
+  // phi: electrostatic potential .
+  // fin: Distribution function.
+  // out: output increment.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double rdvpar2Sq = rdvpar2*rdvpar2;
+  double dvparSq = dxv[1]*dxv[1];
+
+  const double *b_x = &b_i[0];
+  const double *b_y = &b_i[2];
+  const double *b_z = &b_i[4];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
+  hamil[1] = 1.4142135623730951*phi[1]*q_; 
+  hamil[2] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double vmap2 = vmap[1]*vmap[1]; 
+
+  double hamil2[2] = {0.}; 
+  hamil2[0] = hamil[2]*hamil[2]; 
+  hamil2[1] = hamil[4]*hamil[4]; 
+
+  double alphax[6] = {0.}; 
+
+
+
+  double alphavpar[6] = {0.}; 
+
+
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
new file mode 100644
index 0000000000..459582a12d
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
@@ -0,0 +1,53 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // b_i: covariant components of the field aligned unit vector.
+  // apar: parallel component of magnetic vector potential.
+  // phi: electrostatic potential .
+  // fin: Distribution function.
+  // out: output increment.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+  double rdmu2 = 2.0/dxv[2];
+
+  double rdvpar2Sq = rdvpar2*rdvpar2;
+  double dvparSq = dxv[1]*dxv[1];
+
+  const double *b_x = &b_i[0];
+  const double *b_y = &b_i[2];
+  const double *b_z = &b_i[4];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double vmap2 = vmap[1]*vmap[1]; 
+
+  double hamil2[2] = {0.}; 
+  hamil2[0] = hamil[2]*hamil[2]; 
+  hamil2[1] = hamil[8]*hamil[8]; 
+
+  double alphax[12] = {0.}; 
+
+
+
+  double alphavpar[12] = {0.}; 
+
+
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
new file mode 100644
index 0000000000..7b32a1eb31
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -0,0 +1,126 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // b_i: covariant components of the field aligned unit vector.
+  // apar: parallel component of magnetic vector potential.
+  // phi: electrostatic potential .
+  // fin: Distribution function.
+  // out: output increment.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+  double rdmu2 = 2.0/dxv[3];
+
+  double rdvpar2Sq = rdvpar2*rdvpar2;
+  double dvparSq = dxv[2]*dxv[2];
+
+  const double *b_x = &b_i[0];
+  const double *b_y = &b_i[4];
+  const double *b_z = &b_i[8];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
+  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double vmap2 = vmap[1]*vmap[1]; 
+
+  double hamil2[2] = {0.}; 
+  hamil2[0] = hamil[3]*hamil[3]; 
+  hamil2[1] = hamil[16]*hamil[16]; 
+
+  double alphax[24] = {0.}; 
+  alphax[0] = ((-(0.6123724356957944*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]-0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[1] = ((-(1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*apar[2]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]-0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[2] = ((-(0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[3] = ((-(1.369306393762915*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[5] = ((-(0.5511351921262146*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.5511351921262146*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[2]*hamil[3]*jacobtot_inv[3]-1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[6] = ((-(2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.232375754386623*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]-1.369306393762915*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]-1.232375754386623*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[7] = ((-(0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16])-0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[11] = ((-(1.232375754386623*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.232375754386623*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[16]-2.4647515087732463*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[5] += 0.4330127018922193*(alphax[6]*fin[11]+fin[6]*alphax[11]+alphax[3]*fin[7]+fin[3]*alphax[7]+alphax[1]*fin[5]+fin[1]*alphax[5]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[6] += 0.38729833462074165*alphax[11]*fin[20]+0.3872983346207417*(alphax[7]*fin[18]+alphax[6]*fin[17])+0.38729833462074165*alphax[3]*fin[16]+0.4330127018922193*(alphax[5]*fin[11]+fin[5]*alphax[11]+alphax[2]*fin[7]+fin[2]*alphax[7]+alphax[1]*fin[6]+fin[1]*alphax[6]+alphax[0]*fin[3]+fin[0]*alphax[3]); 
+  out[8] += 0.4330127018922193*(alphax[11]*fin[15]+alphax[7]*fin[14]+alphax[6]*fin[13]+alphax[5]*fin[12]+alphax[3]*fin[10]+alphax[2]*fin[9]+alphax[1]*fin[8]+alphax[0]*fin[4]); 
+  out[11] += 0.38729833462074165*alphax[6]*fin[20]+0.3872983346207417*(alphax[3]*fin[18]+alphax[11]*fin[17])+0.38729833462074165*alphax[7]*fin[16]+0.4330127018922193*(alphax[1]*fin[11]+fin[1]*alphax[11]+alphax[0]*fin[7]+fin[0]*alphax[7]+alphax[5]*fin[6]+fin[5]*alphax[6]+alphax[2]*fin[3]+fin[2]*alphax[3]); 
+  out[12] += 0.4330127018922193*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[1]*fin[12]+alphax[7]*fin[10]+alphax[0]*fin[9]+alphax[5]*fin[8]+alphax[2]*fin[4]); 
+  out[13] += 0.3872983346207417*alphax[11]*fin[23]+0.38729833462074165*(alphax[7]*fin[22]+alphax[6]*fin[21])+0.3872983346207417*alphax[3]*fin[19]+0.4330127018922193*(alphax[5]*fin[15]+alphax[2]*fin[14]+alphax[1]*fin[13]+alphax[11]*fin[12]+alphax[0]*fin[10]+alphax[7]*fin[9]+alphax[6]*fin[8]+alphax[3]*fin[4]); 
+  out[15] += 0.3872983346207417*alphax[6]*fin[23]+0.38729833462074165*(alphax[3]*fin[22]+alphax[11]*fin[21])+0.3872983346207417*alphax[7]*fin[19]+0.4330127018922193*(alphax[1]*fin[15]+alphax[0]*fin[14]+alphax[5]*fin[13]+alphax[6]*fin[12]+fin[8]*alphax[11]+alphax[2]*fin[10]+alphax[3]*fin[9]+fin[4]*alphax[7]); 
+  out[17] += 0.43301270189221935*alphax[5]*fin[20]+0.4330127018922193*(alphax[2]*fin[18]+alphax[1]*fin[17])+0.43301270189221935*alphax[0]*fin[16]+0.3872983346207417*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[3]*fin[3]); 
+  out[20] += 0.4330127018922193*alphax[1]*fin[20]+0.43301270189221935*(alphax[0]*fin[18]+alphax[5]*fin[17])+0.4330127018922193*alphax[2]*fin[16]+0.38729833462074165*(alphax[6]*fin[11]+fin[6]*alphax[11]+alphax[3]*fin[7]+fin[3]*alphax[7]); 
+  out[21] += 0.43301270189221935*alphax[5]*fin[23]+0.4330127018922193*(alphax[2]*fin[22]+alphax[1]*fin[21])+0.43301270189221935*alphax[0]*fin[19]+0.38729833462074165*(alphax[11]*fin[15]+alphax[7]*fin[14]+alphax[6]*fin[13]+alphax[3]*fin[10]); 
+  out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
+
+  double alphaz[24] = {0.}; 
+  alphaz[0] = ((0.6123724356957944*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[1] = ((0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[2] = ((1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[3] = ((1.369306393762915*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[5] = ((0.5511351921262146*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[6] = ((0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[7] = ((2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+1.232375754386623*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+1.232375754386623*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[11] = ((1.232375754386623*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.232375754386623*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+2.4647515087732463*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]+0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
+  out[5] += 0.4330127018922193*(alphaz[7]*fin[11]+fin[7]*alphaz[11]+alphaz[3]*fin[6]+fin[3]*alphaz[6]+alphaz[2]*fin[5]+fin[2]*alphaz[5]+alphaz[0]*fin[1]+fin[0]*alphaz[1]); 
+  out[7] += 0.38729833462074165*alphaz[11]*fin[20]+0.3872983346207417*(alphaz[7]*fin[18]+alphaz[6]*fin[17])+0.38729833462074165*alphaz[3]*fin[16]+0.4330127018922193*(alphaz[5]*fin[11]+fin[5]*alphaz[11]+alphaz[2]*fin[7]+fin[2]*alphaz[7]+alphaz[1]*fin[6]+fin[1]*alphaz[6]+alphaz[0]*fin[3]+fin[0]*alphaz[3]); 
+  out[9] += 0.4330127018922193*(alphaz[11]*fin[15]+alphaz[7]*fin[14]+alphaz[6]*fin[13]+alphaz[5]*fin[12]+alphaz[3]*fin[10]+alphaz[2]*fin[9]+alphaz[1]*fin[8]+alphaz[0]*fin[4]); 
+  out[11] += 0.38729833462074165*alphaz[7]*fin[20]+0.3872983346207417*(alphaz[11]*fin[18]+alphaz[3]*fin[17])+0.38729833462074165*alphaz[6]*fin[16]+0.4330127018922193*(alphaz[2]*fin[11]+fin[2]*alphaz[11]+alphaz[5]*fin[7]+fin[5]*alphaz[7]+alphaz[0]*fin[6]+fin[0]*alphaz[6]+alphaz[1]*fin[3]+fin[1]*alphaz[3]); 
+  out[12] += 0.4330127018922193*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[2]*fin[12]+alphaz[6]*fin[10]+alphaz[5]*fin[9]+alphaz[0]*fin[8]+alphaz[1]*fin[4]); 
+  out[14] += 0.3872983346207417*alphaz[11]*fin[23]+0.38729833462074165*(alphaz[7]*fin[22]+alphaz[6]*fin[21])+0.3872983346207417*alphaz[3]*fin[19]+0.4330127018922193*(alphaz[5]*fin[15]+alphaz[2]*fin[14]+alphaz[1]*fin[13]+alphaz[11]*fin[12]+alphaz[0]*fin[10]+alphaz[7]*fin[9]+alphaz[6]*fin[8]+alphaz[3]*fin[4]); 
+  out[15] += 0.3872983346207417*alphaz[7]*fin[23]+0.38729833462074165*(alphaz[11]*fin[22]+alphaz[3]*fin[21])+0.3872983346207417*alphaz[6]*fin[19]+0.4330127018922193*(alphaz[2]*fin[15]+alphaz[5]*fin[14]+alphaz[0]*fin[13]+alphaz[7]*fin[12]+fin[9]*alphaz[11]+alphaz[1]*fin[10]+alphaz[3]*fin[8]+fin[4]*alphaz[6]); 
+  out[18] += 0.43301270189221935*alphaz[5]*fin[20]+0.4330127018922193*(alphaz[2]*fin[18]+alphaz[1]*fin[17])+0.43301270189221935*alphaz[0]*fin[16]+0.3872983346207417*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[3]*fin[3]); 
+  out[20] += 0.4330127018922193*alphaz[2]*fin[20]+0.43301270189221935*(alphaz[5]*fin[18]+alphaz[0]*fin[17])+0.4330127018922193*alphaz[1]*fin[16]+0.38729833462074165*(alphaz[7]*fin[11]+fin[7]*alphaz[11]+alphaz[3]*fin[6]+fin[3]*alphaz[6]); 
+  out[22] += 0.43301270189221935*alphaz[5]*fin[23]+0.4330127018922193*(alphaz[2]*fin[22]+alphaz[1]*fin[21])+0.43301270189221935*alphaz[0]*fin[19]+0.38729833462074165*(alphaz[11]*fin[15]+alphaz[7]*fin[14]+alphaz[6]*fin[13]+alphaz[3]*fin[10]); 
+  out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
+
+  double alphavpar[24] = {0.}; 
+  alphavpar[0] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[5])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[5]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[5]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[5]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[5]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3]-0.6123724356957944*b_y[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*b_y[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*jacobtot_inv[2]*apar[3]*b_y[3]-0.6123724356957944*jacobtot_inv[1]*hamil[2]*apar[3]*b_y[3]-0.3061862178478971*apar[0]*hamil[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[0]*apar[2]*hamil[2]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]-0.3061862178478971*b_y[0]*hamil[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*hamil[2]*apar[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[2]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[2]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[2]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[2]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[2]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[5])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[5]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[5]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[5]+1.1022703842524295*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*hamil[2]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*hamil[2]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*hamil[2]*apar[3]*b_y[3]-0.6123724356957944*apar[1]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.6123724356957944*hamil[1]*apar[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[1]*apar[2]*hamil[2]*b_y[3]+0.5511351921262146*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]-0.6123724356957944*b_y[1]*hamil[2]*jacobtot_inv[2]*apar[3]+0.6123724356957944*hamil[1]*b_y[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*hamil[2]*apar[3]+0.5511351921262146*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[2]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[2]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[2]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[2] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[5]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[5]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[5]-1.1022703842524295*hamil[2]*apar[3]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3]-0.5511351921262146*apar[2]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.6123724356957944*apar[1]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[2]*b_y[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3]-0.5511351921262146*b_y[2]*hamil[2]*jacobtot_inv[2]*apar[3]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[2]*apar[3]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*b_y[2]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[2]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[2]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[4] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[12])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[12]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[12]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[12]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[12]-0.6123724356957944*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[9]+0.6123724356957944*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[5] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[5]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[5]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[5]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[5]-0.5511351921262146*apar[2]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.5511351921262146*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]-0.5511351921262146*b_y[2]*hamil[2]*apar[3]*jacobtot_inv[3]+0.5511351921262146*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[3]-1.1022703842524295*hamil[2]*jacobtot_inv[2]*apar[3]*b_y[3]+1.1022703842524295*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.6123724356957944*jacobtot_inv[0]*apar[1]*hamil[2]*b_y[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*hamil[2]*apar[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*b_y[2]*apar[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[2]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[2]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[8] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[12]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[12]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[12]-0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[9]+1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[8]+0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[8]+0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[9] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[12]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[12]-1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[9]-0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[9]+0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[12] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[12]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[12]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[9]-1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[9]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[9]+0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[8]+1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[6] += 0.4330127018922193*(alphavpar[9]*fin[12]+fin[9]*alphavpar[12]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[7] += 0.4330127018922193*(alphavpar[8]*fin[12]+fin[8]*alphavpar[12]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[10] += 0.4330127018922193*(alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]); 
+  out[11] += 0.4330127018922193*(alphavpar[4]*fin[12]+fin[4]*alphavpar[12]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[13] += 0.4330127018922193*(alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[5]*fin[9]+fin[5]*alphavpar[9]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]); 
+  out[14] += 0.4330127018922193*(alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[0]*fin[9]+fin[0]*alphavpar[9]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]); 
+  out[15] += 0.4330127018922193*(alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[1]*fin[9]+fin[1]*alphavpar[9]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]); 
+  out[16] += 0.9682458365518543*(alphavpar[12]*fin[15]+alphavpar[9]*fin[14]+alphavpar[8]*fin[13]+alphavpar[5]*fin[11]+alphavpar[4]*fin[10]+alphavpar[2]*fin[7]+alphavpar[1]*fin[6]+alphavpar[0]*fin[3]); 
+  out[17] += 0.9682458365518543*(alphavpar[9]*fin[15]+alphavpar[12]*fin[14]+alphavpar[4]*fin[13]+alphavpar[2]*fin[11]+alphavpar[8]*fin[10]+alphavpar[5]*fin[7]+alphavpar[0]*fin[6]+alphavpar[1]*fin[3]); 
+  out[18] += 0.9682458365518543*(alphavpar[8]*fin[15]+alphavpar[4]*fin[14]+alphavpar[12]*fin[13]+alphavpar[1]*fin[11]+alphavpar[9]*fin[10]+alphavpar[0]*fin[7]+alphavpar[5]*fin[6]+alphavpar[2]*fin[3]); 
+  out[19] += 0.9682458365518543*(alphavpar[5]*fin[15]+alphavpar[2]*fin[14]+alphavpar[1]*fin[13]+fin[11]*alphavpar[12]+alphavpar[0]*fin[10]+fin[7]*alphavpar[9]+fin[6]*alphavpar[8]+fin[3]*alphavpar[4]); 
+  out[20] += 0.9682458365518543*(alphavpar[4]*fin[15]+alphavpar[8]*fin[14]+alphavpar[9]*fin[13]+fin[10]*alphavpar[12]+alphavpar[0]*fin[11]+alphavpar[1]*fin[7]+alphavpar[2]*fin[6]+fin[3]*alphavpar[5]); 
+  out[21] += 0.9682458365518543*(alphavpar[2]*fin[15]+alphavpar[5]*fin[14]+alphavpar[0]*fin[13]+fin[7]*alphavpar[12]+alphavpar[9]*fin[11]+alphavpar[1]*fin[10]+fin[3]*alphavpar[8]+alphavpar[4]*fin[6]); 
+  out[22] += 0.9682458365518543*(alphavpar[1]*fin[15]+alphavpar[0]*fin[14]+alphavpar[5]*fin[13]+fin[6]*alphavpar[12]+alphavpar[8]*fin[11]+alphavpar[2]*fin[10]+fin[3]*alphavpar[9]+alphavpar[4]*fin[7]); 
+  out[23] += 0.9682458365518543*(alphavpar[0]*fin[15]+alphavpar[1]*fin[14]+alphavpar[2]*fin[13]+fin[3]*alphavpar[12]+alphavpar[4]*fin[11]+alphavpar[5]*fin[10]+fin[6]*alphavpar[9]+fin[7]*alphavpar[8]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
new file mode 100644
index 0000000000..705fe962bd
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -0,0 +1,239 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // bmag: magnetic field amplitude.
+  // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // b_i: covariant components of the field aligned unit vector.
+  // apar: parallel component of magnetic vector potential.
+  // phi: electrostatic potential .
+  // fin: Distribution function.
+  // out: output increment.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+  double rdmu2 = 2.0/dxv[4];
+
+  double rdvpar2Sq = rdvpar2*rdvpar2;
+  double dvparSq = dxv[3]*dxv[3];
+
+  const double *b_x = &b_i[0];
+  const double *b_y = &b_i[8];
+  const double *b_z = &b_i[16];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_; 
+  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[4] = 2.0*vmapSq[1]*m_; 
+  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[6] = 2.0*phi[4]*q_; 
+  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
+  hamil[8] = 2.0*phi[6]*q_; 
+  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 2.0*phi[7]*q_; 
+  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
+  hamil[32] = 2.0*vmapSq[2]*m_; 
+
+  double vmap2 = vmap[1]*vmap[1]; 
+
+  double hamil2[2] = {0.}; 
+  hamil2[0] = hamil[4]*hamil[4]; 
+  hamil2[1] = hamil[32]*hamil[32]; 
+
+  double alphax[48] = {0.}; 
+  alphax[0] = (((-(0.21650635094610965*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]-0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]+0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*apar[3]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_z[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]+0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[2] = ((-(0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]-0.21650635094610965*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[3] = (((-(0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.4841229182759271*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[6] = ((-(0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7])-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[7] = (((-(0.19485571585149863*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.19485571585149863*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[3]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]+0.19485571585149863*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[2]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[8] = ((-(0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[9] = (((-(0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.43571062644833425*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]+0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[10] = ((-(0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]-0.4841229182759271*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[11] = (((-(0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]+0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[16] = ((-(0.19485571585149863*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[17] = ((-(0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[18] = (((-(0.43571062644833425*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.7842791276070014*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]+0.43571062644833425*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[19] = ((-(0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[26] = ((-(0.43571062644833425*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[6] += 0.3061862178478971*(alphax[18]*fin[26]+fin[18]*alphax[26]+alphax[11]*fin[19]+fin[11]*alphax[19]+alphax[9]*fin[17]+fin[9]*alphax[17]+alphax[7]*fin[16]+fin[7]*alphax[16]+alphax[4]*fin[10]+fin[4]*alphax[10]+alphax[3]*fin[8]+fin[3]*alphax[8]+alphax[1]*fin[6]+fin[1]*alphax[6]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[7] += 0.3061862178478971*(alphax[17]*fin[26]+fin[17]*alphax[26]+alphax[10]*fin[19]+fin[10]*alphax[19]+alphax[9]*fin[18]+fin[9]*alphax[18]+alphax[6]*fin[16]+fin[6]*alphax[16]+alphax[4]*fin[11]+fin[4]*alphax[11]+alphax[2]*fin[8]+fin[2]*alphax[8]+alphax[1]*fin[7]+fin[1]*alphax[7]+alphax[0]*fin[3]+fin[0]*alphax[3]); 
+  out[9] += 0.27386127875258304*alphax[26]*fin[43]+0.273861278752583*(alphax[19]*fin[39]+alphax[18]*fin[38]+alphax[17]*fin[37])+0.27386127875258304*(alphax[11]*fin[35]+alphax[10]*fin[34]+alphax[9]*fin[33])+0.273861278752583*alphax[4]*fin[32]+0.3061862178478971*(alphax[16]*fin[26]+fin[16]*alphax[26]+alphax[8]*fin[19]+fin[8]*alphax[19]+alphax[7]*fin[18]+fin[7]*alphax[18]+alphax[6]*fin[17]+fin[6]*alphax[17]+alphax[3]*fin[11]+fin[3]*alphax[11]+alphax[2]*fin[10]+fin[2]*alphax[10]+alphax[1]*fin[9]+fin[1]*alphax[9]+alphax[0]*fin[4]+fin[0]*alphax[4]); 
+  out[12] += 0.3061862178478971*(alphax[26]*fin[31]+alphax[19]*fin[30]+alphax[18]*fin[29]+alphax[17]*fin[28]+alphax[16]*fin[27]+alphax[11]*fin[25]+alphax[10]*fin[24]+alphax[9]*fin[23]+alphax[8]*fin[22]+alphax[7]*fin[21]+alphax[6]*fin[20]+alphax[4]*fin[15]+alphax[3]*fin[14]+alphax[2]*fin[13]+alphax[1]*fin[12]+alphax[0]*fin[5]); 
+  out[16] += 0.3061862178478971*(alphax[9]*fin[26]+fin[9]*alphax[26]+alphax[4]*fin[19]+fin[4]*alphax[19]+alphax[17]*fin[18]+fin[17]*alphax[18]+alphax[1]*fin[16]+fin[1]*alphax[16]+alphax[10]*fin[11]+fin[10]*alphax[11]+alphax[0]*fin[8]+fin[0]*alphax[8]+alphax[6]*fin[7]+fin[6]*alphax[7]+alphax[2]*fin[3]+fin[2]*alphax[3]); 
+  out[17] += 0.27386127875258304*alphax[18]*fin[43]+0.273861278752583*(alphax[11]*fin[39]+alphax[26]*fin[38]+alphax[9]*fin[37])+0.27386127875258304*(alphax[19]*fin[35]+alphax[4]*fin[34]+alphax[17]*fin[33])+0.273861278752583*alphax[10]*fin[32]+0.3061862178478971*(alphax[7]*fin[26]+fin[7]*alphax[26]+alphax[3]*fin[19]+fin[3]*alphax[19]+alphax[16]*fin[18]+fin[16]*alphax[18]+alphax[1]*fin[17]+fin[1]*alphax[17]+alphax[8]*fin[11]+fin[8]*alphax[11]+alphax[0]*fin[10]+fin[0]*alphax[10]+alphax[6]*fin[9]+fin[6]*alphax[9]+alphax[2]*fin[4]+fin[2]*alphax[4]); 
+  out[18] += 0.27386127875258304*alphax[17]*fin[43]+0.273861278752583*(alphax[10]*fin[39]+alphax[9]*fin[38]+alphax[26]*fin[37])+0.27386127875258304*(alphax[4]*fin[35]+alphax[19]*fin[34]+alphax[18]*fin[33])+0.273861278752583*alphax[11]*fin[32]+0.3061862178478971*(alphax[6]*fin[26]+fin[6]*alphax[26]+alphax[2]*fin[19]+fin[2]*alphax[19]+alphax[1]*fin[18]+fin[1]*alphax[18]+alphax[16]*fin[17]+fin[16]*alphax[17]+alphax[0]*fin[11]+fin[0]*alphax[11]+alphax[8]*fin[10]+fin[8]*alphax[10]+alphax[7]*fin[9]+fin[7]*alphax[9]+alphax[3]*fin[4]+fin[3]*alphax[4]); 
+  out[20] += 0.3061862178478971*(alphax[18]*fin[31]+alphax[11]*fin[30]+alphax[26]*fin[29]+alphax[9]*fin[28]+alphax[7]*fin[27]+alphax[19]*fin[25]+alphax[4]*fin[24]+alphax[17]*fin[23]+alphax[3]*fin[22]+alphax[16]*fin[21]+alphax[1]*fin[20]+alphax[10]*fin[15]+alphax[8]*fin[14]+alphax[0]*fin[13]+alphax[6]*fin[12]+alphax[2]*fin[5]); 
+  out[21] += 0.3061862178478971*(alphax[17]*fin[31]+alphax[10]*fin[30]+alphax[9]*fin[29]+alphax[26]*fin[28]+alphax[6]*fin[27]+alphax[4]*fin[25]+alphax[19]*fin[24]+alphax[18]*fin[23]+alphax[2]*fin[22]+alphax[1]*fin[21]+alphax[16]*fin[20]+alphax[11]*fin[15]+alphax[0]*fin[14]+alphax[8]*fin[13]+alphax[7]*fin[12]+alphax[3]*fin[5]); 
+  out[23] += 0.273861278752583*alphax[26]*fin[47]+0.27386127875258304*(alphax[19]*fin[46]+alphax[18]*fin[45]+alphax[17]*fin[44])+0.273861278752583*(alphax[11]*fin[42]+alphax[10]*fin[41]+alphax[9]*fin[40])+0.27386127875258304*alphax[4]*fin[36]+0.3061862178478971*(alphax[16]*fin[31]+alphax[8]*fin[30]+alphax[7]*fin[29]+alphax[6]*fin[28]+alphax[26]*fin[27]+alphax[3]*fin[25]+alphax[2]*fin[24]+alphax[1]*fin[23]+alphax[19]*fin[22]+alphax[18]*fin[21]+alphax[17]*fin[20]+alphax[0]*fin[15]+alphax[11]*fin[14]+alphax[10]*fin[13]+alphax[9]*fin[12]+alphax[4]*fin[5]); 
+  out[26] += 0.27386127875258304*alphax[9]*fin[43]+0.273861278752583*(alphax[4]*fin[39]+alphax[17]*fin[38]+alphax[18]*fin[37])+0.27386127875258304*(alphax[10]*fin[35]+alphax[11]*fin[34]+alphax[26]*fin[33])+0.273861278752583*alphax[19]*fin[32]+0.3061862178478971*(alphax[1]*fin[26]+fin[1]*alphax[26]+alphax[0]*fin[19]+fin[0]*alphax[19]+alphax[6]*fin[18]+fin[6]*alphax[18]+alphax[7]*fin[17]+fin[7]*alphax[17]+alphax[9]*fin[16]+fin[9]*alphax[16]+alphax[2]*fin[11]+fin[2]*alphax[11]+alphax[3]*fin[10]+fin[3]*alphax[10]+alphax[4]*fin[8]+fin[4]*alphax[8]); 
+  out[27] += 0.3061862178478971*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+alphax[1]*fin[27]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+alphax[0]*fin[22]+alphax[6]*fin[21]+alphax[7]*fin[20]+fin[15]*alphax[19]+fin[12]*alphax[16]+alphax[2]*fin[14]+alphax[3]*fin[13]+fin[5]*alphax[8]); 
+  out[28] += 0.273861278752583*alphax[18]*fin[47]+0.27386127875258304*(alphax[11]*fin[46]+alphax[26]*fin[45]+alphax[9]*fin[44])+0.273861278752583*(alphax[19]*fin[42]+alphax[4]*fin[41]+alphax[17]*fin[40])+0.27386127875258304*alphax[10]*fin[36]+0.3061862178478971*(alphax[7]*fin[31]+alphax[3]*fin[30]+alphax[16]*fin[29]+alphax[1]*fin[28]+alphax[18]*fin[27]+fin[21]*alphax[26]+alphax[8]*fin[25]+alphax[0]*fin[24]+alphax[6]*fin[23]+alphax[11]*fin[22]+alphax[9]*fin[20]+fin[14]*alphax[19]+fin[12]*alphax[17]+alphax[2]*fin[15]+alphax[4]*fin[13]+fin[5]*alphax[10]); 
+  out[29] += 0.273861278752583*alphax[17]*fin[47]+0.27386127875258304*(alphax[10]*fin[46]+alphax[9]*fin[45]+alphax[26]*fin[44])+0.273861278752583*(alphax[4]*fin[42]+alphax[19]*fin[41]+alphax[18]*fin[40])+0.27386127875258304*alphax[11]*fin[36]+0.3061862178478971*(alphax[6]*fin[31]+alphax[2]*fin[30]+alphax[1]*fin[29]+alphax[16]*fin[28]+alphax[17]*fin[27]+fin[20]*alphax[26]+alphax[0]*fin[25]+alphax[8]*fin[24]+alphax[7]*fin[23]+alphax[10]*fin[22]+alphax[9]*fin[21]+fin[13]*alphax[19]+fin[12]*alphax[18]+alphax[3]*fin[15]+alphax[4]*fin[14]+fin[5]*alphax[11]); 
+  out[31] += 0.273861278752583*alphax[9]*fin[47]+0.27386127875258304*(alphax[4]*fin[46]+alphax[17]*fin[45]+alphax[18]*fin[44])+0.273861278752583*(alphax[10]*fin[42]+alphax[11]*fin[41]+alphax[26]*fin[40])+0.27386127875258304*alphax[19]*fin[36]+0.3061862178478971*(alphax[1]*fin[31]+alphax[0]*fin[30]+alphax[6]*fin[29]+alphax[7]*fin[28]+alphax[9]*fin[27]+fin[12]*alphax[26]+alphax[2]*fin[25]+alphax[3]*fin[24]+alphax[16]*fin[23]+alphax[4]*fin[22]+alphax[17]*fin[21]+alphax[18]*fin[20]+fin[5]*alphax[19]+alphax[8]*fin[15]+alphax[10]*fin[14]+alphax[11]*fin[13]); 
+  out[33] += 0.3061862178478971*(alphax[16]*fin[43]+alphax[8]*fin[39]+alphax[7]*fin[38]+alphax[6]*fin[37]+alphax[3]*fin[35]+alphax[2]*fin[34]+alphax[1]*fin[33]+alphax[0]*fin[32])+0.27386127875258304*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[4]*fin[4]); 
+  out[37] += 0.3061862178478971*(alphax[7]*fin[43]+alphax[3]*fin[39]+alphax[16]*fin[38]+alphax[1]*fin[37]+alphax[8]*fin[35]+alphax[0]*fin[34]+alphax[6]*fin[33]+alphax[2]*fin[32])+0.273861278752583*(alphax[18]*fin[26]+fin[18]*alphax[26]+alphax[11]*fin[19]+fin[11]*alphax[19]+alphax[9]*fin[17]+fin[9]*alphax[17]+alphax[4]*fin[10]+fin[4]*alphax[10]); 
+  out[38] += 0.3061862178478971*(alphax[6]*fin[43]+alphax[2]*fin[39]+alphax[1]*fin[38]+alphax[16]*fin[37]+alphax[0]*fin[35]+alphax[8]*fin[34]+alphax[7]*fin[33]+alphax[3]*fin[32])+0.273861278752583*(alphax[17]*fin[26]+fin[17]*alphax[26]+alphax[10]*fin[19]+fin[10]*alphax[19]+alphax[9]*fin[18]+fin[9]*alphax[18]+alphax[4]*fin[11]+fin[4]*alphax[11]); 
+  out[40] += 0.3061862178478971*(alphax[16]*fin[47]+alphax[8]*fin[46]+alphax[7]*fin[45]+alphax[6]*fin[44]+alphax[3]*fin[42]+alphax[2]*fin[41]+alphax[1]*fin[40]+alphax[0]*fin[36])+0.273861278752583*(alphax[26]*fin[31]+alphax[19]*fin[30]+alphax[18]*fin[29]+alphax[17]*fin[28]+alphax[11]*fin[25]+alphax[10]*fin[24]+alphax[9]*fin[23]+alphax[4]*fin[15]); 
+  out[43] += 0.3061862178478971*(alphax[1]*fin[43]+alphax[0]*fin[39]+alphax[6]*fin[38]+alphax[7]*fin[37]+alphax[2]*fin[35]+alphax[3]*fin[34]+alphax[16]*fin[33]+alphax[8]*fin[32])+0.27386127875258304*(alphax[9]*fin[26]+fin[9]*alphax[26]+alphax[4]*fin[19]+fin[4]*alphax[19]+alphax[17]*fin[18]+fin[17]*alphax[18]+alphax[10]*fin[11]+fin[10]*alphax[11]); 
+  out[44] += 0.3061862178478971*(alphax[7]*fin[47]+alphax[3]*fin[46]+alphax[16]*fin[45]+alphax[1]*fin[44]+alphax[8]*fin[42]+alphax[0]*fin[41]+alphax[6]*fin[40]+alphax[2]*fin[36])+0.27386127875258304*(alphax[18]*fin[31]+alphax[11]*fin[30]+alphax[26]*fin[29]+alphax[9]*fin[28]+alphax[19]*fin[25]+alphax[4]*fin[24]+alphax[17]*fin[23]+alphax[10]*fin[15]); 
+  out[45] += 0.3061862178478971*(alphax[6]*fin[47]+alphax[2]*fin[46]+alphax[1]*fin[45]+alphax[16]*fin[44]+alphax[0]*fin[42]+alphax[8]*fin[41]+alphax[7]*fin[40]+alphax[3]*fin[36])+0.27386127875258304*(alphax[17]*fin[31]+alphax[10]*fin[30]+alphax[9]*fin[29]+alphax[26]*fin[28]+alphax[4]*fin[25]+alphax[19]*fin[24]+alphax[18]*fin[23]+alphax[11]*fin[15]); 
+  out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
+
+  double alphay[48] = {0.}; 
+  alphay[0] = (((0.21650635094610965*apar[3]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*b_x[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[5]+0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[4]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*apar[1]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*b_z[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.38971143170299727*hamil[4]*apar[5]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*apar[3]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_x[5]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[0]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.10825317547305482*b_z[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_z[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]+0.21650635094610965*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.10825317547305482*apar[0]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*apar[5]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*apar[1]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_z[5]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.4841229182759271*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.38971143170299727*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.19485571585149863*apar[1]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[3]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[3]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.19485571585149863*b_z[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*apar[1]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[5]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]-0.21650635094610965*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.8714212528966685*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.43571062644833425*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]+0.4841229182759271*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.24206145913796356*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[32]-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.8714212528966685*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.43571062644833425*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]-0.4841229182759271*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]-0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+
+
+  out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
+  out[6] += 0.3061862178478971*(alphay[19]*fin[26]+fin[19]*alphay[26]+alphay[11]*fin[18]+fin[11]*alphay[18]+alphay[10]*fin[17]+fin[10]*alphay[17]+alphay[8]*fin[16]+fin[8]*alphay[16]+alphay[4]*fin[9]+fin[4]*alphay[9]+alphay[3]*fin[7]+fin[3]*alphay[7]+alphay[2]*fin[6]+fin[2]*alphay[6]+alphay[0]*fin[1]+fin[0]*alphay[1]); 
+  out[8] += 0.3061862178478971*(alphay[17]*fin[26]+fin[17]*alphay[26]+alphay[10]*fin[19]+fin[10]*alphay[19]+alphay[9]*fin[18]+fin[9]*alphay[18]+alphay[6]*fin[16]+fin[6]*alphay[16]+alphay[4]*fin[11]+fin[4]*alphay[11]+alphay[2]*fin[8]+fin[2]*alphay[8]+alphay[1]*fin[7]+fin[1]*alphay[7]+alphay[0]*fin[3]+fin[0]*alphay[3]); 
+  out[10] += 0.27386127875258304*alphay[26]*fin[43]+0.273861278752583*(alphay[19]*fin[39]+alphay[18]*fin[38]+alphay[17]*fin[37])+0.27386127875258304*(alphay[11]*fin[35]+alphay[10]*fin[34]+alphay[9]*fin[33])+0.273861278752583*alphay[4]*fin[32]+0.3061862178478971*(alphay[16]*fin[26]+fin[16]*alphay[26]+alphay[8]*fin[19]+fin[8]*alphay[19]+alphay[7]*fin[18]+fin[7]*alphay[18]+alphay[6]*fin[17]+fin[6]*alphay[17]+alphay[3]*fin[11]+fin[3]*alphay[11]+alphay[2]*fin[10]+fin[2]*alphay[10]+alphay[1]*fin[9]+fin[1]*alphay[9]+alphay[0]*fin[4]+fin[0]*alphay[4]); 
+  out[13] += 0.3061862178478971*(alphay[26]*fin[31]+alphay[19]*fin[30]+alphay[18]*fin[29]+alphay[17]*fin[28]+alphay[16]*fin[27]+alphay[11]*fin[25]+alphay[10]*fin[24]+alphay[9]*fin[23]+alphay[8]*fin[22]+alphay[7]*fin[21]+alphay[6]*fin[20]+alphay[4]*fin[15]+alphay[3]*fin[14]+alphay[2]*fin[13]+alphay[1]*fin[12]+alphay[0]*fin[5]); 
+  out[16] += 0.3061862178478971*(alphay[10]*fin[26]+fin[10]*alphay[26]+alphay[17]*fin[19]+fin[17]*alphay[19]+alphay[4]*fin[18]+fin[4]*alphay[18]+alphay[2]*fin[16]+fin[2]*alphay[16]+alphay[9]*fin[11]+fin[9]*alphay[11]+alphay[6]*fin[8]+fin[6]*alphay[8]+alphay[0]*fin[7]+fin[0]*alphay[7]+alphay[1]*fin[3]+fin[1]*alphay[3]); 
+  out[17] += 0.27386127875258304*alphay[19]*fin[43]+0.273861278752583*(alphay[26]*fin[39]+alphay[11]*fin[38]+alphay[10]*fin[37])+0.27386127875258304*(alphay[18]*fin[35]+alphay[17]*fin[34]+alphay[4]*fin[33])+0.273861278752583*alphay[9]*fin[32]+0.3061862178478971*(alphay[8]*fin[26]+fin[8]*alphay[26]+alphay[16]*fin[19]+fin[16]*alphay[19]+alphay[3]*fin[18]+fin[3]*alphay[18]+alphay[2]*fin[17]+fin[2]*alphay[17]+alphay[7]*fin[11]+fin[7]*alphay[11]+alphay[6]*fin[10]+fin[6]*alphay[10]+alphay[0]*fin[9]+fin[0]*alphay[9]+alphay[1]*fin[4]+fin[1]*alphay[4]); 
+  out[19] += 0.27386127875258304*alphay[17]*fin[43]+0.273861278752583*(alphay[10]*fin[39]+alphay[9]*fin[38]+alphay[26]*fin[37])+0.27386127875258304*(alphay[4]*fin[35]+alphay[19]*fin[34]+alphay[18]*fin[33])+0.273861278752583*alphay[11]*fin[32]+0.3061862178478971*(alphay[6]*fin[26]+fin[6]*alphay[26]+alphay[2]*fin[19]+fin[2]*alphay[19]+alphay[1]*fin[18]+fin[1]*alphay[18]+alphay[16]*fin[17]+fin[16]*alphay[17]+alphay[0]*fin[11]+fin[0]*alphay[11]+alphay[8]*fin[10]+fin[8]*alphay[10]+alphay[7]*fin[9]+fin[7]*alphay[9]+alphay[3]*fin[4]+fin[3]*alphay[4]); 
+  out[20] += 0.3061862178478971*(alphay[19]*fin[31]+alphay[26]*fin[30]+alphay[11]*fin[29]+alphay[10]*fin[28]+alphay[8]*fin[27]+alphay[18]*fin[25]+alphay[17]*fin[24]+alphay[4]*fin[23]+alphay[16]*fin[22]+alphay[3]*fin[21]+alphay[2]*fin[20]+alphay[9]*fin[15]+alphay[7]*fin[14]+alphay[6]*fin[13]+alphay[0]*fin[12]+alphay[1]*fin[5]); 
+  out[22] += 0.3061862178478971*(alphay[17]*fin[31]+alphay[10]*fin[30]+alphay[9]*fin[29]+alphay[26]*fin[28]+alphay[6]*fin[27]+alphay[4]*fin[25]+alphay[19]*fin[24]+alphay[18]*fin[23]+alphay[2]*fin[22]+alphay[1]*fin[21]+alphay[16]*fin[20]+alphay[11]*fin[15]+alphay[0]*fin[14]+alphay[8]*fin[13]+alphay[7]*fin[12]+alphay[3]*fin[5]); 
+  out[24] += 0.273861278752583*alphay[26]*fin[47]+0.27386127875258304*(alphay[19]*fin[46]+alphay[18]*fin[45]+alphay[17]*fin[44])+0.273861278752583*(alphay[11]*fin[42]+alphay[10]*fin[41]+alphay[9]*fin[40])+0.27386127875258304*alphay[4]*fin[36]+0.3061862178478971*(alphay[16]*fin[31]+alphay[8]*fin[30]+alphay[7]*fin[29]+alphay[6]*fin[28]+alphay[26]*fin[27]+alphay[3]*fin[25]+alphay[2]*fin[24]+alphay[1]*fin[23]+alphay[19]*fin[22]+alphay[18]*fin[21]+alphay[17]*fin[20]+alphay[0]*fin[15]+alphay[11]*fin[14]+alphay[10]*fin[13]+alphay[9]*fin[12]+alphay[4]*fin[5]); 
+  out[26] += 0.27386127875258304*alphay[10]*fin[43]+0.273861278752583*(alphay[17]*fin[39]+alphay[4]*fin[38]+alphay[19]*fin[37])+0.27386127875258304*(alphay[9]*fin[35]+alphay[26]*fin[34]+alphay[11]*fin[33])+0.273861278752583*alphay[18]*fin[32]+0.3061862178478971*(alphay[2]*fin[26]+fin[2]*alphay[26]+alphay[6]*fin[19]+fin[6]*alphay[19]+alphay[0]*fin[18]+fin[0]*alphay[18]+alphay[8]*fin[17]+fin[8]*alphay[17]+alphay[10]*fin[16]+fin[10]*alphay[16]+alphay[1]*fin[11]+fin[1]*alphay[11]+alphay[3]*fin[9]+fin[3]*alphay[9]+alphay[4]*fin[7]+fin[4]*alphay[7]); 
+  out[27] += 0.3061862178478971*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+alphay[2]*fin[27]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+alphay[6]*fin[22]+alphay[0]*fin[21]+alphay[8]*fin[20]+fin[15]*alphay[18]+fin[13]*alphay[16]+alphay[1]*fin[14]+alphay[3]*fin[12]+fin[5]*alphay[7]); 
+  out[28] += 0.273861278752583*alphay[19]*fin[47]+0.27386127875258304*(alphay[26]*fin[46]+alphay[11]*fin[45]+alphay[10]*fin[44])+0.273861278752583*(alphay[18]*fin[42]+alphay[17]*fin[41]+alphay[4]*fin[40])+0.27386127875258304*alphay[9]*fin[36]+0.3061862178478971*(alphay[8]*fin[31]+alphay[16]*fin[30]+alphay[3]*fin[29]+alphay[2]*fin[28]+alphay[19]*fin[27]+fin[22]*alphay[26]+alphay[7]*fin[25]+alphay[6]*fin[24]+alphay[0]*fin[23]+alphay[11]*fin[21]+alphay[10]*fin[20]+fin[14]*alphay[18]+fin[13]*alphay[17]+alphay[1]*fin[15]+alphay[4]*fin[12]+fin[5]*alphay[9]); 
+  out[30] += 0.273861278752583*alphay[17]*fin[47]+0.27386127875258304*(alphay[10]*fin[46]+alphay[9]*fin[45]+alphay[26]*fin[44])+0.273861278752583*(alphay[4]*fin[42]+alphay[19]*fin[41]+alphay[18]*fin[40])+0.27386127875258304*alphay[11]*fin[36]+0.3061862178478971*(alphay[6]*fin[31]+alphay[2]*fin[30]+alphay[1]*fin[29]+alphay[16]*fin[28]+alphay[17]*fin[27]+fin[20]*alphay[26]+alphay[0]*fin[25]+alphay[8]*fin[24]+alphay[7]*fin[23]+alphay[10]*fin[22]+alphay[9]*fin[21]+fin[13]*alphay[19]+fin[12]*alphay[18]+alphay[3]*fin[15]+alphay[4]*fin[14]+fin[5]*alphay[11]); 
+  out[31] += 0.273861278752583*alphay[10]*fin[47]+0.27386127875258304*(alphay[17]*fin[46]+alphay[4]*fin[45]+alphay[19]*fin[44])+0.273861278752583*(alphay[9]*fin[42]+alphay[26]*fin[41]+alphay[11]*fin[40])+0.27386127875258304*alphay[18]*fin[36]+0.3061862178478971*(alphay[2]*fin[31]+alphay[6]*fin[30]+alphay[0]*fin[29]+alphay[8]*fin[28]+alphay[10]*fin[27]+fin[13]*alphay[26]+alphay[1]*fin[25]+alphay[16]*fin[24]+alphay[3]*fin[23]+alphay[17]*fin[22]+alphay[4]*fin[21]+alphay[19]*fin[20]+fin[5]*alphay[18]+alphay[7]*fin[15]+alphay[9]*fin[14]+alphay[11]*fin[12]); 
+  out[34] += 0.3061862178478971*(alphay[16]*fin[43]+alphay[8]*fin[39]+alphay[7]*fin[38]+alphay[6]*fin[37]+alphay[3]*fin[35]+alphay[2]*fin[34]+alphay[1]*fin[33]+alphay[0]*fin[32])+0.27386127875258304*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[4]*fin[4]); 
+  out[37] += 0.3061862178478971*(alphay[8]*fin[43]+alphay[16]*fin[39]+alphay[3]*fin[38]+alphay[2]*fin[37]+alphay[7]*fin[35]+alphay[6]*fin[34]+alphay[0]*fin[33]+alphay[1]*fin[32])+0.273861278752583*(alphay[19]*fin[26]+fin[19]*alphay[26]+alphay[11]*fin[18]+fin[11]*alphay[18]+alphay[10]*fin[17]+fin[10]*alphay[17]+alphay[4]*fin[9]+fin[4]*alphay[9]); 
+  out[39] += 0.3061862178478971*(alphay[6]*fin[43]+alphay[2]*fin[39]+alphay[1]*fin[38]+alphay[16]*fin[37]+alphay[0]*fin[35]+alphay[8]*fin[34]+alphay[7]*fin[33]+alphay[3]*fin[32])+0.273861278752583*(alphay[17]*fin[26]+fin[17]*alphay[26]+alphay[10]*fin[19]+fin[10]*alphay[19]+alphay[9]*fin[18]+fin[9]*alphay[18]+alphay[4]*fin[11]+fin[4]*alphay[11]); 
+  out[41] += 0.3061862178478971*(alphay[16]*fin[47]+alphay[8]*fin[46]+alphay[7]*fin[45]+alphay[6]*fin[44]+alphay[3]*fin[42]+alphay[2]*fin[41]+alphay[1]*fin[40]+alphay[0]*fin[36])+0.273861278752583*(alphay[26]*fin[31]+alphay[19]*fin[30]+alphay[18]*fin[29]+alphay[17]*fin[28]+alphay[11]*fin[25]+alphay[10]*fin[24]+alphay[9]*fin[23]+alphay[4]*fin[15]); 
+  out[43] += 0.3061862178478971*(alphay[2]*fin[43]+alphay[6]*fin[39]+alphay[0]*fin[38]+alphay[8]*fin[37]+alphay[1]*fin[35]+alphay[16]*fin[34]+alphay[3]*fin[33]+alphay[7]*fin[32])+0.27386127875258304*(alphay[10]*fin[26]+fin[10]*alphay[26]+alphay[17]*fin[19]+fin[17]*alphay[19]+alphay[4]*fin[18]+fin[4]*alphay[18]+alphay[9]*fin[11]+fin[9]*alphay[11]); 
+  out[44] += 0.3061862178478971*(alphay[8]*fin[47]+alphay[16]*fin[46]+alphay[3]*fin[45]+alphay[2]*fin[44]+alphay[7]*fin[42]+alphay[6]*fin[41]+alphay[0]*fin[40]+alphay[1]*fin[36])+0.27386127875258304*(alphay[19]*fin[31]+alphay[26]*fin[30]+alphay[11]*fin[29]+alphay[10]*fin[28]+alphay[18]*fin[25]+alphay[17]*fin[24]+alphay[4]*fin[23]+alphay[9]*fin[15]); 
+  out[46] += 0.3061862178478971*(alphay[6]*fin[47]+alphay[2]*fin[46]+alphay[1]*fin[45]+alphay[16]*fin[44]+alphay[0]*fin[42]+alphay[8]*fin[41]+alphay[7]*fin[40]+alphay[3]*fin[36])+0.27386127875258304*(alphay[17]*fin[31]+alphay[10]*fin[30]+alphay[9]*fin[29]+alphay[26]*fin[28]+alphay[4]*fin[25]+alphay[19]*fin[24]+alphay[18]*fin[23]+alphay[11]*fin[15]); 
+  out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
+
+  double alphaz[48] = {0.}; 
+  alphaz[0] = (((-(0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[4]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.21650635094610965*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[2] = ((0.21650635094610965*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[3] = (((-(0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.4841229182759271*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[6] = ((0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[7] = (((-(0.35074028853269745*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]-0.19485571585149863*b_x[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*apar[2]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*apar[1]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[8] = ((0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]+0.21650635094610965*b_y[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[9] = (((-(0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]-0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[10] = ((0.4841229182759271*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[11] = (((-(0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]-0.43571062644833425*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[16] = ((0.19485571585149863*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_y[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[17] = ((0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[18] = (((-(0.7842791276070014*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]-0.43571062644833425*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.43571062644833425*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[19] = ((0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]+0.4841229182759271*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[26] = ((0.43571062644833425*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]+0.43571062644833425*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
+  out[7] += 0.3061862178478971*(alphaz[19]*fin[26]+fin[19]*alphaz[26]+alphaz[11]*fin[18]+fin[11]*alphaz[18]+alphaz[10]*fin[17]+fin[10]*alphaz[17]+alphaz[8]*fin[16]+fin[8]*alphaz[16]+alphaz[4]*fin[9]+fin[4]*alphaz[9]+alphaz[3]*fin[7]+fin[3]*alphaz[7]+alphaz[2]*fin[6]+fin[2]*alphaz[6]+alphaz[0]*fin[1]+fin[0]*alphaz[1]); 
+  out[8] += 0.3061862178478971*(alphaz[18]*fin[26]+fin[18]*alphaz[26]+alphaz[11]*fin[19]+fin[11]*alphaz[19]+alphaz[9]*fin[17]+fin[9]*alphaz[17]+alphaz[7]*fin[16]+fin[7]*alphaz[16]+alphaz[4]*fin[10]+fin[4]*alphaz[10]+alphaz[3]*fin[8]+fin[3]*alphaz[8]+alphaz[1]*fin[6]+fin[1]*alphaz[6]+alphaz[0]*fin[2]+fin[0]*alphaz[2]); 
+  out[11] += 0.27386127875258304*alphaz[26]*fin[43]+0.273861278752583*(alphaz[19]*fin[39]+alphaz[18]*fin[38]+alphaz[17]*fin[37])+0.27386127875258304*(alphaz[11]*fin[35]+alphaz[10]*fin[34]+alphaz[9]*fin[33])+0.273861278752583*alphaz[4]*fin[32]+0.3061862178478971*(alphaz[16]*fin[26]+fin[16]*alphaz[26]+alphaz[8]*fin[19]+fin[8]*alphaz[19]+alphaz[7]*fin[18]+fin[7]*alphaz[18]+alphaz[6]*fin[17]+fin[6]*alphaz[17]+alphaz[3]*fin[11]+fin[3]*alphaz[11]+alphaz[2]*fin[10]+fin[2]*alphaz[10]+alphaz[1]*fin[9]+fin[1]*alphaz[9]+alphaz[0]*fin[4]+fin[0]*alphaz[4]); 
+  out[14] += 0.3061862178478971*(alphaz[26]*fin[31]+alphaz[19]*fin[30]+alphaz[18]*fin[29]+alphaz[17]*fin[28]+alphaz[16]*fin[27]+alphaz[11]*fin[25]+alphaz[10]*fin[24]+alphaz[9]*fin[23]+alphaz[8]*fin[22]+alphaz[7]*fin[21]+alphaz[6]*fin[20]+alphaz[4]*fin[15]+alphaz[3]*fin[14]+alphaz[2]*fin[13]+alphaz[1]*fin[12]+alphaz[0]*fin[5]); 
+  out[16] += 0.3061862178478971*(alphaz[11]*fin[26]+fin[11]*alphaz[26]+alphaz[18]*fin[19]+fin[18]*alphaz[19]+alphaz[4]*fin[17]+fin[4]*alphaz[17]+alphaz[3]*fin[16]+fin[3]*alphaz[16]+alphaz[9]*fin[10]+fin[9]*alphaz[10]+alphaz[7]*fin[8]+fin[7]*alphaz[8]+alphaz[0]*fin[6]+fin[0]*alphaz[6]+alphaz[1]*fin[2]+fin[1]*alphaz[2]); 
+  out[18] += 0.27386127875258304*alphaz[19]*fin[43]+0.273861278752583*(alphaz[26]*fin[39]+alphaz[11]*fin[38]+alphaz[10]*fin[37])+0.27386127875258304*(alphaz[18]*fin[35]+alphaz[17]*fin[34]+alphaz[4]*fin[33])+0.273861278752583*alphaz[9]*fin[32]+0.3061862178478971*(alphaz[8]*fin[26]+fin[8]*alphaz[26]+alphaz[16]*fin[19]+fin[16]*alphaz[19]+alphaz[3]*fin[18]+fin[3]*alphaz[18]+alphaz[2]*fin[17]+fin[2]*alphaz[17]+alphaz[7]*fin[11]+fin[7]*alphaz[11]+alphaz[6]*fin[10]+fin[6]*alphaz[10]+alphaz[0]*fin[9]+fin[0]*alphaz[9]+alphaz[1]*fin[4]+fin[1]*alphaz[4]); 
+  out[19] += 0.27386127875258304*alphaz[18]*fin[43]+0.273861278752583*(alphaz[11]*fin[39]+alphaz[26]*fin[38]+alphaz[9]*fin[37])+0.27386127875258304*(alphaz[19]*fin[35]+alphaz[4]*fin[34]+alphaz[17]*fin[33])+0.273861278752583*alphaz[10]*fin[32]+0.3061862178478971*(alphaz[7]*fin[26]+fin[7]*alphaz[26]+alphaz[3]*fin[19]+fin[3]*alphaz[19]+alphaz[16]*fin[18]+fin[16]*alphaz[18]+alphaz[1]*fin[17]+fin[1]*alphaz[17]+alphaz[8]*fin[11]+fin[8]*alphaz[11]+alphaz[0]*fin[10]+fin[0]*alphaz[10]+alphaz[6]*fin[9]+fin[6]*alphaz[9]+alphaz[2]*fin[4]+fin[2]*alphaz[4]); 
+  out[21] += 0.3061862178478971*(alphaz[19]*fin[31]+alphaz[26]*fin[30]+alphaz[11]*fin[29]+alphaz[10]*fin[28]+alphaz[8]*fin[27]+alphaz[18]*fin[25]+alphaz[17]*fin[24]+alphaz[4]*fin[23]+alphaz[16]*fin[22]+alphaz[3]*fin[21]+alphaz[2]*fin[20]+alphaz[9]*fin[15]+alphaz[7]*fin[14]+alphaz[6]*fin[13]+alphaz[0]*fin[12]+alphaz[1]*fin[5]); 
+  out[22] += 0.3061862178478971*(alphaz[18]*fin[31]+alphaz[11]*fin[30]+alphaz[26]*fin[29]+alphaz[9]*fin[28]+alphaz[7]*fin[27]+alphaz[19]*fin[25]+alphaz[4]*fin[24]+alphaz[17]*fin[23]+alphaz[3]*fin[22]+alphaz[16]*fin[21]+alphaz[1]*fin[20]+alphaz[10]*fin[15]+alphaz[8]*fin[14]+alphaz[0]*fin[13]+alphaz[6]*fin[12]+alphaz[2]*fin[5]); 
+  out[25] += 0.273861278752583*alphaz[26]*fin[47]+0.27386127875258304*(alphaz[19]*fin[46]+alphaz[18]*fin[45]+alphaz[17]*fin[44])+0.273861278752583*(alphaz[11]*fin[42]+alphaz[10]*fin[41]+alphaz[9]*fin[40])+0.27386127875258304*alphaz[4]*fin[36]+0.3061862178478971*(alphaz[16]*fin[31]+alphaz[8]*fin[30]+alphaz[7]*fin[29]+alphaz[6]*fin[28]+alphaz[26]*fin[27]+alphaz[3]*fin[25]+alphaz[2]*fin[24]+alphaz[1]*fin[23]+alphaz[19]*fin[22]+alphaz[18]*fin[21]+alphaz[17]*fin[20]+alphaz[0]*fin[15]+alphaz[11]*fin[14]+alphaz[10]*fin[13]+alphaz[9]*fin[12]+alphaz[4]*fin[5]); 
+  out[26] += 0.27386127875258304*alphaz[11]*fin[43]+0.273861278752583*(alphaz[18]*fin[39]+alphaz[19]*fin[38]+alphaz[4]*fin[37])+0.27386127875258304*(alphaz[26]*fin[35]+alphaz[9]*fin[34]+alphaz[10]*fin[33])+0.273861278752583*alphaz[17]*fin[32]+0.3061862178478971*(alphaz[3]*fin[26]+fin[3]*alphaz[26]+alphaz[7]*fin[19]+fin[7]*alphaz[19]+alphaz[8]*fin[18]+fin[8]*alphaz[18]+alphaz[0]*fin[17]+fin[0]*alphaz[17]+alphaz[11]*fin[16]+fin[11]*alphaz[16]+alphaz[1]*fin[10]+fin[1]*alphaz[10]+alphaz[2]*fin[9]+fin[2]*alphaz[9]+alphaz[4]*fin[6]+fin[4]*alphaz[6]); 
+  out[27] += 0.3061862178478971*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+alphaz[3]*fin[27]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+alphaz[7]*fin[22]+alphaz[8]*fin[21]+alphaz[0]*fin[20]+fin[15]*alphaz[17]+fin[14]*alphaz[16]+alphaz[1]*fin[13]+alphaz[2]*fin[12]+fin[5]*alphaz[6]); 
+  out[29] += 0.273861278752583*alphaz[19]*fin[47]+0.27386127875258304*(alphaz[26]*fin[46]+alphaz[11]*fin[45]+alphaz[10]*fin[44])+0.273861278752583*(alphaz[18]*fin[42]+alphaz[17]*fin[41]+alphaz[4]*fin[40])+0.27386127875258304*alphaz[9]*fin[36]+0.3061862178478971*(alphaz[8]*fin[31]+alphaz[16]*fin[30]+alphaz[3]*fin[29]+alphaz[2]*fin[28]+alphaz[19]*fin[27]+fin[22]*alphaz[26]+alphaz[7]*fin[25]+alphaz[6]*fin[24]+alphaz[0]*fin[23]+alphaz[11]*fin[21]+alphaz[10]*fin[20]+fin[14]*alphaz[18]+fin[13]*alphaz[17]+alphaz[1]*fin[15]+alphaz[4]*fin[12]+fin[5]*alphaz[9]); 
+  out[30] += 0.273861278752583*alphaz[18]*fin[47]+0.27386127875258304*(alphaz[11]*fin[46]+alphaz[26]*fin[45]+alphaz[9]*fin[44])+0.273861278752583*(alphaz[19]*fin[42]+alphaz[4]*fin[41]+alphaz[17]*fin[40])+0.27386127875258304*alphaz[10]*fin[36]+0.3061862178478971*(alphaz[7]*fin[31]+alphaz[3]*fin[30]+alphaz[16]*fin[29]+alphaz[1]*fin[28]+alphaz[18]*fin[27]+fin[21]*alphaz[26]+alphaz[8]*fin[25]+alphaz[0]*fin[24]+alphaz[6]*fin[23]+alphaz[11]*fin[22]+alphaz[9]*fin[20]+fin[14]*alphaz[19]+fin[12]*alphaz[17]+alphaz[2]*fin[15]+alphaz[4]*fin[13]+fin[5]*alphaz[10]); 
+  out[31] += 0.273861278752583*alphaz[11]*fin[47]+0.27386127875258304*(alphaz[18]*fin[46]+alphaz[19]*fin[45]+alphaz[4]*fin[44])+0.273861278752583*(alphaz[26]*fin[42]+alphaz[9]*fin[41]+alphaz[10]*fin[40])+0.27386127875258304*alphaz[17]*fin[36]+0.3061862178478971*(alphaz[3]*fin[31]+alphaz[7]*fin[30]+alphaz[8]*fin[29]+alphaz[0]*fin[28]+alphaz[11]*fin[27]+fin[14]*alphaz[26]+alphaz[16]*fin[25]+alphaz[1]*fin[24]+alphaz[2]*fin[23]+alphaz[18]*fin[22]+alphaz[19]*fin[21]+alphaz[4]*fin[20]+fin[5]*alphaz[17]+alphaz[6]*fin[15]+alphaz[9]*fin[13]+alphaz[10]*fin[12]); 
+  out[35] += 0.3061862178478971*(alphaz[16]*fin[43]+alphaz[8]*fin[39]+alphaz[7]*fin[38]+alphaz[6]*fin[37]+alphaz[3]*fin[35]+alphaz[2]*fin[34]+alphaz[1]*fin[33]+alphaz[0]*fin[32])+0.27386127875258304*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[4]*fin[4]); 
+  out[38] += 0.3061862178478971*(alphaz[8]*fin[43]+alphaz[16]*fin[39]+alphaz[3]*fin[38]+alphaz[2]*fin[37]+alphaz[7]*fin[35]+alphaz[6]*fin[34]+alphaz[0]*fin[33]+alphaz[1]*fin[32])+0.273861278752583*(alphaz[19]*fin[26]+fin[19]*alphaz[26]+alphaz[11]*fin[18]+fin[11]*alphaz[18]+alphaz[10]*fin[17]+fin[10]*alphaz[17]+alphaz[4]*fin[9]+fin[4]*alphaz[9]); 
+  out[39] += 0.3061862178478971*(alphaz[7]*fin[43]+alphaz[3]*fin[39]+alphaz[16]*fin[38]+alphaz[1]*fin[37]+alphaz[8]*fin[35]+alphaz[0]*fin[34]+alphaz[6]*fin[33]+alphaz[2]*fin[32])+0.273861278752583*(alphaz[18]*fin[26]+fin[18]*alphaz[26]+alphaz[11]*fin[19]+fin[11]*alphaz[19]+alphaz[9]*fin[17]+fin[9]*alphaz[17]+alphaz[4]*fin[10]+fin[4]*alphaz[10]); 
+  out[42] += 0.3061862178478971*(alphaz[16]*fin[47]+alphaz[8]*fin[46]+alphaz[7]*fin[45]+alphaz[6]*fin[44]+alphaz[3]*fin[42]+alphaz[2]*fin[41]+alphaz[1]*fin[40]+alphaz[0]*fin[36])+0.273861278752583*(alphaz[26]*fin[31]+alphaz[19]*fin[30]+alphaz[18]*fin[29]+alphaz[17]*fin[28]+alphaz[11]*fin[25]+alphaz[10]*fin[24]+alphaz[9]*fin[23]+alphaz[4]*fin[15]); 
+  out[43] += 0.3061862178478971*(alphaz[3]*fin[43]+alphaz[7]*fin[39]+alphaz[8]*fin[38]+alphaz[0]*fin[37]+alphaz[16]*fin[35]+alphaz[1]*fin[34]+alphaz[2]*fin[33]+alphaz[6]*fin[32])+0.27386127875258304*(alphaz[11]*fin[26]+fin[11]*alphaz[26]+alphaz[18]*fin[19]+fin[18]*alphaz[19]+alphaz[4]*fin[17]+fin[4]*alphaz[17]+alphaz[9]*fin[10]+fin[9]*alphaz[10]); 
+  out[45] += 0.3061862178478971*(alphaz[8]*fin[47]+alphaz[16]*fin[46]+alphaz[3]*fin[45]+alphaz[2]*fin[44]+alphaz[7]*fin[42]+alphaz[6]*fin[41]+alphaz[0]*fin[40]+alphaz[1]*fin[36])+0.27386127875258304*(alphaz[19]*fin[31]+alphaz[26]*fin[30]+alphaz[11]*fin[29]+alphaz[10]*fin[28]+alphaz[18]*fin[25]+alphaz[17]*fin[24]+alphaz[4]*fin[23]+alphaz[9]*fin[15]); 
+  out[46] += 0.3061862178478971*(alphaz[7]*fin[47]+alphaz[3]*fin[46]+alphaz[16]*fin[45]+alphaz[1]*fin[44]+alphaz[8]*fin[42]+alphaz[0]*fin[41]+alphaz[6]*fin[40]+alphaz[2]*fin[36])+0.27386127875258304*(alphaz[18]*fin[31]+alphaz[11]*fin[30]+alphaz[26]*fin[29]+alphaz[9]*fin[28]+alphaz[19]*fin[25]+alphaz[4]*fin[24]+alphaz[17]*fin[23]+alphaz[10]*fin[15]); 
+  out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
+
+  double alphavpar[48] = {0.}; 
+  alphavpar[0] = (((-(0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[7]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[6]+0.10825317547305482*apar[2]*hamil[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*b_x[3]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[5]*b_x[5]+0.10825317547305482*hamil[3]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[4]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[3]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[3]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[3]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[8]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[6]*apar[7]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[6]-0.21650635094610965*apar[1]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*b_y[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*apar[5]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*hamil[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[3]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[16]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.38971143170299727*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.21650635094610965*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[8]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[7]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[7]+0.10825317547305482*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[6]+0.21650635094610965*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[6]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[6]+0.21650635094610965*apar[1]*hamil[2]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[5]*jacobtot_inv[5]+0.21650635094610965*b_z[1]*hamil[2]*apar[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[5]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[3]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[4]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[3]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[3]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[2]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[2]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[16]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[7]+0.19485571585149863*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[6]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[6]-0.38971143170299727*hamil[2]*apar[5]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*hamil[3]*apar[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_x[5]-0.21650635094610965*hamil[2]*apar[3]*jacobtot_inv[3]*b_x[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[5]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[5]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[5]+0.10825317547305482*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[4]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[3]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[16]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]-0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[7]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[6]*apar[7]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[6]+0.38971143170299727*hamil[1]*apar[5]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[5]*b_y[5]-0.21650635094610965*apar[1]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.21650635094610965*hamil[1]*apar[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[3]*b_y[5]+0.19485571585149863*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[5]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[16]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[7]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[6]-0.19485571585149863*hamil[1]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_z[5]+0.21650635094610965*apar[1]*hamil[2]*jacobtot_inv[3]*b_z[5]-0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*apar[3]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[4]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[2]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[2]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[16])-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[8]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*hamil[6]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[6]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[7]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.21650635094610965*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[6]-0.21650635094610965*hamil[3]*apar[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_y[5]-0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[4]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[16]+0.38971143170299727*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[8]+0.21650635094610965*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[2]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[4]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[16]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[16]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[7]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[6]-0.10825317547305482*apar[0]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[1]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[16]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[16]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[8]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[7]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[6]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[6]-0.38971143170299727*hamil[3]*apar[5]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[5]*jacobtot_inv[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[5]*b_y[5]-0.19485571585149863*apar[3]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[3]*b_y[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[5]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[5]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[5]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[16]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[8]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[7]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[7]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[6]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[6]+0.38971143170299727*hamil[2]*apar[5]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[4]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_z[5]+0.19485571585149863*hamil[2]*apar[3]*jacobtot_inv[3]*b_z[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[5]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[5]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[5]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[3]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[3]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[3]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[21]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[14]+0.10825317547305482*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[21]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[14]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[21]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[12]-0.10825317547305482*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[6] = (((-(0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[16])-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[3]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*hamil[6]*apar[7]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*hamil[6]*apar[7]-0.38971143170299727*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[6]-0.19485571585149863*jacobtot_inv[1]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[8]-0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[7]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[7]+0.38971143170299727*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[6]-0.10825317547305482*apar[2]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[3]*jacobtot_inv[3]*apar[4]*b_y[5]+0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[4]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[16]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[8]+0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[8]+0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*apar[2]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*hamil[2]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[4]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.7014805770653949*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.7014805770653949*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.7014805770653949*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[16]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[16]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[8]+0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[7]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[7]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[7]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[7]+0.35074028853269745*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[7]-0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[6]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[6]-0.19485571585149863*apar[1]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.19485571585149863*b_x[1]*hamil[2]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*apar[5]*b_x[5]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[16]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[8]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[8]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[8]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[7]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[7]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.19485571585149863*apar[3]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*apar[1]*hamil[1]*b_y[5]*jacobtot_inv[5]-0.19485571585149863*b_y[3]*hamil[3]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_y[1]*hamil[1]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[5]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*apar[5]*b_y[5]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[3]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[16]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[16]+0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[8]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[8]-0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[7]-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[7]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[7]-0.35074028853269745*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[6]+0.19485571585149863*hamil[2]*apar[3]*b_z[5]*jacobtot_inv[5]+0.19485571585149863*hamil[2]*b_z[3]*apar[5]*jacobtot_inv[5]-0.19485571585149863*b_z[1]*hamil[1]*apar[4]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[5]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*apar[5]*b_z[5]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[4]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[3]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[3]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[8] = (((-(0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[16])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[6]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[6]-0.10825317547305482*apar[2]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*b_x[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[16]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[7]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[7]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[7]-0.38971143170299727*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[7]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[6]+0.10825317547305482*hamil[1]*apar[2]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*b_y[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[4]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[8]+0.38971143170299727*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[6]*apar[7]+0.38971143170299727*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[6]+0.21650635094610965*b_z[1]*hamil[2]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[4]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[14]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[14]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[21])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[21]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[14]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[12]-0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[12]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[13] = ((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[14]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[14]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[12]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[14] = (((0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[14]+0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[21]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[21]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[14]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[21]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[12]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[16] = (((-(0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[16])-0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[0]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[0]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[7]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[6]-0.19485571585149863*hamil[2]*apar[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_x[5]-0.10825317547305482*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[16]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[7]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[7]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[6]-0.19485571585149863*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[6]+0.19485571585149863*hamil[1]*apar[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[4]*b_y[5]+0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[16]+0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[16]+0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.35074028853269745*b_z[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[5]*apar[7]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[6]+0.10825317547305482*b_z[0]*hamil[2]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[20] = ((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[21]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[12]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[21] = (((0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[21]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[21]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[14]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[21]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[21]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[21]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[14]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[21])-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[21]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[21]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[12]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[22] = ((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[21]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[21]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[14]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[14]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[12]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[27] = ((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[21]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[14]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[14]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[14]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[12]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+
+
+  out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[9] += 0.3061862178478971*(alphavpar[22]*fin[27]+fin[22]*alphavpar[27]+alphavpar[14]*fin[21]+fin[14]*alphavpar[21]+alphavpar[13]*fin[20]+fin[13]*alphavpar[20]+alphavpar[8]*fin[16]+fin[8]*alphavpar[16]+alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[10] += 0.3061862178478971*(alphavpar[21]*fin[27]+fin[21]*alphavpar[27]+alphavpar[14]*fin[22]+fin[14]*alphavpar[22]+alphavpar[12]*fin[20]+fin[12]*alphavpar[20]+alphavpar[7]*fin[16]+fin[7]*alphavpar[16]+alphavpar[5]*fin[13]+fin[5]*alphavpar[13]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[11] += 0.3061862178478971*(alphavpar[20]*fin[27]+fin[20]*alphavpar[27]+alphavpar[13]*fin[22]+fin[13]*alphavpar[22]+alphavpar[12]*fin[21]+fin[12]*alphavpar[21]+alphavpar[6]*fin[16]+fin[6]*alphavpar[16]+alphavpar[5]*fin[14]+fin[5]*alphavpar[14]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[15] += 0.3061862178478971*(alphavpar[16]*fin[27]+fin[16]*alphavpar[27]+alphavpar[8]*fin[22]+fin[8]*alphavpar[22]+alphavpar[7]*fin[21]+fin[7]*alphavpar[21]+alphavpar[6]*fin[20]+fin[6]*alphavpar[20]+alphavpar[3]*fin[14]+fin[3]*alphavpar[14]+alphavpar[2]*fin[13]+fin[2]*alphavpar[13]+alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]); 
+  out[17] += 0.3061862178478971*(alphavpar[14]*fin[27]+fin[14]*alphavpar[27]+alphavpar[21]*fin[22]+fin[21]*alphavpar[22]+alphavpar[5]*fin[20]+fin[5]*alphavpar[20]+alphavpar[3]*fin[16]+fin[3]*alphavpar[16]+alphavpar[12]*fin[13]+fin[12]*alphavpar[13]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[18] += 0.3061862178478971*(alphavpar[13]*fin[27]+fin[13]*alphavpar[27]+alphavpar[20]*fin[22]+fin[20]*alphavpar[22]+alphavpar[5]*fin[21]+fin[5]*alphavpar[21]+alphavpar[2]*fin[16]+fin[2]*alphavpar[16]+alphavpar[12]*fin[14]+fin[12]*alphavpar[14]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[19] += 0.3061862178478971*(alphavpar[12]*fin[27]+fin[12]*alphavpar[27]+alphavpar[5]*fin[22]+fin[5]*alphavpar[22]+alphavpar[20]*fin[21]+fin[20]*alphavpar[21]+alphavpar[1]*fin[16]+fin[1]*alphavpar[16]+alphavpar[13]*fin[14]+fin[13]*alphavpar[14]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
+  out[23] += 0.3061862178478971*(alphavpar[8]*fin[27]+fin[8]*alphavpar[27]+alphavpar[16]*fin[22]+fin[16]*alphavpar[22]+alphavpar[3]*fin[21]+fin[3]*alphavpar[21]+alphavpar[2]*fin[20]+fin[2]*alphavpar[20]+alphavpar[7]*fin[14]+fin[7]*alphavpar[14]+alphavpar[6]*fin[13]+fin[6]*alphavpar[13]+alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]); 
+  out[24] += 0.3061862178478971*(alphavpar[7]*fin[27]+fin[7]*alphavpar[27]+alphavpar[3]*fin[22]+fin[3]*alphavpar[22]+alphavpar[16]*fin[21]+fin[16]*alphavpar[21]+alphavpar[1]*fin[20]+fin[1]*alphavpar[20]+alphavpar[8]*fin[14]+fin[8]*alphavpar[14]+alphavpar[0]*fin[13]+fin[0]*alphavpar[13]+alphavpar[6]*fin[12]+fin[6]*alphavpar[12]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]); 
+  out[25] += 0.3061862178478971*(alphavpar[6]*fin[27]+fin[6]*alphavpar[27]+alphavpar[2]*fin[22]+fin[2]*alphavpar[22]+alphavpar[1]*fin[21]+fin[1]*alphavpar[21]+alphavpar[16]*fin[20]+fin[16]*alphavpar[20]+alphavpar[0]*fin[14]+fin[0]*alphavpar[14]+alphavpar[8]*fin[13]+fin[8]*alphavpar[13]+alphavpar[7]*fin[12]+fin[7]*alphavpar[12]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]); 
+  out[26] += 0.3061862178478971*(alphavpar[5]*fin[27]+fin[5]*alphavpar[27]+alphavpar[12]*fin[22]+fin[12]*alphavpar[22]+alphavpar[13]*fin[21]+fin[13]*alphavpar[21]+alphavpar[14]*fin[20]+fin[14]*alphavpar[20]+alphavpar[0]*fin[16]+fin[0]*alphavpar[16]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]); 
+  out[28] += 0.3061862178478971*(alphavpar[3]*fin[27]+fin[3]*alphavpar[27]+alphavpar[7]*fin[22]+fin[7]*alphavpar[22]+alphavpar[8]*fin[21]+fin[8]*alphavpar[21]+alphavpar[0]*fin[20]+fin[0]*alphavpar[20]+alphavpar[14]*fin[16]+fin[14]*alphavpar[16]+alphavpar[1]*fin[13]+fin[1]*alphavpar[13]+alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]); 
+  out[29] += 0.3061862178478971*(alphavpar[2]*fin[27]+fin[2]*alphavpar[27]+alphavpar[6]*fin[22]+fin[6]*alphavpar[22]+alphavpar[0]*fin[21]+fin[0]*alphavpar[21]+alphavpar[8]*fin[20]+fin[8]*alphavpar[20]+alphavpar[13]*fin[16]+fin[13]*alphavpar[16]+alphavpar[1]*fin[14]+fin[1]*alphavpar[14]+alphavpar[3]*fin[12]+fin[3]*alphavpar[12]+alphavpar[5]*fin[7]+fin[5]*alphavpar[7]); 
+  out[30] += 0.3061862178478971*(alphavpar[1]*fin[27]+fin[1]*alphavpar[27]+alphavpar[0]*fin[22]+fin[0]*alphavpar[22]+alphavpar[6]*fin[21]+fin[6]*alphavpar[21]+alphavpar[7]*fin[20]+fin[7]*alphavpar[20]+alphavpar[12]*fin[16]+fin[12]*alphavpar[16]+alphavpar[2]*fin[14]+fin[2]*alphavpar[14]+alphavpar[3]*fin[13]+fin[3]*alphavpar[13]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]); 
+  out[31] += 0.3061862178478971*(alphavpar[0]*fin[27]+fin[0]*alphavpar[27]+alphavpar[1]*fin[22]+fin[1]*alphavpar[22]+alphavpar[2]*fin[21]+fin[2]*alphavpar[21]+alphavpar[3]*fin[20]+fin[3]*alphavpar[20]+alphavpar[5]*fin[16]+fin[5]*alphavpar[16]+alphavpar[6]*fin[14]+fin[6]*alphavpar[14]+alphavpar[7]*fin[13]+fin[7]*alphavpar[13]+alphavpar[8]*fin[12]+fin[8]*alphavpar[12]); 
+  out[32] += 0.6846531968814573*(alphavpar[27]*fin[31]+alphavpar[22]*fin[30]+alphavpar[21]*fin[29]+alphavpar[20]*fin[28]+alphavpar[16]*fin[26]+alphavpar[14]*fin[25]+alphavpar[13]*fin[24]+alphavpar[12]*fin[23]+alphavpar[8]*fin[19]+alphavpar[7]*fin[18]+alphavpar[6]*fin[17]+alphavpar[5]*fin[15]+alphavpar[3]*fin[11]+alphavpar[2]*fin[10]+alphavpar[1]*fin[9]+alphavpar[0]*fin[4]); 
+  out[33] += 0.6846531968814574*(alphavpar[22]*fin[31]+alphavpar[27]*fin[30]+alphavpar[14]*fin[29]+alphavpar[13]*fin[28]+alphavpar[8]*fin[26]+alphavpar[21]*fin[25]+alphavpar[20]*fin[24]+alphavpar[5]*fin[23]+alphavpar[16]*fin[19]+alphavpar[3]*fin[18]+alphavpar[2]*fin[17]+alphavpar[12]*fin[15]+alphavpar[7]*fin[11]+alphavpar[6]*fin[10]+alphavpar[0]*fin[9]+alphavpar[1]*fin[4]); 
+  out[34] += 0.6846531968814574*(alphavpar[21]*fin[31]+alphavpar[14]*fin[30]+alphavpar[27]*fin[29]+alphavpar[12]*fin[28]+alphavpar[7]*fin[26]+alphavpar[22]*fin[25]+alphavpar[5]*fin[24]+alphavpar[20]*fin[23]+alphavpar[3]*fin[19]+alphavpar[16]*fin[18]+alphavpar[1]*fin[17]+alphavpar[13]*fin[15]+alphavpar[8]*fin[11]+alphavpar[0]*fin[10]+alphavpar[6]*fin[9]+alphavpar[2]*fin[4]); 
+  out[35] += 0.6846531968814574*(alphavpar[20]*fin[31]+alphavpar[13]*fin[30]+alphavpar[12]*fin[29]+alphavpar[27]*fin[28]+alphavpar[6]*fin[26]+alphavpar[5]*fin[25]+alphavpar[22]*fin[24]+alphavpar[21]*fin[23]+alphavpar[2]*fin[19]+alphavpar[1]*fin[18]+alphavpar[16]*fin[17]+alphavpar[14]*fin[15]+alphavpar[0]*fin[11]+alphavpar[8]*fin[10]+alphavpar[7]*fin[9]+alphavpar[3]*fin[4]); 
+  out[36] += 0.6846531968814574*(alphavpar[16]*fin[31]+alphavpar[8]*fin[30]+alphavpar[7]*fin[29]+alphavpar[6]*fin[28]+fin[26]*alphavpar[27]+alphavpar[3]*fin[25]+alphavpar[2]*fin[24]+alphavpar[1]*fin[23]+fin[19]*alphavpar[22]+fin[18]*alphavpar[21]+fin[17]*alphavpar[20]+alphavpar[0]*fin[15]+fin[11]*alphavpar[14]+fin[10]*alphavpar[13]+fin[9]*alphavpar[12]+fin[4]*alphavpar[5]); 
+  out[37] += 0.6846531968814573*(alphavpar[14]*fin[31]+alphavpar[21]*fin[30]+alphavpar[22]*fin[29]+alphavpar[5]*fin[28]+fin[25]*alphavpar[27]+alphavpar[3]*fin[26]+alphavpar[12]*fin[24]+alphavpar[13]*fin[23]+fin[15]*alphavpar[20]+alphavpar[7]*fin[19]+alphavpar[8]*fin[18]+alphavpar[0]*fin[17]+fin[11]*alphavpar[16]+alphavpar[1]*fin[10]+alphavpar[2]*fin[9]+fin[4]*alphavpar[6]); 
+  out[38] += 0.6846531968814573*(alphavpar[13]*fin[31]+alphavpar[20]*fin[30]+alphavpar[5]*fin[29]+alphavpar[22]*fin[28]+fin[24]*alphavpar[27]+alphavpar[2]*fin[26]+alphavpar[12]*fin[25]+alphavpar[14]*fin[23]+fin[15]*alphavpar[21]+alphavpar[6]*fin[19]+alphavpar[0]*fin[18]+alphavpar[8]*fin[17]+fin[10]*alphavpar[16]+alphavpar[1]*fin[11]+alphavpar[3]*fin[9]+fin[4]*alphavpar[7]); 
+  out[39] += 0.6846531968814573*(alphavpar[12]*fin[31]+alphavpar[5]*fin[30]+alphavpar[20]*fin[29]+alphavpar[21]*fin[28]+fin[23]*alphavpar[27]+alphavpar[1]*fin[26]+alphavpar[13]*fin[25]+alphavpar[14]*fin[24]+fin[15]*alphavpar[22]+alphavpar[0]*fin[19]+alphavpar[6]*fin[18]+alphavpar[7]*fin[17]+fin[9]*alphavpar[16]+alphavpar[2]*fin[11]+alphavpar[3]*fin[10]+fin[4]*alphavpar[8]); 
+  out[40] += 0.6846531968814573*(alphavpar[8]*fin[31]+alphavpar[16]*fin[30]+alphavpar[3]*fin[29]+alphavpar[2]*fin[28]+fin[19]*alphavpar[27]+alphavpar[22]*fin[26]+alphavpar[7]*fin[25]+alphavpar[6]*fin[24]+alphavpar[0]*fin[23]+fin[11]*alphavpar[21]+fin[10]*alphavpar[20]+alphavpar[14]*fin[18]+alphavpar[13]*fin[17]+alphavpar[1]*fin[15]+fin[4]*alphavpar[12]+alphavpar[5]*fin[9]); 
+  out[41] += 0.6846531968814573*(alphavpar[7]*fin[31]+alphavpar[3]*fin[30]+alphavpar[16]*fin[29]+alphavpar[1]*fin[28]+fin[18]*alphavpar[27]+alphavpar[21]*fin[26]+alphavpar[8]*fin[25]+alphavpar[0]*fin[24]+alphavpar[6]*fin[23]+fin[11]*alphavpar[22]+fin[9]*alphavpar[20]+alphavpar[14]*fin[19]+alphavpar[12]*fin[17]+alphavpar[2]*fin[15]+fin[4]*alphavpar[13]+alphavpar[5]*fin[10]); 
+  out[42] += 0.6846531968814573*(alphavpar[6]*fin[31]+alphavpar[2]*fin[30]+alphavpar[1]*fin[29]+alphavpar[16]*fin[28]+fin[17]*alphavpar[27]+alphavpar[20]*fin[26]+alphavpar[0]*fin[25]+alphavpar[8]*fin[24]+alphavpar[7]*fin[23]+fin[10]*alphavpar[22]+fin[9]*alphavpar[21]+alphavpar[13]*fin[19]+alphavpar[12]*fin[18]+alphavpar[3]*fin[15]+fin[4]*alphavpar[14]+alphavpar[5]*fin[11]); 
+  out[43] += 0.6846531968814574*(alphavpar[5]*fin[31]+alphavpar[12]*fin[30]+alphavpar[13]*fin[29]+alphavpar[14]*fin[28]+fin[15]*alphavpar[27]+alphavpar[0]*fin[26]+alphavpar[20]*fin[25]+alphavpar[21]*fin[24]+alphavpar[22]*fin[23]+alphavpar[1]*fin[19]+alphavpar[2]*fin[18]+alphavpar[3]*fin[17]+fin[4]*alphavpar[16]+alphavpar[6]*fin[11]+alphavpar[7]*fin[10]+alphavpar[8]*fin[9]); 
+  out[44] += 0.6846531968814574*(alphavpar[3]*fin[31]+alphavpar[7]*fin[30]+alphavpar[8]*fin[29]+alphavpar[0]*fin[28]+fin[11]*alphavpar[27]+alphavpar[14]*fin[26]+alphavpar[16]*fin[25]+alphavpar[1]*fin[24]+alphavpar[2]*fin[23]+fin[18]*alphavpar[22]+fin[19]*alphavpar[21]+fin[4]*alphavpar[20]+alphavpar[5]*fin[17]+alphavpar[6]*fin[15]+fin[9]*alphavpar[13]+fin[10]*alphavpar[12]); 
+  out[45] += 0.6846531968814574*(alphavpar[2]*fin[31]+alphavpar[6]*fin[30]+alphavpar[0]*fin[29]+alphavpar[8]*fin[28]+fin[10]*alphavpar[27]+alphavpar[13]*fin[26]+alphavpar[1]*fin[25]+alphavpar[16]*fin[24]+alphavpar[3]*fin[23]+fin[17]*alphavpar[22]+fin[4]*alphavpar[21]+fin[19]*alphavpar[20]+alphavpar[5]*fin[18]+alphavpar[7]*fin[15]+fin[9]*alphavpar[14]+fin[11]*alphavpar[12]); 
+  out[46] += 0.6846531968814574*(alphavpar[1]*fin[31]+alphavpar[0]*fin[30]+alphavpar[6]*fin[29]+alphavpar[7]*fin[28]+fin[9]*alphavpar[27]+alphavpar[12]*fin[26]+alphavpar[2]*fin[25]+alphavpar[3]*fin[24]+alphavpar[16]*fin[23]+fin[4]*alphavpar[22]+fin[17]*alphavpar[21]+fin[18]*alphavpar[20]+alphavpar[5]*fin[19]+alphavpar[8]*fin[15]+fin[10]*alphavpar[14]+fin[11]*alphavpar[13]); 
+  out[47] += 0.6846531968814573*(alphavpar[0]*fin[31]+alphavpar[1]*fin[30]+alphavpar[2]*fin[29]+alphavpar[3]*fin[28]+fin[4]*alphavpar[27]+alphavpar[5]*fin[26]+alphavpar[6]*fin[25]+alphavpar[7]*fin[24]+alphavpar[8]*fin[23]+fin[9]*alphavpar[22]+fin[10]*alphavpar[21]+fin[11]*alphavpar[20]+alphavpar[12]*fin[19]+alphavpar[13]*fin[18]+alphavpar[14]*fin[17]+fin[15]*alphavpar[16]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
new file mode 100644
index 0000000000..9c26ddd0c7
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
@@ -0,0 +1,25 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double q_, const double m_, const double *apardot,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // q_,m_: species charge and mass.
+  // apardot: time derivative of parallel component of magnetic vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  double alphavpar[6] = {0.}; 
+  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
+  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
+  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
+  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
+
+
+  out[2] += 0.8660254037844386*(alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[3] += 0.8660254037844387*(alphavpar[4]*fin[5]+fin[4]*alphavpar[5])+0.8660254037844386*(alphavpar[2]*fin[3]+fin[2]*alphavpar[3]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[4] += 1.7320508075688774*(alphavpar[3]*fin[5]+fin[3]*alphavpar[5])+1.7320508075688772*(alphavpar[2]*fin[4]+fin[2]*alphavpar[4])+1.9364916731037085*(alphavpar[1]*fin[3]+fin[1]*alphavpar[3]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[5] += 1.7320508075688772*(alphavpar[2]*fin[5]+fin[2]*alphavpar[5])+1.7320508075688774*(alphavpar[3]*fin[4]+fin[3]*alphavpar[4])+1.9364916731037085*(alphavpar[0]*fin[3]+fin[0]*alphavpar[3]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
new file mode 100644
index 0000000000..500c925030
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
@@ -0,0 +1,35 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, const double m_, const double *apardot,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // q_,m_: species charge and mass.
+  // apardot: time derivative of parallel component of magnetic vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  double alphavpar[12] = {0.}; 
+  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
+  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
+  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
+  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
+  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
+  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
+  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
+  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
+  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
+  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
+
+
+  out[2] += 0.6123724356957944*(alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[4] += 0.6123724356957944*(alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[6] += 0.6123724356957944*(alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[7] += 0.6123724356957944*(alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[8] += 1.224744871391589*(alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8])+1.369306393762915*(alphavpar[5]*fin[7]+fin[5]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[9] += 1.224744871391589*(alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8])+1.369306393762915*(alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[10] += 1.224744871391589*(alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8])+1.369306393762915*(alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
+  out[11] += 1.224744871391589*(alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8])+1.369306393762915*(alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
new file mode 100644
index 0000000000..856faccde1
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
@@ -0,0 +1,55 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, const double m_, const double *apardot,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // q_,m_: species charge and mass.
+  // apardot: time derivative of parallel component of magnetic vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  double alphavpar[24] = {0.}; 
+  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
+  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
+  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
+  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
+  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
+  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
+  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
+  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
+  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
+  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
+  alphavpar[12] = -((1.0*apardot[12]*q_)/m_); 
+  alphavpar[13] = -((1.0*apardot[13]*q_)/m_); 
+  alphavpar[14] = -((1.0*apardot[14]*q_)/m_); 
+  alphavpar[15] = -((1.0*apardot[15]*q_)/m_); 
+  alphavpar[16] = -((1.0*apardot[16]*q_)/m_); 
+  alphavpar[17] = -((1.0*apardot[17]*q_)/m_); 
+  alphavpar[18] = -((1.0*apardot[18]*q_)/m_); 
+  alphavpar[19] = -((1.0*apardot[19]*q_)/m_); 
+  alphavpar[20] = -((1.0*apardot[20]*q_)/m_); 
+  alphavpar[21] = -((1.0*apardot[21]*q_)/m_); 
+  alphavpar[22] = -((1.0*apardot[22]*q_)/m_); 
+  alphavpar[23] = -((1.0*apardot[23]*q_)/m_); 
+
+
+  out[3] += 0.4330127018922193*(alphavpar[23]*fin[23]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[19]*fin[19]+alphavpar[18]*fin[18]+alphavpar[17]*fin[17]+alphavpar[16]*fin[16]+alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[6] += 0.43301270189221935*(alphavpar[22]*fin[23]+fin[22]*alphavpar[23]+alphavpar[19]*fin[21]+fin[19]*alphavpar[21]+alphavpar[18]*fin[20]+fin[18]*alphavpar[20]+alphavpar[16]*fin[17]+fin[16]*alphavpar[17])+0.4330127018922193*(alphavpar[14]*fin[15]+fin[14]*alphavpar[15]+alphavpar[10]*fin[13]+fin[10]*alphavpar[13]+alphavpar[9]*fin[12]+fin[9]*alphavpar[12]+alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[7] += 0.43301270189221935*(alphavpar[21]*fin[23]+fin[21]*alphavpar[23]+alphavpar[19]*fin[22]+fin[19]*alphavpar[22]+alphavpar[17]*fin[20]+fin[17]*alphavpar[20]+alphavpar[16]*fin[18]+fin[16]*alphavpar[18])+0.4330127018922193*(alphavpar[13]*fin[15]+fin[13]*alphavpar[15]+alphavpar[10]*fin[14]+fin[10]*alphavpar[14]+alphavpar[8]*fin[12]+fin[8]*alphavpar[12]+alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[10] += 0.43301270189221935*(alphavpar[20]*fin[23]+fin[20]*alphavpar[23]+alphavpar[18]*fin[22]+fin[18]*alphavpar[22]+alphavpar[17]*fin[21]+fin[17]*alphavpar[21]+alphavpar[16]*fin[19]+fin[16]*alphavpar[19])+0.4330127018922193*(alphavpar[11]*fin[15]+fin[11]*alphavpar[15]+alphavpar[7]*fin[14]+fin[7]*alphavpar[14]+alphavpar[6]*fin[13]+fin[6]*alphavpar[13]+alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[3]*fin[10]+fin[3]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]); 
+  out[11] += 0.4330127018922193*(alphavpar[19]*fin[23]+fin[19]*alphavpar[23]+alphavpar[21]*fin[22]+fin[21]*alphavpar[22]+alphavpar[16]*fin[20]+fin[16]*alphavpar[20]+alphavpar[17]*fin[18]+fin[17]*alphavpar[18]+alphavpar[10]*fin[15]+fin[10]*alphavpar[15]+alphavpar[13]*fin[14]+fin[13]*alphavpar[14]+alphavpar[4]*fin[12]+fin[4]*alphavpar[12]+alphavpar[3]*fin[11]+fin[3]*alphavpar[11]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[13] += 0.4330127018922193*(alphavpar[18]*fin[23]+fin[18]*alphavpar[23]+alphavpar[20]*fin[22]+fin[20]*alphavpar[22]+alphavpar[16]*fin[21]+fin[16]*alphavpar[21]+alphavpar[17]*fin[19]+fin[17]*alphavpar[19]+alphavpar[7]*fin[15]+fin[7]*alphavpar[15]+alphavpar[11]*fin[14]+fin[11]*alphavpar[14]+alphavpar[3]*fin[13]+fin[3]*alphavpar[13]+alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[5]*fin[9]+fin[5]*alphavpar[9]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]); 
+  out[14] += 0.4330127018922193*(alphavpar[17]*fin[23]+fin[17]*alphavpar[23]+alphavpar[16]*fin[22]+fin[16]*alphavpar[22]+alphavpar[20]*fin[21]+fin[20]*alphavpar[21]+alphavpar[18]*fin[19]+fin[18]*alphavpar[19]+alphavpar[6]*fin[15]+fin[6]*alphavpar[15]+alphavpar[3]*fin[14]+fin[3]*alphavpar[14]+alphavpar[11]*fin[13]+fin[11]*alphavpar[13]+alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[0]*fin[9]+fin[0]*alphavpar[9]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]); 
+  out[15] += 0.43301270189221935*(alphavpar[16]*fin[23]+fin[16]*alphavpar[23]+alphavpar[17]*fin[22]+fin[17]*alphavpar[22]+alphavpar[18]*fin[21]+fin[18]*alphavpar[21]+alphavpar[19]*fin[20]+fin[19]*alphavpar[20])+0.4330127018922193*(alphavpar[3]*fin[15]+fin[3]*alphavpar[15]+alphavpar[6]*fin[14]+fin[6]*alphavpar[14]+alphavpar[7]*fin[13]+fin[7]*alphavpar[13]+alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[1]*fin[9]+fin[1]*alphavpar[9]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]); 
+  out[16] += 0.8660254037844387*(alphavpar[15]*fin[23]+fin[15]*alphavpar[23])+0.8660254037844386*(alphavpar[14]*fin[22]+fin[14]*alphavpar[22]+alphavpar[13]*fin[21]+fin[13]*alphavpar[21]+alphavpar[11]*fin[20]+fin[11]*alphavpar[20])+0.8660254037844387*(alphavpar[10]*fin[19]+fin[10]*alphavpar[19]+alphavpar[7]*fin[18]+fin[7]*alphavpar[18]+alphavpar[6]*fin[17]+fin[6]*alphavpar[17])+0.8660254037844386*(alphavpar[3]*fin[16]+fin[3]*alphavpar[16])+0.9682458365518543*(alphavpar[12]*fin[15]+fin[12]*alphavpar[15]+alphavpar[9]*fin[14]+fin[9]*alphavpar[14]+alphavpar[8]*fin[13]+fin[8]*alphavpar[13]+alphavpar[5]*fin[11]+fin[5]*alphavpar[11]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[17] += 0.8660254037844386*(alphavpar[14]*fin[23]+fin[14]*alphavpar[23])+0.8660254037844387*(alphavpar[15]*fin[22]+fin[15]*alphavpar[22]+alphavpar[10]*fin[21]+fin[10]*alphavpar[21]+alphavpar[7]*fin[20]+fin[7]*alphavpar[20])+0.8660254037844386*(alphavpar[13]*fin[19]+fin[13]*alphavpar[19]+alphavpar[11]*fin[18]+fin[11]*alphavpar[18]+alphavpar[3]*fin[17]+fin[3]*alphavpar[17])+0.8660254037844387*(alphavpar[6]*fin[16]+fin[6]*alphavpar[16])+0.9682458365518543*(alphavpar[9]*fin[15]+fin[9]*alphavpar[15]+alphavpar[12]*fin[14]+fin[12]*alphavpar[14]+alphavpar[4]*fin[13]+fin[4]*alphavpar[13]+alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[5]*fin[7]+fin[5]*alphavpar[7]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[18] += 0.8660254037844386*(alphavpar[13]*fin[23]+fin[13]*alphavpar[23])+0.8660254037844387*(alphavpar[10]*fin[22]+fin[10]*alphavpar[22]+alphavpar[15]*fin[21]+fin[15]*alphavpar[21]+alphavpar[6]*fin[20]+fin[6]*alphavpar[20])+0.8660254037844386*(alphavpar[14]*fin[19]+fin[14]*alphavpar[19]+alphavpar[3]*fin[18]+fin[3]*alphavpar[18]+alphavpar[11]*fin[17]+fin[11]*alphavpar[17])+0.8660254037844387*(alphavpar[7]*fin[16]+fin[7]*alphavpar[16])+0.9682458365518543*(alphavpar[8]*fin[15]+fin[8]*alphavpar[15]+alphavpar[4]*fin[14]+fin[4]*alphavpar[14]+alphavpar[12]*fin[13]+fin[12]*alphavpar[13]+alphavpar[1]*fin[11]+fin[1]*alphavpar[11]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
+  out[19] += 0.8660254037844386*(alphavpar[11]*fin[23]+fin[11]*alphavpar[23])+0.8660254037844387*(alphavpar[7]*fin[22]+fin[7]*alphavpar[22]+alphavpar[6]*fin[21]+fin[6]*alphavpar[21]+alphavpar[15]*fin[20]+fin[15]*alphavpar[20])+0.8660254037844386*(alphavpar[3]*fin[19]+fin[3]*alphavpar[19]+alphavpar[14]*fin[18]+fin[14]*alphavpar[18]+alphavpar[13]*fin[17]+fin[13]*alphavpar[17])+0.8660254037844387*(alphavpar[10]*fin[16]+fin[10]*alphavpar[16])+0.9682458365518543*(alphavpar[5]*fin[15]+fin[5]*alphavpar[15]+alphavpar[2]*fin[14]+fin[2]*alphavpar[14]+alphavpar[1]*fin[13]+fin[1]*alphavpar[13]+alphavpar[11]*fin[12]+fin[11]*alphavpar[12]+alphavpar[0]*fin[10]+fin[0]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
+  out[20] += 0.8660254037844387*(alphavpar[10]*fin[23]+fin[10]*alphavpar[23])+0.8660254037844386*(alphavpar[13]*fin[22]+fin[13]*alphavpar[22]+alphavpar[14]*fin[21]+fin[14]*alphavpar[21]+alphavpar[3]*fin[20]+fin[3]*alphavpar[20])+0.8660254037844387*(alphavpar[15]*fin[19]+fin[15]*alphavpar[19]+alphavpar[6]*fin[18]+fin[6]*alphavpar[18]+alphavpar[7]*fin[17]+fin[7]*alphavpar[17])+0.8660254037844386*(alphavpar[11]*fin[16]+fin[11]*alphavpar[16])+0.9682458365518543*(alphavpar[4]*fin[15]+fin[4]*alphavpar[15]+alphavpar[8]*fin[14]+fin[8]*alphavpar[14]+alphavpar[9]*fin[13]+fin[9]*alphavpar[13]+alphavpar[10]*fin[12]+fin[10]*alphavpar[12]+alphavpar[0]*fin[11]+fin[0]*alphavpar[11]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]); 
+  out[21] += 0.8660254037844387*(alphavpar[7]*fin[23]+fin[7]*alphavpar[23])+0.8660254037844386*(alphavpar[11]*fin[22]+fin[11]*alphavpar[22]+alphavpar[3]*fin[21]+fin[3]*alphavpar[21]+alphavpar[14]*fin[20]+fin[14]*alphavpar[20])+0.8660254037844387*(alphavpar[6]*fin[19]+fin[6]*alphavpar[19]+alphavpar[15]*fin[18]+fin[15]*alphavpar[18]+alphavpar[10]*fin[17]+fin[10]*alphavpar[17])+0.8660254037844386*(alphavpar[13]*fin[16]+fin[13]*alphavpar[16])+0.9682458365518543*(alphavpar[2]*fin[15]+fin[2]*alphavpar[15]+alphavpar[5]*fin[14]+fin[5]*alphavpar[14]+alphavpar[0]*fin[13]+fin[0]*alphavpar[13]+alphavpar[7]*fin[12]+fin[7]*alphavpar[12]+alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[1]*fin[10]+fin[1]*alphavpar[10]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]); 
+  out[22] += 0.8660254037844387*(alphavpar[6]*fin[23]+fin[6]*alphavpar[23])+0.8660254037844386*(alphavpar[3]*fin[22]+fin[3]*alphavpar[22]+alphavpar[11]*fin[21]+fin[11]*alphavpar[21]+alphavpar[13]*fin[20]+fin[13]*alphavpar[20])+0.8660254037844387*(alphavpar[7]*fin[19]+fin[7]*alphavpar[19]+alphavpar[10]*fin[18]+fin[10]*alphavpar[18]+alphavpar[15]*fin[17]+fin[15]*alphavpar[17])+0.8660254037844386*(alphavpar[14]*fin[16]+fin[14]*alphavpar[16])+0.9682458365518543*(alphavpar[1]*fin[15]+fin[1]*alphavpar[15]+alphavpar[0]*fin[14]+fin[0]*alphavpar[14]+alphavpar[5]*fin[13]+fin[5]*alphavpar[13]+alphavpar[6]*fin[12]+fin[6]*alphavpar[12]+alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[3]*fin[9]+fin[3]*alphavpar[9]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]); 
+  out[23] += 0.8660254037844386*(alphavpar[3]*fin[23]+fin[3]*alphavpar[23])+0.8660254037844387*(alphavpar[6]*fin[22]+fin[6]*alphavpar[22]+alphavpar[7]*fin[21]+fin[7]*alphavpar[21]+alphavpar[10]*fin[20]+fin[10]*alphavpar[20])+0.8660254037844386*(alphavpar[11]*fin[19]+fin[11]*alphavpar[19]+alphavpar[13]*fin[18]+fin[13]*alphavpar[18]+alphavpar[14]*fin[17]+fin[14]*alphavpar[17])+0.8660254037844387*(alphavpar[15]*fin[16]+fin[15]*alphavpar[16])+0.9682458365518543*(alphavpar[0]*fin[15]+fin[0]*alphavpar[15]+alphavpar[1]*fin[14]+fin[1]*alphavpar[14]+alphavpar[2]*fin[13]+fin[2]*alphavpar[13]+alphavpar[3]*fin[12]+fin[3]*alphavpar[12]+alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[5]*fin[10]+fin[5]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
new file mode 100644
index 0000000000..805c88b9b2
--- /dev/null
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
@@ -0,0 +1,95 @@
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, const double m_, const double *apardot,
+    const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  // q_,m_: species charge and mass.
+  // apardot: time derivative of parallel component of magnetic vector potential.
+  // fin: Distribution function.
+  // out: output increment.
+
+  double alphavpar[48] = {0.}; 
+  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
+  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
+  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
+  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
+  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
+  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
+  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
+  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
+  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
+  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
+  alphavpar[12] = -((1.0*apardot[12]*q_)/m_); 
+  alphavpar[13] = -((1.0*apardot[13]*q_)/m_); 
+  alphavpar[14] = -((1.0*apardot[14]*q_)/m_); 
+  alphavpar[15] = -((1.0*apardot[15]*q_)/m_); 
+  alphavpar[16] = -((1.0*apardot[16]*q_)/m_); 
+  alphavpar[17] = -((1.0*apardot[17]*q_)/m_); 
+  alphavpar[18] = -((1.0*apardot[18]*q_)/m_); 
+  alphavpar[19] = -((1.0*apardot[19]*q_)/m_); 
+  alphavpar[20] = -((1.0*apardot[20]*q_)/m_); 
+  alphavpar[21] = -((1.0*apardot[21]*q_)/m_); 
+  alphavpar[22] = -((1.0*apardot[22]*q_)/m_); 
+  alphavpar[23] = -((1.0*apardot[23]*q_)/m_); 
+  alphavpar[24] = -((1.0*apardot[24]*q_)/m_); 
+  alphavpar[25] = -((1.0*apardot[25]*q_)/m_); 
+  alphavpar[26] = -((1.0*apardot[26]*q_)/m_); 
+  alphavpar[27] = -((1.0*apardot[27]*q_)/m_); 
+  alphavpar[28] = -((1.0*apardot[28]*q_)/m_); 
+  alphavpar[29] = -((1.0*apardot[29]*q_)/m_); 
+  alphavpar[30] = -((1.0*apardot[30]*q_)/m_); 
+  alphavpar[31] = -((1.0*apardot[31]*q_)/m_); 
+  alphavpar[32] = -((1.0*apardot[32]*q_)/m_); 
+  alphavpar[33] = -((1.0*apardot[33]*q_)/m_); 
+  alphavpar[34] = -((1.0*apardot[34]*q_)/m_); 
+  alphavpar[35] = -((1.0*apardot[35]*q_)/m_); 
+  alphavpar[36] = -((1.0*apardot[36]*q_)/m_); 
+  alphavpar[37] = -((1.0*apardot[37]*q_)/m_); 
+  alphavpar[38] = -((1.0*apardot[38]*q_)/m_); 
+  alphavpar[39] = -((1.0*apardot[39]*q_)/m_); 
+  alphavpar[40] = -((1.0*apardot[40]*q_)/m_); 
+  alphavpar[41] = -((1.0*apardot[41]*q_)/m_); 
+  alphavpar[42] = -((1.0*apardot[42]*q_)/m_); 
+  alphavpar[43] = -((1.0*apardot[43]*q_)/m_); 
+  alphavpar[44] = -((1.0*apardot[44]*q_)/m_); 
+  alphavpar[45] = -((1.0*apardot[45]*q_)/m_); 
+  alphavpar[46] = -((1.0*apardot[46]*q_)/m_); 
+  alphavpar[47] = -((1.0*apardot[47]*q_)/m_); 
+
+
+  out[4] += 0.3061862178478971*(alphavpar[47]*fin[47]+alphavpar[46]*fin[46]+alphavpar[45]*fin[45]+alphavpar[44]*fin[44]+alphavpar[43]*fin[43]+alphavpar[42]*fin[42]+alphavpar[41]*fin[41]+alphavpar[40]*fin[40]+alphavpar[39]*fin[39]+alphavpar[38]*fin[38]+alphavpar[37]*fin[37]+alphavpar[36]*fin[36]+alphavpar[35]*fin[35]+alphavpar[34]*fin[34]+alphavpar[33]*fin[33]+alphavpar[32]*fin[32]+alphavpar[31]*fin[31]+alphavpar[30]*fin[30]+alphavpar[29]*fin[29]+alphavpar[28]*fin[28]+alphavpar[27]*fin[27]+alphavpar[26]*fin[26]+alphavpar[25]*fin[25]+alphavpar[24]*fin[24]+alphavpar[23]*fin[23]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[19]*fin[19]+alphavpar[18]*fin[18]+alphavpar[17]*fin[17]+alphavpar[16]*fin[16]+alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[9] += 0.3061862178478971*(alphavpar[46]*fin[47]+fin[46]*alphavpar[47]+alphavpar[42]*fin[45]+fin[42]*alphavpar[45]+alphavpar[41]*fin[44]+fin[41]*alphavpar[44]+alphavpar[39]*fin[43]+fin[39]*alphavpar[43]+alphavpar[36]*fin[40]+fin[36]*alphavpar[40]+alphavpar[35]*fin[38]+fin[35]*alphavpar[38]+alphavpar[34]*fin[37]+fin[34]*alphavpar[37]+alphavpar[32]*fin[33]+fin[32]*alphavpar[33]+alphavpar[30]*fin[31]+fin[30]*alphavpar[31]+alphavpar[25]*fin[29]+fin[25]*alphavpar[29]+alphavpar[24]*fin[28]+fin[24]*alphavpar[28]+alphavpar[22]*fin[27]+fin[22]*alphavpar[27]+alphavpar[19]*fin[26]+fin[19]*alphavpar[26]+alphavpar[15]*fin[23]+fin[15]*alphavpar[23]+alphavpar[14]*fin[21]+fin[14]*alphavpar[21]+alphavpar[13]*fin[20]+fin[13]*alphavpar[20]+alphavpar[11]*fin[18]+fin[11]*alphavpar[18]+alphavpar[10]*fin[17]+fin[10]*alphavpar[17]+alphavpar[8]*fin[16]+fin[8]*alphavpar[16]+alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[10] += 0.3061862178478971*(alphavpar[45]*fin[47]+fin[45]*alphavpar[47]+alphavpar[42]*fin[46]+fin[42]*alphavpar[46]+alphavpar[40]*fin[44]+fin[40]*alphavpar[44]+alphavpar[38]*fin[43]+fin[38]*alphavpar[43]+alphavpar[36]*fin[41]+fin[36]*alphavpar[41]+alphavpar[35]*fin[39]+fin[35]*alphavpar[39]+alphavpar[33]*fin[37]+fin[33]*alphavpar[37]+alphavpar[32]*fin[34]+fin[32]*alphavpar[34]+alphavpar[29]*fin[31]+fin[29]*alphavpar[31]+alphavpar[25]*fin[30]+fin[25]*alphavpar[30]+alphavpar[23]*fin[28]+fin[23]*alphavpar[28]+alphavpar[21]*fin[27]+fin[21]*alphavpar[27]+alphavpar[18]*fin[26]+fin[18]*alphavpar[26]+alphavpar[15]*fin[24]+fin[15]*alphavpar[24]+alphavpar[14]*fin[22]+fin[14]*alphavpar[22]+alphavpar[12]*fin[20]+fin[12]*alphavpar[20]+alphavpar[11]*fin[19]+fin[11]*alphavpar[19]+alphavpar[9]*fin[17]+fin[9]*alphavpar[17]+alphavpar[7]*fin[16]+fin[7]*alphavpar[16]+alphavpar[5]*fin[13]+fin[5]*alphavpar[13]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[11] += 0.3061862178478971*(alphavpar[44]*fin[47]+fin[44]*alphavpar[47]+alphavpar[41]*fin[46]+fin[41]*alphavpar[46]+alphavpar[40]*fin[45]+fin[40]*alphavpar[45]+alphavpar[37]*fin[43]+fin[37]*alphavpar[43]+alphavpar[36]*fin[42]+fin[36]*alphavpar[42]+alphavpar[34]*fin[39]+fin[34]*alphavpar[39]+alphavpar[33]*fin[38]+fin[33]*alphavpar[38]+alphavpar[32]*fin[35]+fin[32]*alphavpar[35]+alphavpar[28]*fin[31]+fin[28]*alphavpar[31]+alphavpar[24]*fin[30]+fin[24]*alphavpar[30]+alphavpar[23]*fin[29]+fin[23]*alphavpar[29]+alphavpar[20]*fin[27]+fin[20]*alphavpar[27]+alphavpar[17]*fin[26]+fin[17]*alphavpar[26]+alphavpar[15]*fin[25]+fin[15]*alphavpar[25]+alphavpar[13]*fin[22]+fin[13]*alphavpar[22]+alphavpar[12]*fin[21]+fin[12]*alphavpar[21]+alphavpar[10]*fin[19]+fin[10]*alphavpar[19]+alphavpar[9]*fin[18]+fin[9]*alphavpar[18]+alphavpar[6]*fin[16]+fin[6]*alphavpar[16]+alphavpar[5]*fin[14]+fin[5]*alphavpar[14]+alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[15] += 0.3061862178478971*(alphavpar[43]*fin[47]+fin[43]*alphavpar[47]+alphavpar[39]*fin[46]+fin[39]*alphavpar[46]+alphavpar[38]*fin[45]+fin[38]*alphavpar[45]+alphavpar[37]*fin[44]+fin[37]*alphavpar[44]+alphavpar[35]*fin[42]+fin[35]*alphavpar[42]+alphavpar[34]*fin[41]+fin[34]*alphavpar[41]+alphavpar[33]*fin[40]+fin[33]*alphavpar[40]+alphavpar[32]*fin[36]+fin[32]*alphavpar[36]+alphavpar[26]*fin[31]+fin[26]*alphavpar[31]+alphavpar[19]*fin[30]+fin[19]*alphavpar[30]+alphavpar[18]*fin[29]+fin[18]*alphavpar[29]+alphavpar[17]*fin[28]+fin[17]*alphavpar[28]+alphavpar[16]*fin[27]+fin[16]*alphavpar[27]+alphavpar[11]*fin[25]+fin[11]*alphavpar[25]+alphavpar[10]*fin[24]+fin[10]*alphavpar[24]+alphavpar[9]*fin[23]+fin[9]*alphavpar[23]+alphavpar[8]*fin[22]+fin[8]*alphavpar[22]+alphavpar[7]*fin[21]+fin[7]*alphavpar[21]+alphavpar[6]*fin[20]+fin[6]*alphavpar[20]+alphavpar[4]*fin[15]+fin[4]*alphavpar[15]+alphavpar[3]*fin[14]+fin[3]*alphavpar[14]+alphavpar[2]*fin[13]+fin[2]*alphavpar[13]+alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]); 
+  out[17] += 0.3061862178478971*(alphavpar[42]*fin[47]+fin[42]*alphavpar[47]+alphavpar[45]*fin[46]+fin[45]*alphavpar[46]+alphavpar[36]*fin[44]+fin[36]*alphavpar[44]+alphavpar[35]*fin[43]+fin[35]*alphavpar[43]+alphavpar[40]*fin[41]+fin[40]*alphavpar[41]+alphavpar[38]*fin[39]+fin[38]*alphavpar[39]+alphavpar[32]*fin[37]+fin[32]*alphavpar[37]+alphavpar[33]*fin[34]+fin[33]*alphavpar[34]+alphavpar[25]*fin[31]+fin[25]*alphavpar[31]+alphavpar[29]*fin[30]+fin[29]*alphavpar[30]+alphavpar[15]*fin[28]+fin[15]*alphavpar[28]+alphavpar[14]*fin[27]+fin[14]*alphavpar[27]+alphavpar[11]*fin[26]+fin[11]*alphavpar[26]+alphavpar[23]*fin[24]+fin[23]*alphavpar[24]+alphavpar[21]*fin[22]+fin[21]*alphavpar[22]+alphavpar[5]*fin[20]+fin[5]*alphavpar[20]+alphavpar[18]*fin[19]+fin[18]*alphavpar[19]+alphavpar[4]*fin[17]+fin[4]*alphavpar[17]+alphavpar[3]*fin[16]+fin[3]*alphavpar[16]+alphavpar[12]*fin[13]+fin[12]*alphavpar[13]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[18] += 0.3061862178478971*(alphavpar[41]*fin[47]+fin[41]*alphavpar[47]+alphavpar[44]*fin[46]+fin[44]*alphavpar[46]+alphavpar[36]*fin[45]+fin[36]*alphavpar[45]+alphavpar[34]*fin[43]+fin[34]*alphavpar[43]+alphavpar[40]*fin[42]+fin[40]*alphavpar[42]+alphavpar[37]*fin[39]+fin[37]*alphavpar[39]+alphavpar[32]*fin[38]+fin[32]*alphavpar[38]+alphavpar[33]*fin[35]+fin[33]*alphavpar[35]+alphavpar[24]*fin[31]+fin[24]*alphavpar[31]+alphavpar[28]*fin[30]+fin[28]*alphavpar[30]+alphavpar[15]*fin[29]+fin[15]*alphavpar[29]+alphavpar[13]*fin[27]+fin[13]*alphavpar[27]+alphavpar[10]*fin[26]+fin[10]*alphavpar[26]+alphavpar[23]*fin[25]+fin[23]*alphavpar[25]+alphavpar[20]*fin[22]+fin[20]*alphavpar[22]+alphavpar[5]*fin[21]+fin[5]*alphavpar[21]+alphavpar[17]*fin[19]+fin[17]*alphavpar[19]+alphavpar[4]*fin[18]+fin[4]*alphavpar[18]+alphavpar[2]*fin[16]+fin[2]*alphavpar[16]+alphavpar[12]*fin[14]+fin[12]*alphavpar[14]+alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[19] += 0.3061862178478971*(alphavpar[40]*fin[47]+fin[40]*alphavpar[47]+alphavpar[36]*fin[46]+fin[36]*alphavpar[46]+alphavpar[44]*fin[45]+fin[44]*alphavpar[45]+alphavpar[33]*fin[43]+fin[33]*alphavpar[43]+alphavpar[41]*fin[42]+fin[41]*alphavpar[42]+alphavpar[32]*fin[39]+fin[32]*alphavpar[39]+alphavpar[37]*fin[38]+fin[37]*alphavpar[38]+alphavpar[34]*fin[35]+fin[34]*alphavpar[35]+alphavpar[23]*fin[31]+fin[23]*alphavpar[31]+alphavpar[15]*fin[30]+fin[15]*alphavpar[30]+alphavpar[28]*fin[29]+fin[28]*alphavpar[29]+alphavpar[12]*fin[27]+fin[12]*alphavpar[27]+alphavpar[9]*fin[26]+fin[9]*alphavpar[26]+alphavpar[24]*fin[25]+fin[24]*alphavpar[25]+alphavpar[5]*fin[22]+fin[5]*alphavpar[22]+alphavpar[20]*fin[21]+fin[20]*alphavpar[21]+alphavpar[4]*fin[19]+fin[4]*alphavpar[19]+alphavpar[17]*fin[18]+fin[17]*alphavpar[18]+alphavpar[1]*fin[16]+fin[1]*alphavpar[16]+alphavpar[13]*fin[14]+fin[13]*alphavpar[14]+alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
+  out[23] += 0.3061862178478971*(alphavpar[39]*fin[47]+fin[39]*alphavpar[47]+alphavpar[43]*fin[46]+fin[43]*alphavpar[46]+alphavpar[35]*fin[45]+fin[35]*alphavpar[45]+alphavpar[34]*fin[44]+fin[34]*alphavpar[44]+alphavpar[38]*fin[42]+fin[38]*alphavpar[42]+alphavpar[37]*fin[41]+fin[37]*alphavpar[41]+alphavpar[32]*fin[40]+fin[32]*alphavpar[40]+alphavpar[33]*fin[36]+fin[33]*alphavpar[36]+alphavpar[19]*fin[31]+fin[19]*alphavpar[31]+alphavpar[26]*fin[30]+fin[26]*alphavpar[30]+alphavpar[11]*fin[29]+fin[11]*alphavpar[29]+alphavpar[10]*fin[28]+fin[10]*alphavpar[28]+alphavpar[8]*fin[27]+fin[8]*alphavpar[27]+alphavpar[18]*fin[25]+fin[18]*alphavpar[25]+alphavpar[17]*fin[24]+fin[17]*alphavpar[24]+alphavpar[4]*fin[23]+fin[4]*alphavpar[23]+alphavpar[16]*fin[22]+fin[16]*alphavpar[22]+alphavpar[3]*fin[21]+fin[3]*alphavpar[21]+alphavpar[2]*fin[20]+fin[2]*alphavpar[20]+alphavpar[9]*fin[15]+fin[9]*alphavpar[15]+alphavpar[7]*fin[14]+fin[7]*alphavpar[14]+alphavpar[6]*fin[13]+fin[6]*alphavpar[13]+alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]); 
+  out[24] += 0.3061862178478971*(alphavpar[38]*fin[47]+fin[38]*alphavpar[47]+alphavpar[35]*fin[46]+fin[35]*alphavpar[46]+alphavpar[43]*fin[45]+fin[43]*alphavpar[45]+alphavpar[33]*fin[44]+fin[33]*alphavpar[44]+alphavpar[39]*fin[42]+fin[39]*alphavpar[42]+alphavpar[32]*fin[41]+fin[32]*alphavpar[41]+alphavpar[37]*fin[40]+fin[37]*alphavpar[40]+alphavpar[34]*fin[36]+fin[34]*alphavpar[36]+alphavpar[18]*fin[31]+fin[18]*alphavpar[31]+alphavpar[11]*fin[30]+fin[11]*alphavpar[30]+alphavpar[26]*fin[29]+fin[26]*alphavpar[29]+alphavpar[9]*fin[28]+fin[9]*alphavpar[28]+alphavpar[7]*fin[27]+fin[7]*alphavpar[27]+alphavpar[19]*fin[25]+fin[19]*alphavpar[25]+alphavpar[4]*fin[24]+fin[4]*alphavpar[24]+alphavpar[17]*fin[23]+fin[17]*alphavpar[23]+alphavpar[3]*fin[22]+fin[3]*alphavpar[22]+alphavpar[16]*fin[21]+fin[16]*alphavpar[21]+alphavpar[1]*fin[20]+fin[1]*alphavpar[20]+alphavpar[10]*fin[15]+fin[10]*alphavpar[15]+alphavpar[8]*fin[14]+fin[8]*alphavpar[14]+alphavpar[0]*fin[13]+fin[0]*alphavpar[13]+alphavpar[6]*fin[12]+fin[6]*alphavpar[12]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]); 
+  out[25] += 0.3061862178478971*(alphavpar[37]*fin[47]+fin[37]*alphavpar[47]+alphavpar[34]*fin[46]+fin[34]*alphavpar[46]+alphavpar[33]*fin[45]+fin[33]*alphavpar[45]+alphavpar[43]*fin[44]+fin[43]*alphavpar[44]+alphavpar[32]*fin[42]+fin[32]*alphavpar[42]+alphavpar[39]*fin[41]+fin[39]*alphavpar[41]+alphavpar[38]*fin[40]+fin[38]*alphavpar[40]+alphavpar[35]*fin[36]+fin[35]*alphavpar[36]+alphavpar[17]*fin[31]+fin[17]*alphavpar[31]+alphavpar[10]*fin[30]+fin[10]*alphavpar[30]+alphavpar[9]*fin[29]+fin[9]*alphavpar[29]+alphavpar[26]*fin[28]+fin[26]*alphavpar[28]+alphavpar[6]*fin[27]+fin[6]*alphavpar[27]+alphavpar[4]*fin[25]+fin[4]*alphavpar[25]+alphavpar[19]*fin[24]+fin[19]*alphavpar[24]+alphavpar[18]*fin[23]+fin[18]*alphavpar[23]+alphavpar[2]*fin[22]+fin[2]*alphavpar[22]+alphavpar[1]*fin[21]+fin[1]*alphavpar[21]+alphavpar[16]*fin[20]+fin[16]*alphavpar[20]+alphavpar[11]*fin[15]+fin[11]*alphavpar[15]+alphavpar[0]*fin[14]+fin[0]*alphavpar[14]+alphavpar[8]*fin[13]+fin[8]*alphavpar[13]+alphavpar[7]*fin[12]+fin[7]*alphavpar[12]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]); 
+  out[26] += 0.3061862178478971*(alphavpar[36]*fin[47]+fin[36]*alphavpar[47]+alphavpar[40]*fin[46]+fin[40]*alphavpar[46]+alphavpar[41]*fin[45]+fin[41]*alphavpar[45]+alphavpar[42]*fin[44]+fin[42]*alphavpar[44]+alphavpar[32]*fin[43]+fin[32]*alphavpar[43]+alphavpar[33]*fin[39]+fin[33]*alphavpar[39]+alphavpar[34]*fin[38]+fin[34]*alphavpar[38]+alphavpar[35]*fin[37]+fin[35]*alphavpar[37]+alphavpar[15]*fin[31]+fin[15]*alphavpar[31]+alphavpar[23]*fin[30]+fin[23]*alphavpar[30]+alphavpar[24]*fin[29]+fin[24]*alphavpar[29]+alphavpar[25]*fin[28]+fin[25]*alphavpar[28]+alphavpar[5]*fin[27]+fin[5]*alphavpar[27]+alphavpar[4]*fin[26]+fin[4]*alphavpar[26]+alphavpar[12]*fin[22]+fin[12]*alphavpar[22]+alphavpar[13]*fin[21]+fin[13]*alphavpar[21]+alphavpar[14]*fin[20]+fin[14]*alphavpar[20]+alphavpar[9]*fin[19]+fin[9]*alphavpar[19]+alphavpar[10]*fin[18]+fin[10]*alphavpar[18]+alphavpar[11]*fin[17]+fin[11]*alphavpar[17]+alphavpar[0]*fin[16]+fin[0]*alphavpar[16]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]); 
+  out[28] += 0.3061862178478971*(alphavpar[35]*fin[47]+fin[35]*alphavpar[47]+alphavpar[38]*fin[46]+fin[38]*alphavpar[46]+alphavpar[39]*fin[45]+fin[39]*alphavpar[45]+alphavpar[32]*fin[44]+fin[32]*alphavpar[44]+alphavpar[42]*fin[43]+fin[42]*alphavpar[43]+alphavpar[33]*fin[41]+fin[33]*alphavpar[41]+alphavpar[34]*fin[40]+fin[34]*alphavpar[40]+alphavpar[36]*fin[37]+fin[36]*alphavpar[37]+alphavpar[11]*fin[31]+fin[11]*alphavpar[31]+alphavpar[18]*fin[30]+fin[18]*alphavpar[30]+alphavpar[19]*fin[29]+fin[19]*alphavpar[29]+alphavpar[4]*fin[28]+fin[4]*alphavpar[28]+alphavpar[3]*fin[27]+fin[3]*alphavpar[27]+alphavpar[25]*fin[26]+fin[25]*alphavpar[26]+alphavpar[9]*fin[24]+fin[9]*alphavpar[24]+alphavpar[10]*fin[23]+fin[10]*alphavpar[23]+alphavpar[7]*fin[22]+fin[7]*alphavpar[22]+alphavpar[8]*fin[21]+fin[8]*alphavpar[21]+alphavpar[0]*fin[20]+fin[0]*alphavpar[20]+alphavpar[15]*fin[17]+fin[15]*alphavpar[17]+alphavpar[14]*fin[16]+fin[14]*alphavpar[16]+alphavpar[1]*fin[13]+fin[1]*alphavpar[13]+alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]); 
+  out[29] += 0.3061862178478971*(alphavpar[34]*fin[47]+fin[34]*alphavpar[47]+alphavpar[37]*fin[46]+fin[37]*alphavpar[46]+alphavpar[32]*fin[45]+fin[32]*alphavpar[45]+alphavpar[39]*fin[44]+fin[39]*alphavpar[44]+alphavpar[41]*fin[43]+fin[41]*alphavpar[43]+alphavpar[33]*fin[42]+fin[33]*alphavpar[42]+alphavpar[35]*fin[40]+fin[35]*alphavpar[40]+alphavpar[36]*fin[38]+fin[36]*alphavpar[38]+alphavpar[10]*fin[31]+fin[10]*alphavpar[31]+alphavpar[17]*fin[30]+fin[17]*alphavpar[30]+alphavpar[4]*fin[29]+fin[4]*alphavpar[29]+alphavpar[19]*fin[28]+fin[19]*alphavpar[28]+alphavpar[2]*fin[27]+fin[2]*alphavpar[27]+alphavpar[24]*fin[26]+fin[24]*alphavpar[26]+alphavpar[9]*fin[25]+fin[9]*alphavpar[25]+alphavpar[11]*fin[23]+fin[11]*alphavpar[23]+alphavpar[6]*fin[22]+fin[6]*alphavpar[22]+alphavpar[0]*fin[21]+fin[0]*alphavpar[21]+alphavpar[8]*fin[20]+fin[8]*alphavpar[20]+alphavpar[15]*fin[18]+fin[15]*alphavpar[18]+alphavpar[13]*fin[16]+fin[13]*alphavpar[16]+alphavpar[1]*fin[14]+fin[1]*alphavpar[14]+alphavpar[3]*fin[12]+fin[3]*alphavpar[12]+alphavpar[5]*fin[7]+fin[5]*alphavpar[7]); 
+  out[30] += 0.3061862178478971*(alphavpar[33]*fin[47]+fin[33]*alphavpar[47]+alphavpar[32]*fin[46]+fin[32]*alphavpar[46]+alphavpar[37]*fin[45]+fin[37]*alphavpar[45]+alphavpar[38]*fin[44]+fin[38]*alphavpar[44]+alphavpar[40]*fin[43]+fin[40]*alphavpar[43]+alphavpar[34]*fin[42]+fin[34]*alphavpar[42]+alphavpar[35]*fin[41]+fin[35]*alphavpar[41]+alphavpar[36]*fin[39]+fin[36]*alphavpar[39]+alphavpar[9]*fin[31]+fin[9]*alphavpar[31]+alphavpar[4]*fin[30]+fin[4]*alphavpar[30]+alphavpar[17]*fin[29]+fin[17]*alphavpar[29]+alphavpar[18]*fin[28]+fin[18]*alphavpar[28]+alphavpar[1]*fin[27]+fin[1]*alphavpar[27]+alphavpar[23]*fin[26]+fin[23]*alphavpar[26]+alphavpar[10]*fin[25]+fin[10]*alphavpar[25]+alphavpar[11]*fin[24]+fin[11]*alphavpar[24]+alphavpar[0]*fin[22]+fin[0]*alphavpar[22]+alphavpar[6]*fin[21]+fin[6]*alphavpar[21]+alphavpar[7]*fin[20]+fin[7]*alphavpar[20]+alphavpar[15]*fin[19]+fin[15]*alphavpar[19]+alphavpar[12]*fin[16]+fin[12]*alphavpar[16]+alphavpar[2]*fin[14]+fin[2]*alphavpar[14]+alphavpar[3]*fin[13]+fin[3]*alphavpar[13]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]); 
+  out[31] += 0.3061862178478971*(alphavpar[32]*fin[47]+fin[32]*alphavpar[47]+alphavpar[33]*fin[46]+fin[33]*alphavpar[46]+alphavpar[34]*fin[45]+fin[34]*alphavpar[45]+alphavpar[35]*fin[44]+fin[35]*alphavpar[44]+alphavpar[36]*fin[43]+fin[36]*alphavpar[43]+alphavpar[37]*fin[42]+fin[37]*alphavpar[42]+alphavpar[38]*fin[41]+fin[38]*alphavpar[41]+alphavpar[39]*fin[40]+fin[39]*alphavpar[40]+alphavpar[4]*fin[31]+fin[4]*alphavpar[31]+alphavpar[9]*fin[30]+fin[9]*alphavpar[30]+alphavpar[10]*fin[29]+fin[10]*alphavpar[29]+alphavpar[11]*fin[28]+fin[11]*alphavpar[28]+alphavpar[0]*fin[27]+fin[0]*alphavpar[27]+alphavpar[15]*fin[26]+fin[15]*alphavpar[26]+alphavpar[17]*fin[25]+fin[17]*alphavpar[25]+alphavpar[18]*fin[24]+fin[18]*alphavpar[24]+alphavpar[19]*fin[23]+fin[19]*alphavpar[23]+alphavpar[1]*fin[22]+fin[1]*alphavpar[22]+alphavpar[2]*fin[21]+fin[2]*alphavpar[21]+alphavpar[3]*fin[20]+fin[3]*alphavpar[20]+alphavpar[5]*fin[16]+fin[5]*alphavpar[16]+alphavpar[6]*fin[14]+fin[6]*alphavpar[14]+alphavpar[7]*fin[13]+fin[7]*alphavpar[13]+alphavpar[8]*fin[12]+fin[8]*alphavpar[12]); 
+  out[32] += 0.6123724356957944*(alphavpar[31]*fin[47]+fin[31]*alphavpar[47]+alphavpar[30]*fin[46]+fin[30]*alphavpar[46]+alphavpar[29]*fin[45]+fin[29]*alphavpar[45]+alphavpar[28]*fin[44]+fin[28]*alphavpar[44]+alphavpar[26]*fin[43]+fin[26]*alphavpar[43]+alphavpar[25]*fin[42]+fin[25]*alphavpar[42]+alphavpar[24]*fin[41]+fin[24]*alphavpar[41]+alphavpar[23]*fin[40]+fin[23]*alphavpar[40]+alphavpar[19]*fin[39]+fin[19]*alphavpar[39]+alphavpar[18]*fin[38]+fin[18]*alphavpar[38]+alphavpar[17]*fin[37]+fin[17]*alphavpar[37]+alphavpar[15]*fin[36]+fin[15]*alphavpar[36]+alphavpar[11]*fin[35]+fin[11]*alphavpar[35]+alphavpar[10]*fin[34]+fin[10]*alphavpar[34]+alphavpar[9]*fin[33]+fin[9]*alphavpar[33]+alphavpar[4]*fin[32]+fin[4]*alphavpar[32])+0.6846531968814573*(alphavpar[27]*fin[31]+fin[27]*alphavpar[31]+alphavpar[22]*fin[30]+fin[22]*alphavpar[30]+alphavpar[21]*fin[29]+fin[21]*alphavpar[29]+alphavpar[20]*fin[28]+fin[20]*alphavpar[28]+alphavpar[16]*fin[26]+fin[16]*alphavpar[26]+alphavpar[14]*fin[25]+fin[14]*alphavpar[25]+alphavpar[13]*fin[24]+fin[13]*alphavpar[24]+alphavpar[12]*fin[23]+fin[12]*alphavpar[23]+alphavpar[8]*fin[19]+fin[8]*alphavpar[19]+alphavpar[7]*fin[18]+fin[7]*alphavpar[18]+alphavpar[6]*fin[17]+fin[6]*alphavpar[17]+alphavpar[5]*fin[15]+fin[5]*alphavpar[15]+alphavpar[3]*fin[11]+fin[3]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[1]*fin[9]+fin[1]*alphavpar[9]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]); 
+  out[33] += 0.6123724356957944*(alphavpar[30]*fin[47]+fin[30]*alphavpar[47]+alphavpar[31]*fin[46]+fin[31]*alphavpar[46]+alphavpar[25]*fin[45]+fin[25]*alphavpar[45]+alphavpar[24]*fin[44]+fin[24]*alphavpar[44]+alphavpar[19]*fin[43]+fin[19]*alphavpar[43]+alphavpar[29]*fin[42]+fin[29]*alphavpar[42]+alphavpar[28]*fin[41]+fin[28]*alphavpar[41]+alphavpar[15]*fin[40]+fin[15]*alphavpar[40]+alphavpar[26]*fin[39]+fin[26]*alphavpar[39]+alphavpar[11]*fin[38]+fin[11]*alphavpar[38]+alphavpar[10]*fin[37]+fin[10]*alphavpar[37]+alphavpar[23]*fin[36]+fin[23]*alphavpar[36]+alphavpar[18]*fin[35]+fin[18]*alphavpar[35]+alphavpar[17]*fin[34]+fin[17]*alphavpar[34]+alphavpar[4]*fin[33]+fin[4]*alphavpar[33]+alphavpar[9]*fin[32]+fin[9]*alphavpar[32])+0.6846531968814574*(alphavpar[22]*fin[31]+fin[22]*alphavpar[31]+alphavpar[27]*fin[30]+fin[27]*alphavpar[30]+alphavpar[14]*fin[29]+fin[14]*alphavpar[29]+alphavpar[13]*fin[28]+fin[13]*alphavpar[28]+alphavpar[8]*fin[26]+fin[8]*alphavpar[26]+alphavpar[21]*fin[25]+fin[21]*alphavpar[25]+alphavpar[20]*fin[24]+fin[20]*alphavpar[24]+alphavpar[5]*fin[23]+fin[5]*alphavpar[23]+alphavpar[16]*fin[19]+fin[16]*alphavpar[19]+alphavpar[3]*fin[18]+fin[3]*alphavpar[18]+alphavpar[2]*fin[17]+fin[2]*alphavpar[17]+alphavpar[12]*fin[15]+fin[12]*alphavpar[15]+alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[0]*fin[9]+fin[0]*alphavpar[9]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]); 
+  out[34] += 0.6123724356957944*(alphavpar[29]*fin[47]+fin[29]*alphavpar[47]+alphavpar[25]*fin[46]+fin[25]*alphavpar[46]+alphavpar[31]*fin[45]+fin[31]*alphavpar[45]+alphavpar[23]*fin[44]+fin[23]*alphavpar[44]+alphavpar[18]*fin[43]+fin[18]*alphavpar[43]+alphavpar[30]*fin[42]+fin[30]*alphavpar[42]+alphavpar[15]*fin[41]+fin[15]*alphavpar[41]+alphavpar[28]*fin[40]+fin[28]*alphavpar[40]+alphavpar[11]*fin[39]+fin[11]*alphavpar[39]+alphavpar[26]*fin[38]+fin[26]*alphavpar[38]+alphavpar[9]*fin[37]+fin[9]*alphavpar[37]+alphavpar[24]*fin[36]+fin[24]*alphavpar[36]+alphavpar[19]*fin[35]+fin[19]*alphavpar[35]+alphavpar[4]*fin[34]+fin[4]*alphavpar[34]+alphavpar[17]*fin[33]+fin[17]*alphavpar[33]+alphavpar[10]*fin[32]+fin[10]*alphavpar[32])+0.6846531968814574*(alphavpar[21]*fin[31]+fin[21]*alphavpar[31]+alphavpar[14]*fin[30]+fin[14]*alphavpar[30]+alphavpar[27]*fin[29]+fin[27]*alphavpar[29]+alphavpar[12]*fin[28]+fin[12]*alphavpar[28]+alphavpar[7]*fin[26]+fin[7]*alphavpar[26]+alphavpar[22]*fin[25]+fin[22]*alphavpar[25]+alphavpar[5]*fin[24]+fin[5]*alphavpar[24]+alphavpar[20]*fin[23]+fin[20]*alphavpar[23]+alphavpar[3]*fin[19]+fin[3]*alphavpar[19]+alphavpar[16]*fin[18]+fin[16]*alphavpar[18]+alphavpar[1]*fin[17]+fin[1]*alphavpar[17]+alphavpar[13]*fin[15]+fin[13]*alphavpar[15]+alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[0]*fin[10]+fin[0]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]); 
+  out[35] += 0.6123724356957944*(alphavpar[28]*fin[47]+fin[28]*alphavpar[47]+alphavpar[24]*fin[46]+fin[24]*alphavpar[46]+alphavpar[23]*fin[45]+fin[23]*alphavpar[45]+alphavpar[31]*fin[44]+fin[31]*alphavpar[44]+alphavpar[17]*fin[43]+fin[17]*alphavpar[43]+alphavpar[15]*fin[42]+fin[15]*alphavpar[42]+alphavpar[30]*fin[41]+fin[30]*alphavpar[41]+alphavpar[29]*fin[40]+fin[29]*alphavpar[40]+alphavpar[10]*fin[39]+fin[10]*alphavpar[39]+alphavpar[9]*fin[38]+fin[9]*alphavpar[38]+alphavpar[26]*fin[37]+fin[26]*alphavpar[37]+alphavpar[25]*fin[36]+fin[25]*alphavpar[36]+alphavpar[4]*fin[35]+fin[4]*alphavpar[35]+alphavpar[19]*fin[34]+fin[19]*alphavpar[34]+alphavpar[18]*fin[33]+fin[18]*alphavpar[33]+alphavpar[11]*fin[32]+fin[11]*alphavpar[32])+0.6846531968814574*(alphavpar[20]*fin[31]+fin[20]*alphavpar[31]+alphavpar[13]*fin[30]+fin[13]*alphavpar[30]+alphavpar[12]*fin[29]+fin[12]*alphavpar[29]+alphavpar[27]*fin[28]+fin[27]*alphavpar[28]+alphavpar[6]*fin[26]+fin[6]*alphavpar[26]+alphavpar[5]*fin[25]+fin[5]*alphavpar[25]+alphavpar[22]*fin[24]+fin[22]*alphavpar[24]+alphavpar[21]*fin[23]+fin[21]*alphavpar[23]+alphavpar[2]*fin[19]+fin[2]*alphavpar[19]+alphavpar[1]*fin[18]+fin[1]*alphavpar[18]+alphavpar[16]*fin[17]+fin[16]*alphavpar[17]+alphavpar[14]*fin[15]+fin[14]*alphavpar[15]+alphavpar[0]*fin[11]+fin[0]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
+  out[36] += 0.6123724356957944*(alphavpar[26]*fin[47]+fin[26]*alphavpar[47]+alphavpar[19]*fin[46]+fin[19]*alphavpar[46]+alphavpar[18]*fin[45]+fin[18]*alphavpar[45]+alphavpar[17]*fin[44]+fin[17]*alphavpar[44]+alphavpar[31]*fin[43]+fin[31]*alphavpar[43]+alphavpar[11]*fin[42]+fin[11]*alphavpar[42]+alphavpar[10]*fin[41]+fin[10]*alphavpar[41]+alphavpar[9]*fin[40]+fin[9]*alphavpar[40]+alphavpar[30]*fin[39]+fin[30]*alphavpar[39]+alphavpar[29]*fin[38]+fin[29]*alphavpar[38]+alphavpar[28]*fin[37]+fin[28]*alphavpar[37]+alphavpar[4]*fin[36]+fin[4]*alphavpar[36]+alphavpar[25]*fin[35]+fin[25]*alphavpar[35]+alphavpar[24]*fin[34]+fin[24]*alphavpar[34]+alphavpar[23]*fin[33]+fin[23]*alphavpar[33]+alphavpar[15]*fin[32]+fin[15]*alphavpar[32])+0.6846531968814574*(alphavpar[16]*fin[31]+fin[16]*alphavpar[31]+alphavpar[8]*fin[30]+fin[8]*alphavpar[30]+alphavpar[7]*fin[29]+fin[7]*alphavpar[29]+alphavpar[6]*fin[28]+fin[6]*alphavpar[28]+alphavpar[26]*fin[27]+fin[26]*alphavpar[27]+alphavpar[3]*fin[25]+fin[3]*alphavpar[25]+alphavpar[2]*fin[24]+fin[2]*alphavpar[24]+alphavpar[1]*fin[23]+fin[1]*alphavpar[23]+alphavpar[19]*fin[22]+fin[19]*alphavpar[22]+alphavpar[18]*fin[21]+fin[18]*alphavpar[21]+alphavpar[17]*fin[20]+fin[17]*alphavpar[20]+alphavpar[0]*fin[15]+fin[0]*alphavpar[15]+alphavpar[11]*fin[14]+fin[11]*alphavpar[14]+alphavpar[10]*fin[13]+fin[10]*alphavpar[13]+alphavpar[9]*fin[12]+fin[9]*alphavpar[12]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]); 
+  out[37] += 0.6123724356957944*(alphavpar[25]*fin[47]+fin[25]*alphavpar[47]+alphavpar[29]*fin[46]+fin[29]*alphavpar[46]+alphavpar[30]*fin[45]+fin[30]*alphavpar[45]+alphavpar[15]*fin[44]+fin[15]*alphavpar[44]+alphavpar[11]*fin[43]+fin[11]*alphavpar[43]+alphavpar[31]*fin[42]+fin[31]*alphavpar[42]+alphavpar[23]*fin[41]+fin[23]*alphavpar[41]+alphavpar[24]*fin[40]+fin[24]*alphavpar[40]+alphavpar[18]*fin[39]+fin[18]*alphavpar[39]+alphavpar[19]*fin[38]+fin[19]*alphavpar[38]+alphavpar[4]*fin[37]+fin[4]*alphavpar[37]+alphavpar[28]*fin[36]+fin[28]*alphavpar[36]+alphavpar[26]*fin[35]+fin[26]*alphavpar[35]+alphavpar[9]*fin[34]+fin[9]*alphavpar[34]+alphavpar[10]*fin[33]+fin[10]*alphavpar[33]+alphavpar[17]*fin[32]+fin[17]*alphavpar[32])+0.6846531968814573*(alphavpar[14]*fin[31]+fin[14]*alphavpar[31]+alphavpar[21]*fin[30]+fin[21]*alphavpar[30]+alphavpar[22]*fin[29]+fin[22]*alphavpar[29]+alphavpar[5]*fin[28]+fin[5]*alphavpar[28]+alphavpar[25]*fin[27]+fin[25]*alphavpar[27]+alphavpar[3]*fin[26]+fin[3]*alphavpar[26]+alphavpar[12]*fin[24]+fin[12]*alphavpar[24]+alphavpar[13]*fin[23]+fin[13]*alphavpar[23]+alphavpar[15]*fin[20]+fin[15]*alphavpar[20]+alphavpar[7]*fin[19]+fin[7]*alphavpar[19]+alphavpar[8]*fin[18]+fin[8]*alphavpar[18]+alphavpar[0]*fin[17]+fin[0]*alphavpar[17]+alphavpar[11]*fin[16]+fin[11]*alphavpar[16]+alphavpar[1]*fin[10]+fin[1]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]); 
+  out[38] += 0.6123724356957944*(alphavpar[24]*fin[47]+fin[24]*alphavpar[47]+alphavpar[28]*fin[46]+fin[28]*alphavpar[46]+alphavpar[15]*fin[45]+fin[15]*alphavpar[45]+alphavpar[30]*fin[44]+fin[30]*alphavpar[44]+alphavpar[10]*fin[43]+fin[10]*alphavpar[43]+alphavpar[23]*fin[42]+fin[23]*alphavpar[42]+alphavpar[31]*fin[41]+fin[31]*alphavpar[41]+alphavpar[25]*fin[40]+fin[25]*alphavpar[40]+alphavpar[17]*fin[39]+fin[17]*alphavpar[39]+alphavpar[4]*fin[38]+fin[4]*alphavpar[38]+alphavpar[19]*fin[37]+fin[19]*alphavpar[37]+alphavpar[29]*fin[36]+fin[29]*alphavpar[36]+alphavpar[9]*fin[35]+fin[9]*alphavpar[35]+alphavpar[26]*fin[34]+fin[26]*alphavpar[34]+alphavpar[11]*fin[33]+fin[11]*alphavpar[33]+alphavpar[18]*fin[32]+fin[18]*alphavpar[32])+0.6846531968814573*(alphavpar[13]*fin[31]+fin[13]*alphavpar[31]+alphavpar[20]*fin[30]+fin[20]*alphavpar[30]+alphavpar[5]*fin[29]+fin[5]*alphavpar[29]+alphavpar[22]*fin[28]+fin[22]*alphavpar[28]+alphavpar[24]*fin[27]+fin[24]*alphavpar[27]+alphavpar[2]*fin[26]+fin[2]*alphavpar[26]+alphavpar[12]*fin[25]+fin[12]*alphavpar[25]+alphavpar[14]*fin[23]+fin[14]*alphavpar[23]+alphavpar[15]*fin[21]+fin[15]*alphavpar[21]+alphavpar[6]*fin[19]+fin[6]*alphavpar[19]+alphavpar[0]*fin[18]+fin[0]*alphavpar[18]+alphavpar[8]*fin[17]+fin[8]*alphavpar[17]+alphavpar[10]*fin[16]+fin[10]*alphavpar[16]+alphavpar[1]*fin[11]+fin[1]*alphavpar[11]+alphavpar[3]*fin[9]+fin[3]*alphavpar[9]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]); 
+  out[39] += 0.6123724356957944*(alphavpar[23]*fin[47]+fin[23]*alphavpar[47]+alphavpar[15]*fin[46]+fin[15]*alphavpar[46]+alphavpar[28]*fin[45]+fin[28]*alphavpar[45]+alphavpar[29]*fin[44]+fin[29]*alphavpar[44]+alphavpar[9]*fin[43]+fin[9]*alphavpar[43]+alphavpar[24]*fin[42]+fin[24]*alphavpar[42]+alphavpar[25]*fin[41]+fin[25]*alphavpar[41]+alphavpar[31]*fin[40]+fin[31]*alphavpar[40]+alphavpar[4]*fin[39]+fin[4]*alphavpar[39]+alphavpar[17]*fin[38]+fin[17]*alphavpar[38]+alphavpar[18]*fin[37]+fin[18]*alphavpar[37]+alphavpar[30]*fin[36]+fin[30]*alphavpar[36]+alphavpar[10]*fin[35]+fin[10]*alphavpar[35]+alphavpar[11]*fin[34]+fin[11]*alphavpar[34]+alphavpar[26]*fin[33]+fin[26]*alphavpar[33]+alphavpar[19]*fin[32]+fin[19]*alphavpar[32])+0.6846531968814573*(alphavpar[12]*fin[31]+fin[12]*alphavpar[31]+alphavpar[5]*fin[30]+fin[5]*alphavpar[30]+alphavpar[20]*fin[29]+fin[20]*alphavpar[29]+alphavpar[21]*fin[28]+fin[21]*alphavpar[28]+alphavpar[23]*fin[27]+fin[23]*alphavpar[27]+alphavpar[1]*fin[26]+fin[1]*alphavpar[26]+alphavpar[13]*fin[25]+fin[13]*alphavpar[25]+alphavpar[14]*fin[24]+fin[14]*alphavpar[24]+alphavpar[15]*fin[22]+fin[15]*alphavpar[22]+alphavpar[0]*fin[19]+fin[0]*alphavpar[19]+alphavpar[6]*fin[18]+fin[6]*alphavpar[18]+alphavpar[7]*fin[17]+fin[7]*alphavpar[17]+alphavpar[9]*fin[16]+fin[9]*alphavpar[16]+alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[3]*fin[10]+fin[3]*alphavpar[10]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8]); 
+  out[40] += 0.6123724356957944*(alphavpar[19]*fin[47]+fin[19]*alphavpar[47]+alphavpar[26]*fin[46]+fin[26]*alphavpar[46]+alphavpar[11]*fin[45]+fin[11]*alphavpar[45]+alphavpar[10]*fin[44]+fin[10]*alphavpar[44]+alphavpar[30]*fin[43]+fin[30]*alphavpar[43]+alphavpar[18]*fin[42]+fin[18]*alphavpar[42]+alphavpar[17]*fin[41]+fin[17]*alphavpar[41]+alphavpar[4]*fin[40]+fin[4]*alphavpar[40]+alphavpar[31]*fin[39]+fin[31]*alphavpar[39]+alphavpar[25]*fin[38]+fin[25]*alphavpar[38]+alphavpar[24]*fin[37]+fin[24]*alphavpar[37]+alphavpar[9]*fin[36]+fin[9]*alphavpar[36]+alphavpar[29]*fin[35]+fin[29]*alphavpar[35]+alphavpar[28]*fin[34]+fin[28]*alphavpar[34]+alphavpar[15]*fin[33]+fin[15]*alphavpar[33]+alphavpar[23]*fin[32]+fin[23]*alphavpar[32])+0.6846531968814573*(alphavpar[8]*fin[31]+fin[8]*alphavpar[31]+alphavpar[16]*fin[30]+fin[16]*alphavpar[30]+alphavpar[3]*fin[29]+fin[3]*alphavpar[29]+alphavpar[2]*fin[28]+fin[2]*alphavpar[28]+alphavpar[19]*fin[27]+fin[19]*alphavpar[27]+alphavpar[22]*fin[26]+fin[22]*alphavpar[26]+alphavpar[7]*fin[25]+fin[7]*alphavpar[25]+alphavpar[6]*fin[24]+fin[6]*alphavpar[24]+alphavpar[0]*fin[23]+fin[0]*alphavpar[23]+alphavpar[11]*fin[21]+fin[11]*alphavpar[21]+alphavpar[10]*fin[20]+fin[10]*alphavpar[20]+alphavpar[14]*fin[18]+fin[14]*alphavpar[18]+alphavpar[13]*fin[17]+fin[13]*alphavpar[17]+alphavpar[1]*fin[15]+fin[1]*alphavpar[15]+alphavpar[4]*fin[12]+fin[4]*alphavpar[12]+alphavpar[5]*fin[9]+fin[5]*alphavpar[9]); 
+  out[41] += 0.6123724356957944*(alphavpar[18]*fin[47]+fin[18]*alphavpar[47]+alphavpar[11]*fin[46]+fin[11]*alphavpar[46]+alphavpar[26]*fin[45]+fin[26]*alphavpar[45]+alphavpar[9]*fin[44]+fin[9]*alphavpar[44]+alphavpar[29]*fin[43]+fin[29]*alphavpar[43]+alphavpar[19]*fin[42]+fin[19]*alphavpar[42]+alphavpar[4]*fin[41]+fin[4]*alphavpar[41]+alphavpar[17]*fin[40]+fin[17]*alphavpar[40]+alphavpar[25]*fin[39]+fin[25]*alphavpar[39]+alphavpar[31]*fin[38]+fin[31]*alphavpar[38]+alphavpar[23]*fin[37]+fin[23]*alphavpar[37]+alphavpar[10]*fin[36]+fin[10]*alphavpar[36]+alphavpar[30]*fin[35]+fin[30]*alphavpar[35]+alphavpar[15]*fin[34]+fin[15]*alphavpar[34]+alphavpar[28]*fin[33]+fin[28]*alphavpar[33]+alphavpar[24]*fin[32]+fin[24]*alphavpar[32])+0.6846531968814573*(alphavpar[7]*fin[31]+fin[7]*alphavpar[31]+alphavpar[3]*fin[30]+fin[3]*alphavpar[30]+alphavpar[16]*fin[29]+fin[16]*alphavpar[29]+alphavpar[1]*fin[28]+fin[1]*alphavpar[28]+alphavpar[18]*fin[27]+fin[18]*alphavpar[27]+alphavpar[21]*fin[26]+fin[21]*alphavpar[26]+alphavpar[8]*fin[25]+fin[8]*alphavpar[25]+alphavpar[0]*fin[24]+fin[0]*alphavpar[24]+alphavpar[6]*fin[23]+fin[6]*alphavpar[23]+alphavpar[11]*fin[22]+fin[11]*alphavpar[22]+alphavpar[9]*fin[20]+fin[9]*alphavpar[20]+alphavpar[14]*fin[19]+fin[14]*alphavpar[19]+alphavpar[12]*fin[17]+fin[12]*alphavpar[17]+alphavpar[2]*fin[15]+fin[2]*alphavpar[15]+alphavpar[4]*fin[13]+fin[4]*alphavpar[13]+alphavpar[5]*fin[10]+fin[5]*alphavpar[10]); 
+  out[42] += 0.6123724356957944*(alphavpar[17]*fin[47]+fin[17]*alphavpar[47]+alphavpar[10]*fin[46]+fin[10]*alphavpar[46]+alphavpar[9]*fin[45]+fin[9]*alphavpar[45]+alphavpar[26]*fin[44]+fin[26]*alphavpar[44]+alphavpar[28]*fin[43]+fin[28]*alphavpar[43]+alphavpar[4]*fin[42]+fin[4]*alphavpar[42]+alphavpar[19]*fin[41]+fin[19]*alphavpar[41]+alphavpar[18]*fin[40]+fin[18]*alphavpar[40]+alphavpar[24]*fin[39]+fin[24]*alphavpar[39]+alphavpar[23]*fin[38]+fin[23]*alphavpar[38]+alphavpar[31]*fin[37]+fin[31]*alphavpar[37]+alphavpar[11]*fin[36]+fin[11]*alphavpar[36]+alphavpar[15]*fin[35]+fin[15]*alphavpar[35]+alphavpar[30]*fin[34]+fin[30]*alphavpar[34]+alphavpar[29]*fin[33]+fin[29]*alphavpar[33]+alphavpar[25]*fin[32]+fin[25]*alphavpar[32])+0.6846531968814573*(alphavpar[6]*fin[31]+fin[6]*alphavpar[31]+alphavpar[2]*fin[30]+fin[2]*alphavpar[30]+alphavpar[1]*fin[29]+fin[1]*alphavpar[29]+alphavpar[16]*fin[28]+fin[16]*alphavpar[28]+alphavpar[17]*fin[27]+fin[17]*alphavpar[27]+alphavpar[20]*fin[26]+fin[20]*alphavpar[26]+alphavpar[0]*fin[25]+fin[0]*alphavpar[25]+alphavpar[8]*fin[24]+fin[8]*alphavpar[24]+alphavpar[7]*fin[23]+fin[7]*alphavpar[23]+alphavpar[10]*fin[22]+fin[10]*alphavpar[22]+alphavpar[9]*fin[21]+fin[9]*alphavpar[21]+alphavpar[13]*fin[19]+fin[13]*alphavpar[19]+alphavpar[12]*fin[18]+fin[12]*alphavpar[18]+alphavpar[3]*fin[15]+fin[3]*alphavpar[15]+alphavpar[4]*fin[14]+fin[4]*alphavpar[14]+alphavpar[5]*fin[11]+fin[5]*alphavpar[11]); 
+  out[43] += 0.6123724356957944*(alphavpar[15]*fin[47]+fin[15]*alphavpar[47]+alphavpar[23]*fin[46]+fin[23]*alphavpar[46]+alphavpar[24]*fin[45]+fin[24]*alphavpar[45]+alphavpar[25]*fin[44]+fin[25]*alphavpar[44]+alphavpar[4]*fin[43]+fin[4]*alphavpar[43]+alphavpar[28]*fin[42]+fin[28]*alphavpar[42]+alphavpar[29]*fin[41]+fin[29]*alphavpar[41]+alphavpar[30]*fin[40]+fin[30]*alphavpar[40]+alphavpar[9]*fin[39]+fin[9]*alphavpar[39]+alphavpar[10]*fin[38]+fin[10]*alphavpar[38]+alphavpar[11]*fin[37]+fin[11]*alphavpar[37]+alphavpar[31]*fin[36]+fin[31]*alphavpar[36]+alphavpar[17]*fin[35]+fin[17]*alphavpar[35]+alphavpar[18]*fin[34]+fin[18]*alphavpar[34]+alphavpar[19]*fin[33]+fin[19]*alphavpar[33]+alphavpar[26]*fin[32]+fin[26]*alphavpar[32])+0.6846531968814574*(alphavpar[5]*fin[31]+fin[5]*alphavpar[31]+alphavpar[12]*fin[30]+fin[12]*alphavpar[30]+alphavpar[13]*fin[29]+fin[13]*alphavpar[29]+alphavpar[14]*fin[28]+fin[14]*alphavpar[28]+alphavpar[15]*fin[27]+fin[15]*alphavpar[27]+alphavpar[0]*fin[26]+fin[0]*alphavpar[26]+alphavpar[20]*fin[25]+fin[20]*alphavpar[25]+alphavpar[21]*fin[24]+fin[21]*alphavpar[24]+alphavpar[22]*fin[23]+fin[22]*alphavpar[23]+alphavpar[1]*fin[19]+fin[1]*alphavpar[19]+alphavpar[2]*fin[18]+fin[2]*alphavpar[18]+alphavpar[3]*fin[17]+fin[3]*alphavpar[17]+alphavpar[4]*fin[16]+fin[4]*alphavpar[16]+alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]); 
+  out[44] += 0.6123724356957944*(alphavpar[11]*fin[47]+fin[11]*alphavpar[47]+alphavpar[18]*fin[46]+fin[18]*alphavpar[46]+alphavpar[19]*fin[45]+fin[19]*alphavpar[45]+alphavpar[4]*fin[44]+fin[4]*alphavpar[44]+alphavpar[25]*fin[43]+fin[25]*alphavpar[43]+alphavpar[26]*fin[42]+fin[26]*alphavpar[42]+alphavpar[9]*fin[41]+fin[9]*alphavpar[41]+alphavpar[10]*fin[40]+fin[10]*alphavpar[40]+alphavpar[29]*fin[39]+fin[29]*alphavpar[39]+alphavpar[30]*fin[38]+fin[30]*alphavpar[38]+alphavpar[15]*fin[37]+fin[15]*alphavpar[37]+alphavpar[17]*fin[36]+fin[17]*alphavpar[36]+alphavpar[31]*fin[35]+fin[31]*alphavpar[35]+alphavpar[23]*fin[34]+fin[23]*alphavpar[34]+alphavpar[24]*fin[33]+fin[24]*alphavpar[33]+alphavpar[28]*fin[32]+fin[28]*alphavpar[32])+0.6846531968814574*(alphavpar[3]*fin[31]+fin[3]*alphavpar[31]+alphavpar[7]*fin[30]+fin[7]*alphavpar[30]+alphavpar[8]*fin[29]+fin[8]*alphavpar[29]+alphavpar[0]*fin[28]+fin[0]*alphavpar[28]+alphavpar[11]*fin[27]+fin[11]*alphavpar[27]+alphavpar[14]*fin[26]+fin[14]*alphavpar[26]+alphavpar[16]*fin[25]+fin[16]*alphavpar[25]+alphavpar[1]*fin[24]+fin[1]*alphavpar[24]+alphavpar[2]*fin[23]+fin[2]*alphavpar[23]+alphavpar[18]*fin[22]+fin[18]*alphavpar[22]+alphavpar[19]*fin[21]+fin[19]*alphavpar[21]+alphavpar[4]*fin[20]+fin[4]*alphavpar[20]+alphavpar[5]*fin[17]+fin[5]*alphavpar[17]+alphavpar[6]*fin[15]+fin[6]*alphavpar[15]+alphavpar[9]*fin[13]+fin[9]*alphavpar[13]+alphavpar[10]*fin[12]+fin[10]*alphavpar[12]); 
+  out[45] += 0.6123724356957944*(alphavpar[10]*fin[47]+fin[10]*alphavpar[47]+alphavpar[17]*fin[46]+fin[17]*alphavpar[46]+alphavpar[4]*fin[45]+fin[4]*alphavpar[45]+alphavpar[19]*fin[44]+fin[19]*alphavpar[44]+alphavpar[24]*fin[43]+fin[24]*alphavpar[43]+alphavpar[9]*fin[42]+fin[9]*alphavpar[42]+alphavpar[26]*fin[41]+fin[26]*alphavpar[41]+alphavpar[11]*fin[40]+fin[11]*alphavpar[40]+alphavpar[28]*fin[39]+fin[28]*alphavpar[39]+alphavpar[15]*fin[38]+fin[15]*alphavpar[38]+alphavpar[30]*fin[37]+fin[30]*alphavpar[37]+alphavpar[18]*fin[36]+fin[18]*alphavpar[36]+alphavpar[23]*fin[35]+fin[23]*alphavpar[35]+alphavpar[31]*fin[34]+fin[31]*alphavpar[34]+alphavpar[25]*fin[33]+fin[25]*alphavpar[33]+alphavpar[29]*fin[32]+fin[29]*alphavpar[32])+0.6846531968814574*(alphavpar[2]*fin[31]+fin[2]*alphavpar[31]+alphavpar[6]*fin[30]+fin[6]*alphavpar[30]+alphavpar[0]*fin[29]+fin[0]*alphavpar[29]+alphavpar[8]*fin[28]+fin[8]*alphavpar[28]+alphavpar[10]*fin[27]+fin[10]*alphavpar[27]+alphavpar[13]*fin[26]+fin[13]*alphavpar[26]+alphavpar[1]*fin[25]+fin[1]*alphavpar[25]+alphavpar[16]*fin[24]+fin[16]*alphavpar[24]+alphavpar[3]*fin[23]+fin[3]*alphavpar[23]+alphavpar[17]*fin[22]+fin[17]*alphavpar[22]+alphavpar[4]*fin[21]+fin[4]*alphavpar[21]+alphavpar[19]*fin[20]+fin[19]*alphavpar[20]+alphavpar[5]*fin[18]+fin[5]*alphavpar[18]+alphavpar[7]*fin[15]+fin[7]*alphavpar[15]+alphavpar[9]*fin[14]+fin[9]*alphavpar[14]+alphavpar[11]*fin[12]+fin[11]*alphavpar[12]); 
+  out[46] += 0.6123724356957944*(alphavpar[9]*fin[47]+fin[9]*alphavpar[47]+alphavpar[4]*fin[46]+fin[4]*alphavpar[46]+alphavpar[17]*fin[45]+fin[17]*alphavpar[45]+alphavpar[18]*fin[44]+fin[18]*alphavpar[44]+alphavpar[23]*fin[43]+fin[23]*alphavpar[43]+alphavpar[10]*fin[42]+fin[10]*alphavpar[42]+alphavpar[11]*fin[41]+fin[11]*alphavpar[41]+alphavpar[26]*fin[40]+fin[26]*alphavpar[40]+alphavpar[15]*fin[39]+fin[15]*alphavpar[39]+alphavpar[28]*fin[38]+fin[28]*alphavpar[38]+alphavpar[29]*fin[37]+fin[29]*alphavpar[37]+alphavpar[19]*fin[36]+fin[19]*alphavpar[36]+alphavpar[24]*fin[35]+fin[24]*alphavpar[35]+alphavpar[25]*fin[34]+fin[25]*alphavpar[34]+alphavpar[31]*fin[33]+fin[31]*alphavpar[33]+alphavpar[30]*fin[32]+fin[30]*alphavpar[32])+0.6846531968814574*(alphavpar[1]*fin[31]+fin[1]*alphavpar[31]+alphavpar[0]*fin[30]+fin[0]*alphavpar[30]+alphavpar[6]*fin[29]+fin[6]*alphavpar[29]+alphavpar[7]*fin[28]+fin[7]*alphavpar[28]+alphavpar[9]*fin[27]+fin[9]*alphavpar[27]+alphavpar[12]*fin[26]+fin[12]*alphavpar[26]+alphavpar[2]*fin[25]+fin[2]*alphavpar[25]+alphavpar[3]*fin[24]+fin[3]*alphavpar[24]+alphavpar[16]*fin[23]+fin[16]*alphavpar[23]+alphavpar[4]*fin[22]+fin[4]*alphavpar[22]+alphavpar[17]*fin[21]+fin[17]*alphavpar[21]+alphavpar[18]*fin[20]+fin[18]*alphavpar[20]+alphavpar[5]*fin[19]+fin[5]*alphavpar[19]+alphavpar[8]*fin[15]+fin[8]*alphavpar[15]+alphavpar[10]*fin[14]+fin[10]*alphavpar[14]+alphavpar[11]*fin[13]+fin[11]*alphavpar[13]); 
+  out[47] += 0.6123724356957944*(alphavpar[4]*fin[47]+fin[4]*alphavpar[47]+alphavpar[9]*fin[46]+fin[9]*alphavpar[46]+alphavpar[10]*fin[45]+fin[10]*alphavpar[45]+alphavpar[11]*fin[44]+fin[11]*alphavpar[44]+alphavpar[15]*fin[43]+fin[15]*alphavpar[43]+alphavpar[17]*fin[42]+fin[17]*alphavpar[42]+alphavpar[18]*fin[41]+fin[18]*alphavpar[41]+alphavpar[19]*fin[40]+fin[19]*alphavpar[40]+alphavpar[23]*fin[39]+fin[23]*alphavpar[39]+alphavpar[24]*fin[38]+fin[24]*alphavpar[38]+alphavpar[25]*fin[37]+fin[25]*alphavpar[37]+alphavpar[26]*fin[36]+fin[26]*alphavpar[36]+alphavpar[28]*fin[35]+fin[28]*alphavpar[35]+alphavpar[29]*fin[34]+fin[29]*alphavpar[34]+alphavpar[30]*fin[33]+fin[30]*alphavpar[33]+alphavpar[31]*fin[32]+fin[31]*alphavpar[32])+0.6846531968814573*(alphavpar[0]*fin[31]+fin[0]*alphavpar[31]+alphavpar[1]*fin[30]+fin[1]*alphavpar[30]+alphavpar[2]*fin[29]+fin[2]*alphavpar[29]+alphavpar[3]*fin[28]+fin[3]*alphavpar[28]+alphavpar[4]*fin[27]+fin[4]*alphavpar[27]+alphavpar[5]*fin[26]+fin[5]*alphavpar[26]+alphavpar[6]*fin[25]+fin[6]*alphavpar[25]+alphavpar[7]*fin[24]+fin[7]*alphavpar[24]+alphavpar[8]*fin[23]+fin[8]*alphavpar[23]+alphavpar[9]*fin[22]+fin[9]*alphavpar[22]+alphavpar[10]*fin[21]+fin[10]*alphavpar[21]+alphavpar[11]*fin[20]+fin[11]*alphavpar[20]+alphavpar[12]*fin[19]+fin[12]*alphavpar[19]+alphavpar[13]*fin[18]+fin[13]*alphavpar[18]+alphavpar[14]*fin[17]+fin[14]*alphavpar[17]+alphavpar[15]*fin[16]+fin[15]*alphavpar[16]); 
+
+  return 0.; 
+} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index 0d0ee1dcb7..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,18 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_1x1v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_edge, const double *vmap_prime_skin,
-    const double *flux_surf_edge, const double *flux_surf_skin, 
-    const int edge, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
-  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
-  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
-  // edge: determines if the update is for the left edge (-1) or right edge (+1).
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index 640fa5f1d1..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,18 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_1x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_edge, const double *vmap_prime_skin,
-    const double *flux_surf_edge, const double *flux_surf_skin, 
-    const int edge, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
-  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
-  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
-  // edge: determines if the update is for the left edge (-1) or right edge (+1).
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index 363c18ba47..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,18 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_2x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_edge, const double *vmap_prime_skin,
-    const double *flux_surf_edge, const double *flux_surf_skin, 
-    const int edge, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
-  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
-  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
-  // edge: determines if the update is for the left edge (-1) or right edge (+1).
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 912a590a66..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,18 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_3x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_edge, const double *vmap_prime_skin,
-    const double *flux_surf_edge, const double *flux_surf_skin, 
-    const int edge, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_edge,vmap_prime_skin: velocity space mapping derivative in edge and skin cells.
-  // flux_surf_edge: Surface expansion of phase space flux on the lower edges of the edge cell.
-  // flux_surf_skin: Surface expansion of phase space flux on the lower edges of the skin cell.
-  // edge: determines if the update is for the left edge (-1) or right edge (+1).
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index 98e85d2209..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,17 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_1x1v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
-    const double *flux_surf_l, const double *flux_surf_r, 
-    double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
-  // flux_surf_l: Surface expansion of phase space flux on the left.
-  // flux_surf_r: Surface expansion of phase space flux on the right.
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index 7abe4f702f..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,17 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_1x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
-    const double *flux_surf_l, const double *flux_surf_r, 
-    double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
-  // flux_surf_l: Surface expansion of phase space flux on the left.
-  // flux_surf_r: Surface expansion of phase space flux on the right.
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index daeebb1c56..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,17 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_2x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
-    const double *flux_surf_l, const double *flux_surf_r, 
-    double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
-  // flux_surf_l: Surface expansion of phase space flux on the left.
-  // flux_surf_r: Surface expansion of phase space flux on the right.
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 5e3a3a38e7..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,17 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h>
-#include <gkyl_basis_gkhyb_3x2v_p1_upwind_quad_to_modal.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r,
-    const double *flux_surf_l, const double *flux_surf_r, 
-    double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_c,vmap_prime_r: velocity space mapping derivative in left, center and right cells.
-  // flux_surf_l: Surface expansion of phase space flux on the left.
-  // flux_surf_r: Surface expansion of phase space flux on the right.
-  // out: output increment in center cell.
-
-  return 0.0; 
-
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
deleted file mode 100644
index 3eb7e85c0e..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x1v_ser_p1.c
+++ /dev/null
@@ -1,19 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *apar,
-    const double *apardot, const double *rtg33inv, const double *bioverJB,
-    const double *fin, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential .
-  // apar: parallel component of vector potential.
-  // fin: Distribution function.
-  // out: output increment.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
deleted file mode 100644
index 971767445c..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_1x2v_ser_p1.c
+++ /dev/null
@@ -1,19 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *apar,
-    const double *apardot, const double *rtg33inv, const double *bioverJB,
-    const double *fin, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential .
-  // apar: parallel component of vector potential.
-  // fin: Distribution function.
-  // out: output increment.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
deleted file mode 100644
index 273c7fcf79..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_2x2v_ser_p1.c
+++ /dev/null
@@ -1,19 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *apar,
-    const double *apardot, const double *rtg33inv, const double *bioverJB,
-    const double *fin, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential .
-  // apar: parallel component of vector potential.
-  // fin: Distribution function.
-  // out: output increment.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
deleted file mode 100644
index cfb0840e3d..0000000000
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_em_vol_3x2v_ser_p1.c
+++ /dev/null
@@ -1,19 +0,0 @@
-#include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *apar,
-    const double *apardot, const double *rtg33inv, const double *bioverJB,
-    const double *fin, double* GKYL_RESTRICT out) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential .
-  // apar: parallel component of vector potential.
-  // fin: Distribution function.
-  // out: output increment.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
index 830cf6a25e..3a54018e34 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
+++ b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
@@ -228,137 +228,61 @@ GKYL_CU_DH double dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1(const double *w,
               const double *flux_surf_edge, const double *flux_surf_skin, 
               const int edge, double* GKYL_RESTRICT out); 
 
-              GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x1v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x1v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p2(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_1x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p2(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_1x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p2(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p2(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
 
-GKYL_CU_DH double dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p2(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(const double *w, const double *dxv,
-            const double *vmap, const double *vmapSq, const double q_, const double m_,
-            const double *bmag, const double *apar, const double *apardot,
-            const double *rtg33inv, const double* bioverJB,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p2(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+
+GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const double *dxv, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const double *bmag, const double *jacobtot_inv,
+            const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfx_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfx_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfy_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfy_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfz_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfz_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
-              const double *flux_surf_l, const double *flux_surf_r, 
-              double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1(const double *w, const double *dxv,
-              const double *vmap_prime_edge, const double *vmap_prime_skin, 
-              const double *flux_surf_edge, const double *flux_surf_skin, 
-              const int edge, double* GKYL_RESTRICT out); 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
 
 
 EXTERN_C_END
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..fe8446683c
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,65 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential (here it will be apardot).
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+
+  double *flux_surf_nodal = &flux_surf[3]; 
+  double cfl = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+
+
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..81f0720ca2
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,83 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential (here it will be apardot).
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+
+  double *flux_surf_nodal = &flux_surf[6]; 
+  double cfl = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+
+
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..e0e51c38ad
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,124 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential (here it will be apardot).
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+
+
+
+  alpha_quad = -q_/m_*(0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..ca88d98d0d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,205 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential (here it will be apardot).
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+
+  double *flux_surf_nodal = &flux_surf[72]; 
+  double cfl = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+
+
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[8] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[9] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[10] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[11] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[12] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[13] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[14] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[15] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 02aed87ff6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 985bf5ff5b..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 58032fe55a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 366399870d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 9ee1465433..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 0d7b7b5a25..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index fb4e3657d6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index a1e3efe0f1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 22417fa638..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 085ae07617..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 2edce2b85a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index d3be656a7e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index ba50f2ddbe..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index f456e80f01..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 4fe40b27ef..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 1d32b32127..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 461dac1bf7..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 11ea44c05a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 08d186e133..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 856155d7b3..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 8f3f6f1ea1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index dc927940a8..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 47f50f2516..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index a87c9b3ef1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 686d3fae37..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index bf8b075f11..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 2b39f7d630..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 2cf8ffecdd..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 5837b618aa..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 16282609e6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 35655d48b5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index f39f17c36a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index e3046b01f8..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 77014e76cc..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 4e4fb4bb6e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 6a56f51740..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index 3977e7acc0..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 0b5dbee65d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 414ef9f8d4..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 89aad8d3fe..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
deleted file mode 100644
index f8b28d3d49..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 9504159d0d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
deleted file mode 100644
index d0cde6b276..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index 9897d3b63f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index 0f82c703ea..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index 62c373ef5d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 7a22e7c4be..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 1fccf45fb9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 7b7ec7808a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 6984c52216..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
deleted file mode 100644
index d701443e15..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 70ca233a21..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 60fc96ea32..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 0ec404bc74..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_em_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  return 0.; 
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index ad3734b58e..d238da4c5a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 59a43322bb..8b28a452a8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 5022256ab7..9525d51831 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -67,6 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -76,6 +80,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -85,6 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -94,6 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -103,6 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -112,6 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -131,6 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -140,6 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -149,6 +167,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,6 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -167,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -176,6 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 59e7d2cc46..62b3bbfb0f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -70,6 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -79,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -97,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -106,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -115,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -134,6 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -152,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,6 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,6 +235,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -216,6 +246,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -234,6 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -243,6 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,6 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -271,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -280,6 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -289,6 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -298,6 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -307,6 +355,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 31fa960356..0d3cc97515 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -67,6 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -76,6 +80,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -85,6 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -94,6 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -103,6 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -112,6 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -131,6 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -140,6 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -149,6 +167,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -158,6 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -167,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -176,6 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index ad63fb6149..61775349c6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -72,6 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -81,6 +85,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -90,6 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,6 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -136,6 +150,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,6 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,6 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,6 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,6 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,6 +205,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,6 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,6 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,6 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,6 +270,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,6 +281,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,6 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -273,6 +313,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -282,6 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -291,6 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,6 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -309,6 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 4764aab565..ab2a44e03d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -70,6 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -79,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -88,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -97,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -106,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -115,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,6 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -152,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,6 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -207,6 +235,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -216,6 +246,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -225,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -234,6 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -243,6 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,6 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -271,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -280,6 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -289,6 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -298,6 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -307,6 +355,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 29fc18e21c..9839938bde 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 438f8f354a..59741c6716 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 1e08261e4f..7c5f27f3a4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -81,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -90,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -99,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -108,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -117,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -126,6 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -145,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -163,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -172,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -190,6 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index fe0b02073f..4427f8496b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -96,6 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -105,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,6 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -123,6 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -132,6 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -141,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -160,6 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -169,6 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -178,6 +196,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,6 +207,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -196,6 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -205,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -224,6 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -233,6 +261,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -242,6 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -260,6 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -269,6 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,6 +326,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -297,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -306,6 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -315,6 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -324,6 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -333,6 +381,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 7ba71bc887..b46843a5f3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -81,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -90,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -99,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -108,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -117,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -126,6 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -145,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -163,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -172,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -190,6 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index b5e4f00c47..fed15e4318 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -98,6 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -107,6 +111,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -116,6 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,6 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -134,6 +144,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,6 +155,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -162,6 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,6 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,6 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,6 +220,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,6 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,6 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -244,6 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,6 +285,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,6 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,6 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,6 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -308,6 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -317,6 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -326,6 +372,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -335,6 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index fa4ad444f6..07abcbccac 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -96,6 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -105,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -114,6 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -123,6 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -132,6 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -141,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -160,6 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -169,6 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -178,6 +196,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,6 +207,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -196,6 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -205,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -224,6 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -233,6 +261,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -242,6 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -260,6 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -269,6 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -288,6 +326,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -297,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -306,6 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -315,6 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -324,6 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -333,6 +381,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 77d6899c97..3e0e9a58ee 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 8c2aac9ad9..57462146c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 7e1113c075..669c837aa1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -81,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -90,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -99,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -108,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -117,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -126,6 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -145,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -163,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -172,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -190,6 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 34dc77abfd..3d6a5ada15 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -96,6 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -105,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -114,6 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -123,6 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -132,6 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -141,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -160,6 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -169,6 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -178,6 +196,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -187,6 +207,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -196,6 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -205,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -224,6 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -233,6 +261,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -242,6 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -260,6 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -269,6 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -288,6 +326,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -297,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -306,6 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -315,6 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -324,6 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -333,6 +381,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index a8c95150bb..ccae8140f5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -81,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -90,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -99,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -108,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -117,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -126,6 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -145,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -163,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -172,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -190,6 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index 1dd20085ee..661696e018 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -98,6 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,6 +111,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,6 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,6 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,6 +144,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,6 +155,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,6 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,6 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,6 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,6 +220,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,6 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,6 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,6 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,6 +285,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,6 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,6 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,6 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,6 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,6 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,6 +372,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,6 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index 714859fda8..2cc78a65c5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -96,6 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -105,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -114,6 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -123,6 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -132,6 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -141,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -160,6 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -169,6 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -178,6 +196,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -187,6 +207,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -196,6 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -205,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -224,6 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -233,6 +261,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -242,6 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -260,6 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -269,6 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -288,6 +326,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -297,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -306,6 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -315,6 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -324,6 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -333,6 +381,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 96559ef1af..6184d536a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index cf1154a0a0..a2da499294 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index 21f961c76a..4ca93d910c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index b90d9d2cf1..43d4ce97f4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 389c6dfd3c..403e5afe85 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 9d37e91383..55a1af88c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 79c057a02c..a71b45ec40 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index e3bafd60df..a9079ef2ed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 0a47ab8b76..6646198205 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 6c3a483186..6284a429d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 65c8ab4aae..944529819a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index cca595b0a8..b45acf2030 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 1521d880c2..1be9740d4c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 834ddf4599..b2df2b4cc8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 2cf58ff30c..9ccf675e30 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index 4a3cedd54b..e600c37586 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -44,11 +45,17 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -56,8 +63,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -67,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -82,8 +95,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -93,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -108,8 +127,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -119,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -134,8 +159,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -145,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -154,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 7f79f3f395..4b11599eab 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -49,11 +50,17 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -61,8 +68,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -72,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -87,8 +100,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -98,6 +116,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -113,8 +132,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -124,6 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -139,8 +164,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -150,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -165,8 +196,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -176,6 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -191,8 +228,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -202,6 +244,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -217,8 +260,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -228,6 +276,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -243,8 +292,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -254,6 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -263,6 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index 8f1e074287..c6fa855f0b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index c3c52aed1f..8e0df1984a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index 34d2f41dc4..a602b33749 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index 21d32c281c..8907a70957 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index 986892352c..a7d42b1e38 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
new file mode 100644
index 0000000000..5f1299df4e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
@@ -0,0 +1,11 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  return 0.0; 
+}
\ No newline at end of file
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index da915ecfda..2aec3997b1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -37,11 +38,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -49,9 +56,15 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1])/q_; 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
@@ -66,9 +79,15 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1])/q_; 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
@@ -77,6 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index e64b6b58e3..3701b42301 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -39,11 +40,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -51,9 +58,15 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -62,7 +75,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -77,9 +92,15 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -88,7 +109,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -97,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 1f56aa7c43..9103273342 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -44,11 +45,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -56,9 +63,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -68,6 +83,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -82,9 +101,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -94,6 +121,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -108,9 +139,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -120,6 +159,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -134,9 +177,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -146,6 +197,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -154,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 55fccbb259..fdda705971 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *JfL, const double *JfR,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
     double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +17,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -49,11 +50,17 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -61,9 +68,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -72,7 +90,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -87,9 +112,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -98,7 +134,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -113,9 +156,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -124,7 +178,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -139,9 +200,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -150,7 +222,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -165,9 +244,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -176,7 +266,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -191,9 +288,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -202,7 +310,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -217,9 +332,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -228,7 +354,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -243,9 +376,20 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
 
-
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -254,7 +398,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -263,6 +414,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
+
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
 
   return cfl/vmap_prime_min*2.5*rdvpar2; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
new file mode 100644
index 0000000000..b47331bf64
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
@@ -0,0 +1,11 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+    return 0.0; 
+}
\ No newline at end of file
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 0ef83c4598..8351564ace 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index dcf075bb2a..afb03ca1e1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index 9a7bc20564..5e8c3cbef7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -67,6 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -76,6 +80,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -85,6 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -94,6 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -103,6 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -112,6 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -131,6 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -140,6 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -149,6 +167,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,6 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -167,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -176,6 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index eeea1a9283..da41a35c4e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -70,6 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -79,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -97,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -106,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -115,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -134,6 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -152,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,6 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,6 +235,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -216,6 +246,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -234,6 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -243,6 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,6 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -271,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -280,6 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -289,6 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -298,6 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -307,6 +355,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index 293d963b5c..4a910b6a1b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -67,6 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -76,6 +80,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -85,6 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -94,6 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -103,6 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -112,6 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -131,6 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -140,6 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -149,6 +167,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -158,6 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -167,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -176,6 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 512224cc62..c36a81b5de 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -72,6 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -81,6 +85,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -90,6 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,6 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -136,6 +150,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,6 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,6 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,6 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,6 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,6 +205,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,6 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,6 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,6 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,6 +270,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,6 +281,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,6 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -273,6 +313,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -282,6 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -291,6 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,6 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -309,6 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index e135bebf06..b803b6bfb4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -3,7 +3,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -17,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -70,6 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -79,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -88,6 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -97,6 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -106,6 +116,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -115,6 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,6 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,6 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -152,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,6 +181,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,6 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,6 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -207,6 +235,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -216,6 +246,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -225,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -234,6 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -243,6 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,6 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -271,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -280,6 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -289,6 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -298,6 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -307,6 +355,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index 5b20c9ed63..8719415313 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -13,7 +13,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
@@ -21,7 +21,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
@@ -29,7 +29,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
@@ -37,54 +37,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
@@ -93,7 +53,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -101,7 +61,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -109,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -117,54 +77,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
@@ -173,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -181,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -189,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -197,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -205,7 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -213,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -221,7 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -229,14 +149,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -244,7 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -252,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -260,7 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -268,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -276,7 +196,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -284,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -292,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -300,157 +220,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
@@ -459,7 +236,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -467,7 +244,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -475,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -483,7 +260,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -491,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -499,7 +276,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -507,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -515,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -523,7 +300,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -531,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -539,7 +316,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -547,14 +324,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -562,7 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -570,7 +347,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -578,7 +355,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -586,7 +363,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -594,7 +371,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -602,7 +379,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -610,7 +387,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -618,7 +395,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -626,7 +403,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -634,7 +411,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -642,7 +419,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
@@ -650,669 +427,63 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
                   double* GKYL_RESTRICT flux_surf); 
+
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
               const double *w, const double *dxv,
               const double *vmap_prime_l, const double *vmap_prime_r, 
               const double *vmap, const double *vmapSq, const double q_, const double m_, 
               const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
               double* GKYL_RESTRICT flux_surf); 
 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf);
 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
+    const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_r, 
+    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+    const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+    double* GKYL_RESTRICT flux_surf); 
 
 EXTERN_C_END
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 5d8aac4631..f7ad52c76b 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -46,9 +46,15 @@ gkyl_gyrokinetic_set_auxfields(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_gyr
 struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_cell_threshold, const bool no_by, const bool add_em,
+  const double charge, const double mass, double skip_cell_threshold, 
+  const bool no_by, const bool is_em, const bool add_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
+
+  // gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
+  // const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
+  // const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
+  // const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
@@ -77,6 +83,8 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   gyrokinetic->eqn.boundary_diag_term = boundary_diag;
 
   const gkyl_dg_gyrokinetic_vol_kern_list *vol_kernels, *vol_no_by_kernels;
+  const gkyl_dg_gyrokinetic_vol_add_apar_kern_list *vol_add_apar_kernels;
+  const gkyl_dg_gyrokinetic_vol_kern_list *vol_add_apardot_kernels;
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_x_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_y_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_z_kernels; 
@@ -89,6 +97,8 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   switch (cbasis->b_type) {
     case GKYL_BASIS_MODAL_SERENDIPITY:
       vol_kernels = ser_vol_kernels;
+      vol_add_apar_kernels = ser_add_apar_vol_kernels;
+      vol_add_apardot_kernels = ser_add_apardot_vol_kernels;
       surf_x_kernels = ser_surf_x_kernels;
       surf_y_kernels = ser_surf_y_kernels;
       surf_z_kernels = ser_surf_z_kernels;
@@ -110,9 +120,16 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
     gyrokinetic->eqn.vol_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
+    if (add_apardot)
+      gyrokinetic->eqn.vol_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+    else
+      gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
+  // gyrokinetic->vol_add_apar_term = COLLESS_TYPE == GKYL_GK_COLLISIONLESS_EM ? CK(vol_add_apar_kernels,cdim,vdim,poly_order) 
+  // : kernel_dg_gyrokinetic_vol_return_zero;
+  gyrokinetic->vol_add_apar_term = is_em ? CK(vol_add_apar_kernels,cdim,vdim,poly_order) : kernel_dg_gyrokinetic_vol_return_zero;
+
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
   if (cdim>1)
     gyrokinetic->surf[1] = CK(surf_y_kernels,cdim,vdim,poly_order);
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index ecf3b34003..d454ad4af6 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -15,12 +15,14 @@ gkyl_dg_updater_gyrokinetic_acquire_eqn(const gkyl_dg_updater_gyrokinetic* gyrok
   return gkyl_dg_eqn_acquire(gyrokinetic->eqn_gyrokinetic);
 }
 
+// TODO: remove add_em flag and replace by the collisionless enum type.
+
 struct gkyl_dg_updater_gyrokinetic*
 gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid, 
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom, 
+  const bool no_by, const bool is_em, const bool add_apardot, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -28,7 +30,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, no_by, add_em, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, no_by, is_em, add_apardot, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index a3183db174..85bba2e56f 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -9,11 +9,16 @@
 #include <gkyl_gk_collisionless_flux_priv.h>
 #include <gkyl_util.h>
 
+// TODO: remove add_em flag and replace by the collisionless enum type.
+// TODO: Combine apar and ES kernel together to allow the add Apardot only option.
+// TODO: In particular I have to have the same signature for each kernels regardless of whether they add EM terms or not,
+//       so that we can pass apar, or apardot if needed.
+
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by, const bool add_em,
-  const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const double charge, const double mass, const bool no_by, const bool is_em,
+  const bool add_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
 {
@@ -35,24 +40,28 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
-  up->add_em = add_em;
+  up->is_em = is_em;
+  up->add_apardot = add_apardot;
   up->gk_geom = gkyl_gk_geometry_acquire(gk_geom);
   up->dg_geom = gkyl_dg_geom_acquire(dg_geom);
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
-  if (no_by) {
-    if (add_em) {
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_no_by_edge_surf_conf_kern(d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_no_by_surf_vpar_kern(cdim, vdim, poly_order);
-    } else {
+  // Set apardot function to zero by default.
+  up->flux_surfvpar_add_apardot[0] = get_gk_collisionless_flux_surfvpar_zero_kern();
+  
+  // Choose appropriate kernels.
+  if (add_apardot){
+    // If we only add Apardot terms to the flux, we set every conf flux_surf kernel to 0 and we cable the vpar one to the
+    // appropriate add Apardot kernel (no conf surf contributions).
+    for (int d=0; d<cdim; ++d) {
+      up->flux_surf[d] = get_gk_collisionless_flux_surf_zero_kern();
+      up->flux_surf_edge_lo[d] = get_gk_collisionless_flux_surf_zero_kern();
+      up->flux_surf_edge_up[d] = get_gk_collisionless_flux_surf_zero_kern();
+    }
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
+  } else {
+    if (no_by) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
         up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
@@ -62,18 +71,6 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
           poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
       }
       up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
-    }
-  } else {
-    if (add_em) {
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_add_em_surf_conf_kern(d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_em_surf_vpar_kern(cdim, vdim, poly_order);
     } else {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
@@ -96,7 +93,8 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
 void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
-  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
+  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
+  const struct gkyl_array *phi, const struct gkyl_array *apar,
   const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 {
 #ifdef GKYL_HAVE_CUDA
@@ -133,6 +131,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
 
     const double *bmag_d = gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = gkyl_array_cfetch(phi, loc_conf);
+    const double *apar_d = gkyl_array_cfetch(apar, loc_conf);
     const double *vmap_d = gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -156,11 +155,11 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
       if (idx[dir] == phase_range->lower[dir]) {
         // Lower domain/block boundary.
         cflrate_d[0] += up->flux_surf_edge_lo[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
       } else {
         // Interior, lower cell surface.
         cflrate_d[0] += up->flux_surf[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
       }
 
       // Upper domain/block boundary.
@@ -187,7 +186,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
         double* flux_surf_ext_d = gkyl_array_fetch(flux_surf, loc_phase_ext);
 
         cflrate_ext_d[0] += up->flux_surf_edge_up[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_ext_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_ext_d);
       }  
     }
   }
@@ -206,6 +205,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
 
     const double *bmag_d = gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = gkyl_array_cfetch(phi, loc_conf);
+    const double *apar_d = gkyl_array_cfetch(apar, loc_conf);
     const double *vmap_d = gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -228,10 +228,8 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
     const struct gkyl_dg_vol_geom *dgv = gkyl_dg_geom_get_vol(up->dg_geom, idx);
     const struct gkyl_gk_dg_vol_geom *gkdgv = gkyl_gk_dg_geom_get_vol(up->gk_dg_geom, idx);
     cflrate_d[0] += up->flux_surfvpar[0](xc, up->phase_grid.dx, vpL, vpR, vmap_d, vmapSq_d, up->charge, up->mass,
-      dgv, gkdgv, bmag_d, phi_d,  fL, fR, flux_surf_d);
+      dgv, gkdgv, bmag_d, phi_d, apar_d, fL, fR, flux_surf_d);
   }
-
-
 }
 
 void gkyl_gk_collisionless_flux_release(gkyl_gk_collisionless_flux *up)
diff --git a/gyrokinetic/zero/gk_dg_geom.c b/gyrokinetic/zero/gk_dg_geom.c
index 43edc7fd6a..16c43be256 100644
--- a/gyrokinetic/zero/gk_dg_geom.c
+++ b/gyrokinetic/zero/gk_dg_geom.c
@@ -160,6 +160,16 @@ gkyl_gk_dg_geom_populate_vol(struct gkyl_dg_geom *dg_geom, struct gkyl_gk_dg_geo
       gkdgv[qvloc].dualcurlbhat.x[0] = global_val[0];
       gkdgv[qvloc].dualcurlbhat.x[1] = global_val[1];
       gkdgv[qvloc].dualcurlbhat.x[2] = global_val[2];
+
+      // set g_ij components
+      global_val = gkyl_array_cfetch(gk_geom->geo_int.g_ij_nodal, global_loc);
+      gkdgv[qvloc].g_13 = global_val[2]; // g_{13}
+      gkdgv[qvloc].g_23 = global_val[4]; // g_{23}
+      gkdgv[qvloc].g_33 = global_val[5]; // g_{33}
+
+      // set magnitude of e_3
+      global_val = gkyl_array_cfetch(gk_geom->geo_int.dualmag_nodal, global_loc);
+      gkdgv[qvloc].mag_e_3 = global_val[2]; // |e^3|
     }
   }
 }
diff --git a/gyrokinetic/zero/gk_geometry.c b/gyrokinetic/zero/gk_geometry.c
index 4974f95fd0..55e5c0efb8 100644
--- a/gyrokinetic/zero/gk_geometry.c
+++ b/gyrokinetic/zero/gk_geometry.c
@@ -373,6 +373,7 @@ gkyl_gk_geometry_deflate(const struct gk_geometry* up_3d, struct gkyl_gk_geometr
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.B3_nodal, up->geo_int.B3_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.bmag_nodal, up->geo_int.bmag_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.dualcurlbhat_nodal, up->geo_int.dualcurlbhat_nodal, 3);
+  gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.dualmag_nodal, up->geo_int.dualmag_nodal, 3);
   gkyl_deflate_geo_release(deflator);
 
   if (up->grid.ndim==1) {
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index 4699b69acf..7aea13e2a7 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -28,7 +28,8 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param no_by Whether to neglect the toroidal field (b_y=0)
- * @param add_em Whether the updater only adds EM terms.
+ * @param is_em Whether the updater only adds EM terms.
+ * @param add_apardot Whether to add the AparDot terms only.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -37,7 +38,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom,
+  const bool no_by, const bool is_em, const bool add_apardot, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 33bf5f7e6f..4b65faa4c4 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -12,6 +12,16 @@
 #include <gkyl_dg_gyrokinetic.h>
 
 // Types for various kernels.
+typedef double (*dg_gyrokinetic_vol_add_apar_t)(const double *w, const double *dxv, 
+  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+  const double *bmag, const double *jacobtot_inv, const double *b_i, const double *phi, 
+  const double *apar, const double *fin, double* GKYL_RESTRICT out);
+
+typedef double (*dg_gyrokinetic_vol_add_apardot_t)(const double *w, const double *dxv, 
+  const double *vmap, const double *vmapSq,const double q_, const double m_, 
+  const double *bmag, const double *jacobtot_inv, const double *b_i, const double *phi, 
+  const double *apardot, const double *fin, double* GKYL_RESTRICT out);
+
 typedef double (*dg_gyrokinetic_surf_t)( const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
   const double *flux_surf_l, const double *flux_surf_r, double* GKYL_RESTRICT out
@@ -33,6 +43,7 @@ static struct { int vdim[3]; } cv_index[] = {
 
 // for use in kernel tables
 typedef struct { vol_termf_t kernels[3]; } gkyl_dg_gyrokinetic_vol_kern_list;
+typedef struct { dg_gyrokinetic_vol_add_apar_t kernels[3]; } gkyl_dg_gyrokinetic_vol_add_apar_kern_list;
 typedef struct { dg_gyrokinetic_surf_t kernels[3]; } gkyl_dg_gyrokinetic_surf_kern_list;
 typedef struct { dg_gyrokinetic_boundary_surf_t kernels[3]; } gkyl_dg_gyrokinetic_boundary_surf_kern_list;
 
@@ -40,6 +51,7 @@ struct dg_gyrokinetic {
   struct gkyl_dg_eqn eqn; // Base object.
   int cdim; // Config-space dimensions.
   int pdim; // Phase-space dimensions.
+  dg_gyrokinetic_vol_add_apar_t vol_add_apar_term; // Additional volume term for Apar contribution.
   dg_gyrokinetic_surf_t surf[4]; // Surface terms.
   dg_gyrokinetic_boundary_surf_t boundary_surf[4]; // Surface terms for velocity boundary.
   struct gkyl_range conf_range; // Configuration space range.
@@ -74,7 +86,8 @@ kernel_dg_gyrokinetic_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_vol_1x1v_ser_p1(xc, dx,
+  double cfl = 0.0;
+  cfl = dg_gyrokinetic_vol_1x1v_ser_p1(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -84,6 +97,17 @@ kernel_dg_gyrokinetic_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
     qIn, qRhsOut);
+  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
+    qIn, qRhsOut);
+  return cfl;
 }
 
 GKYL_CU_DH
@@ -103,7 +127,8 @@ kernel_dg_gyrokinetic_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_vol_1x2v_ser_p1(xc, dx,
+  double cfl = 0.0;
+  cfl = dg_gyrokinetic_vol_1x2v_ser_p1(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -113,6 +138,17 @@ kernel_dg_gyrokinetic_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
     qIn, qRhsOut);
+  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
+    qIn, qRhsOut);
+  return cfl;
 }
 
 GKYL_CU_DH
@@ -132,7 +168,8 @@ kernel_dg_gyrokinetic_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_vol_2x2v_ser_p1(xc, dx,
+  double cfl = 0.0;
+  cfl = dg_gyrokinetic_vol_2x2v_ser_p1(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -142,6 +179,17 @@ kernel_dg_gyrokinetic_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
     qIn, qRhsOut);
+  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
+    qIn, qRhsOut);
+  return cfl;
 }
 
 GKYL_CU_DH
@@ -161,7 +209,8 @@ kernel_dg_gyrokinetic_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_vol_3x2v_ser_p1(xc, dx,
+  double cfl = 0.0;
+  cfl = dg_gyrokinetic_vol_3x2v_ser_p1(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -171,6 +220,17 @@ kernel_dg_gyrokinetic_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
     qIn, qRhsOut);
+  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
+    qIn, qRhsOut);
+  return cfl;
 }
 
 // Volume kernel list.
@@ -260,143 +320,39 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_no_by_vol_kernels[] = {
   { NULL, kernel_dg_gyrokinetic_no_by_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-//
-// Serendipity surface kernels general geometry
-//
-// Surface kernel list: x-direction
+// Electromagnetic serendipity volume kernels general geometry.
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_x_kernels[] = {
+static const gkyl_dg_gyrokinetic_vol_add_apar_kern_list ser_add_apar_vol_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_add_apar_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_apar_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_add_apar_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_surfx_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_add_apar_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-// Surface kernel list: y-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_y_kernels[] = {
-  // 1x kernels
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  // 2x kernels
-  { NULL, dg_gyrokinetic_surfy_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Surface kernel list: z-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_z_kernels[] = {
-  // 1x kernels
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  // 2x kernels
-  { NULL, NULL, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Acceleration surface kernel list: vpar-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_vpar_kernels[] = {
-  // 1x kernels
-  { NULL, dg_gyrokinetic_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_surfvpar_1x2v_ser_p1, NULL }, // 1
-  // 2x kernels
-  { NULL, dg_gyrokinetic_surfvpar_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_surfvpar_3x2v_ser_p1, NULL }, // 3
-};
-
-// Conf-space advection boundary surface kernel list: x-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_x_kernels[] = {
-  // 1x kernels
-  { NULL, dg_gyrokinetic_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-  // 2x kernels
-  { NULL, dg_gyrokinetic_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Conf-space advection boundary surface kernel list: y-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_y_kernels[] = {
-  // 1x kernels
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  // 2x kernels
-  { NULL, dg_gyrokinetic_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Conf-space advection boundary surface kernel list: z-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_z_kernels[] = {
-  // 1x kernels
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  // 2x kernels
-  { NULL, NULL, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Acceleration boundary surface kernel (zero-flux BCs) list: vpar-direction
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_vpar_kernels[] = {
-  // 1x kernels
-  { NULL, dg_gyrokinetic_boundary_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_boundary_surfvpar_1x2v_ser_p1, NULL }, // 1
-  // 2x kernels
-  { NULL, dg_gyrokinetic_boundary_surfvpar_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1, NULL }, // 3
-};
-
-//
-// Serendipity volume kernels general geometry
-// Need to be separated like this for GPU build
-//
-
 GKYL_CU_DH
 static double
-kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+kernel_dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
   const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
 {
-  
   struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
 
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
+  
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_vol_1x1v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+  return dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(
     gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
 }
 
 GKYL_CU_DH
 static double
-kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+kernel_dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
   const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
 {
   struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
@@ -404,28 +360,17 @@ kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
+  
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_vol_1x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+  return dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(
     gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
 }
 
 GKYL_CU_DH
 static double
-kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+kernel_dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
   const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
 {
   struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
@@ -433,28 +378,17 @@ kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
+  
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_vol_2x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+  return dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(
     gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
 }
 
 GKYL_CU_DH
 static double
-kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+kernel_dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
   const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
 {
   struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
@@ -463,208 +397,132 @@ kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, cons
     return 0.;
   }
   
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_vol_3x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+  return dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(
     gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
 }
 
-// Volume kernel list.
+// Electromagnetic volume kernel list (apardot).
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_vol_kernels[] = {
+static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_apardot_vol_kernels[] = {
   // 1x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1, NULL }, // 1
+  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_2x2v_ser_p1, NULL }, // 2
+  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_3x2v_ser_p1, NULL }, // 3
+  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-//
-// Serendipity volume kernels general geometry, no toroidal field (by=0)
-// Need to be separated like this for GPU build
-//
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
+// To turn off EM effects:
+#include <gkyl_dg_gyrokinetic_kernels.h> 
+GKYL_CU_DH double kernel_dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  return 0.; 
+} 
 
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-}
-
-// Volume kernel list.
-GKYL_CU_D
-static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_em_no_by_vol_kernels[] = {
-  // 1x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, kernel_dg_gyrokinetic_add_em_vol_1x2v_ser_p1, NULL }, // 1
-  // 2x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_no_by_vol_2x2v_ser_p1, NULL }, // 2
-  // 3x kernels
-  { NULL, kernel_dg_gyrokinetic_add_em_no_by_vol_3x2v_ser_p1, NULL }, // 3
-};
 
 //
 // Serendipity surface kernels general geometry
 //
 // Surface kernel list: x-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_x_kernels[] = {
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_x_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_em_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_em_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_surfx_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_surfx_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_surfx_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Surface kernel list: y-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_y_kernels[] = {
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_y_kernels[] = {
   // 1x kernels
   { NULL, NULL, NULL }, // 0
   { NULL, NULL, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_surfy_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_surfy_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Surface kernel list: z-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_z_kernels[] = {
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_z_kernels[] = {
   // 1x kernels
   { NULL, NULL, NULL }, // 0
   { NULL, NULL, NULL }, // 1
   // 2x kernels
   { NULL, NULL, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_surfz_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Acceleration surface kernel list: vpar-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_surf_kern_list ser_add_em_surf_vpar_kernels[] = {
+static const gkyl_dg_gyrokinetic_surf_kern_list ser_surf_vpar_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_surfvpar_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_surfvpar_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_surfvpar_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
 // Conf-space advection boundary surface kernel list: x-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_x_kernels[] = {
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_x_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_em_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_boundary_surfx_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_boundary_surfx_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_boundary_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Conf-space advection boundary surface kernel list: y-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_y_kernels[] = {
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_y_kernels[] = {
   // 1x kernels
   { NULL, NULL, NULL }, // 0
   { NULL, NULL, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_boundary_surfy_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_boundary_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Conf-space advection boundary surface kernel list: z-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_z_kernels[] = {
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_z_kernels[] = {
   // 1x kernels
   { NULL, NULL, NULL }, // 0
   { NULL, NULL, NULL }, // 1
   // 2x kernels
   { NULL, NULL, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_boundary_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Acceleration boundary surface kernel (zero-flux BCs) list: vpar-direction
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_add_em_boundary_surf_vpar_kernels[] = {
+static const gkyl_dg_gyrokinetic_boundary_surf_kern_list ser_boundary_surf_vpar_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_boundary_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_boundary_surfvpar_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_boundary_surfvpar_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, dg_gyrokinetic_add_em_boundary_surfvpar_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
 // "Choose Kernel" based on cdim, vdim and polyorder
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 6a3168695f..0cffbb84a9 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -30,7 +30,8 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param no_by Whether to neglect the toroidal field (b_y=0)
- * @param add_em Whether to add electromagnetic terms
+ * @param is_em Whether to add electromagnetic terms
+ * @param add_apardot Whether to add the AparDot terms only.
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -41,7 +42,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  const bool no_by, const bool add_em, const struct gk_geometry *gk_geom,
+  const bool no_by, const bool is_em, const bool add_apartdot, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
@@ -70,6 +71,19 @@ void gkyl_dg_updater_gyrokinetic_advance(gkyl_dg_updater_gyrokinetic *gyrokineti
   const struct gkyl_range *update_rng, const struct gkyl_array* GKYL_RESTRICT fIn,
   struct gkyl_array* GKYL_RESTRICT cflrate, struct gkyl_array* GKYL_RESTRICT rhs);
 
+/**
+ * Add Apardot electromagnetic contribution to the RHS.
+ * 
+ * @param gyrokinetic 
+ * @param update_rng 
+ * @param fIn 
+ * @param cflrate 
+ * @param rhs 
+ */
+void gkyl_dg_updater_gyrokinetic_add_apardot(gkyl_dg_updater_gyrokinetic *gyrokinetic,
+  const struct gkyl_range *update_rng, const struct gkyl_array* GKYL_RESTRICT fIn,
+  struct gkyl_array* GKYL_RESTRICT cflrate, struct gkyl_array* GKYL_RESTRICT rhs);
+
 /**
  * Return total time spent in gyrokinetic equation
  *
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic_priv.h
index 4a31af8325..0cf74cda77 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic_priv.h
@@ -5,9 +5,12 @@
 #include <gkyl_dg_updater_gyrokinetic.h>
 
 struct gkyl_dg_updater_gyrokinetic {
-  bool use_gpu; // Boolean for if the update is performed on GPUs
-  struct gkyl_dg_eqn *eqn_gyrokinetic; // Equation object
-  struct gkyl_hyper_dg *up_gyrokinetic; // solvers for specific gyrokinetic equation
+  bool use_gpu; // Boolean for if the update is performed on GPUs.
+  struct gkyl_dg_eqn *eqn_gyrokinetic; // Equation object.
+  struct gkyl_hyper_dg *up_gyrokinetic; // Solvers for specific gyrokinetic equation.
 
-  double gyrokinetic_tm; // total time spent in computing gyrokinetic equation
+  struct gkyl_dg_eqn *eqn_add_apardot_gyrokinetic; // Equation object to only add Apardot contribution.
+  struct gkyl_hyper_dg *up_add_apardot_gyrokinetic; // Solver to only add Apardot contribution.
+
+  double gyrokinetic_tm; // Total time spent in computing gyrokinetic equation.
 };
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index 47fdbb6918..fccb1e96d6 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -23,7 +23,8 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * @param charge Species charge.
  * @param mass Species mass.
  * @param no_by Whether to neglect the toroidal field (b_y=0).
- * @param add_em Whether this updater is meant to add EM terms only.
+ * @param is_em Whether this updater is EM.
+ * @param add_apardot Whether this updater is meant to add Apardot terms only.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
@@ -34,8 +35,8 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by, const bool add_em,
-  const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const double charge, const double mass, const bool no_by, const bool is_em,
+  const bool add_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
 
@@ -52,13 +53,15 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
  * @param conf_ext_range Extended configuration space range (so we obtain geo quantities at all the needed surfaces).
  * @param phase_ext_range Extended Phase space range (so we obtain alpha_surf at all the needed surfaces).
  * @param phi Electrostatic potential.
+ * @param apar Parallel component of vector potential.
  * @param fin Distribution function.
  * @param flux_surf Output surface expansion in a cell on the *lower* edge in each direction.
  * @param clfrate Output CFL rate.
  */
 void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
-  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
+  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
+  const struct gkyl_array *phi, const struct gkyl_array *apar,
   const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index bc01805ce9..e715cfc0e0 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -14,14 +14,15 @@ typedef double (*gk_collisionless_flux_surf_t)(const double *w, const double *dx
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-  const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
+  const double *apar, const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
 
 typedef double (*gk_collisionless_flux_surfvpar_t)( 
   const double *w, const double *dxv, 
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-  const double *bmag, const double *phi, const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
+  const double *bmag, const double *phi, const double *apar,
+  const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
 
 // The cv_index[cd].vdim[vd] is used to index the various list of
 // kernels below.
@@ -46,8 +47,12 @@ struct gkyl_gk_collisionless_flux {
   gk_collisionless_flux_surf_t flux_surf_edge_up[GKYL_MAX_CDIM]; // kernel for computing surface expansion of phase space flux.
                                                         // at upper configuration space edge
   gk_collisionless_flux_surfvpar_t flux_surfvpar[1]; // kernel for computing surface expansion of phase space flux alpha
+  
+  gk_collisionless_flux_surfvpar_t flux_surfvpar_add_apardot[1]; // kernel for adding dA_par/dt terms to surface expansion of phase space flux.
+
   double charge, mass;
-  bool add_em; // wheter it is meant to only add electromagnetic terms.
+  bool is_em; // Whether it is electromagnetic.
+  bool add_apardot; // Whether it is meant to only add Apardot terms.
   const struct gk_geometry *gk_geom; // Pointer to geometry struct.
   const struct gkyl_dg_geom *dg_geom; // Pointer to vol dg geometry struct.
   const struct gkyl_gk_dg_geom *gk_dg_geom; // Pointer to vol gk dg geometry struct.
@@ -427,369 +432,34 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_o
 
 //
 // Electromagnetic serendipity surface kernels.
-//
-// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_edge_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_edge_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_em_surfvpar_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_surfvpar_3x2v_ser_p1, NULL }, // 3
-};
-
-//
-// Kernels used at multiblock boundaries.
-//
-
-// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-
-//
-// Serendipity surface kernels without toroidal field (by=0)
-//
-// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
+// Parallel electric field term.
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_em_no_by_surfvpar_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
-};
-
-//
-// Kernels used at multiblock boundaries.
-//
-
-// Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_apardot_surfvpar_kernels[] = {
+  { NULL, gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
-// Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-// Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-};
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_add_em_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_add_em_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+get_gk_collisionless_flux_surf_zero_kern()
 {
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
+  return gk_collisionless_flux_surf_return_zero;
 }
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_add_em_surf_vpar_kern(int cdim, int vdim, int poly_order)
-{
-  return ser_gk_collisionless_flux_add_em_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_add_em_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+get_gk_collisionless_flux_surfvpar_zero_kern()
 {
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)                                       
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)                                       
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-}
-
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_add_em_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
-{
-  if (bc == GKYL_BC_GK_SKIP) {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
-  else {
-    if (dir == 0)
-      return ser_gk_collisionless_flux_add_em_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 1)
-      return ser_gk_collisionless_flux_add_em_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else if (dir == 2)
-      return ser_gk_collisionless_flux_add_em_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-    else
-      return NULL;
-  }
+  return gk_collisionless_flux_surfvpar_return_zero;
 }
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_add_em_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
+choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_add_em_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_add_apardot_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 #ifdef GKYL_HAVE_CUDA
diff --git a/gyrokinetic/zero/gkyl_gk_dg_geom.h b/gyrokinetic/zero/gkyl_gk_dg_geom.h
index 838b018382..41cb2d6482 100644
--- a/gyrokinetic/zero/gkyl_gk_dg_geom.h
+++ b/gyrokinetic/zero/gkyl_gk_dg_geom.h
@@ -22,6 +22,10 @@ struct gkyl_gk_dg_vol_geom {
   double bmag; // |B|
   double B3; // n^3 \cdot \vec{B}
   struct gkyl_vec3 dualcurlbhat; // duals dotted with curl(bhat)
+  double g_13; // metric tensor component g_{13} = e_1 . e_3
+  double g_23; // metric tensor component g_{23} = e_2 . e_3
+  double g_33; // metric tensor component g_{33} = e_3 . e_3
+  double mag_e_3; // magnitude of e_3
 };
 
 

From 70bcd7eb30b5d2ef1b6f23d220f28071a5000470 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 5 Nov 2025 18:24:47 -0500
Subject: [PATCH 029/181] microfix of a bug that occured during the merge of
 main

---
 gyrokinetic/apps/gyrokinetic.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 3996ecb59b..e8d87e028e 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -881,7 +881,7 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
       // MF 2024/09/27/: Need the cast here for consistency. Fixing
       // this may require removing 'const' from a lot of places.
       gyrokinetic_calc_field_enabled(app, t0, (const struct gkyl_array **) distf, bflux);
-    else {
+    } else {
       if (app->field->info.init_field_profile == 0)
         // Read the field.
         gk_field_file_import_init(app, app->field->info.init_from_file);

From fcf2904a07beb5b7e2a3d64a70db87ada5d634cb Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 09:52:04 -0500
Subject: [PATCH 030/181] manualy port the collisionless_id and use it to
 decide if we add apar and apardot terms.

---
 core/zero/gkyl_eqn_type.h                     |  1 +
 gyrokinetic/apps/gk_species_collisionless.c   | 22 +++++++++----------
 gyrokinetic/zero/dg_gyrokinetic.c             | 11 +++++-----
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |  4 ++--
 gyrokinetic/zero/gk_collisionless_flux.c      | 14 +++++-------
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |  8 +++----
 .../zero/gkyl_dg_updater_gyrokinetic.h        |  7 +++---
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h | 21 +++++++++---------
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  2 +-
 9 files changed, 43 insertions(+), 47 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 73b458e3d4..8fc42b6e36 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -178,6 +178,7 @@ enum gkyl_gk_anomalous_diff_id {
 enum gkyl_gk_collisionless_type {
   GKYL_GK_COLLISIONLESS_NONE = 0, // Turns off collisionless terms.
   GKYL_GK_COLLISIONLESS_ES, // Electrostatic.
+  GKYL_GK_COLLISIONLESS_ES_NO_BY, // Electrostatic, w/o toroidal field (b_y=0).
   GKYL_GK_COLLISIONLESS_EM_BPERP, // Electromagnetic with B_perp fluctuations.
   GKYL_GK_COLLISIONLESS_EM_BPAR, // Electromagnetic with B_par fluctuations.
   GKYL_GK_COLLISIONLESS_EM, // Electromagnetic with B_perp and B_par fluctuations.
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 84a7156d16..67dd8b4a96 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -132,9 +132,9 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       bctype_conf[GKYL_MAX_CDIM+d] = gks->upper_bc[d].type;
     }
 
-    bool add_apardot = false;
+    bool only_apardot = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -142,20 +142,20 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
     
     if (gkcls->is_em) {
-      add_apardot = true;
+      only_apardot = true;
       // Create a special flux operator that only adds the AparDot contribution.
-      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis,
-        gks->info.charge, gks->info.mass, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom,
-        app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
+      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+      gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
+      app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
       // Create solver that only adds AparDot terms.
-      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis,
-        &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gks->info.skip_cell_threshold, gkcls->no_by, gkcls->is_em, add_apardot, app->gk_geom, gks->vel_map,
-        &aux_inp, app->use_gpu);
+      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+      &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+      gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
+      &aux_inp, app->use_gpu);
     }
           
     // Methods chosen at runtime.
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index f7ad52c76b..187b3d8d01 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -47,7 +47,7 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  const bool no_by, const bool is_em, const bool add_apardot,
+  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 
@@ -116,19 +116,18 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       break;
   }
 
-  if (no_by) {
+  if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
     gyrokinetic->eqn.vol_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    if (add_apardot)
+    if (only_apardot)
       gyrokinetic->eqn.vol_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
     else
       gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
-  // gyrokinetic->vol_add_apar_term = COLLESS_TYPE == GKYL_GK_COLLISIONLESS_EM ? CK(vol_add_apar_kernels,cdim,vdim,poly_order) 
-  // : kernel_dg_gyrokinetic_vol_return_zero;
-  gyrokinetic->vol_add_apar_term = is_em ? CK(vol_add_apar_kernels,cdim,vdim,poly_order) : kernel_dg_gyrokinetic_vol_return_zero;
+  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM  ? 
+    CK(vol_add_apar_kernels,cdim,vdim,poly_order) : kernel_dg_gyrokinetic_vol_return_zero;
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
   if (cdim>1)
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index d454ad4af6..322aa2558d 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -22,7 +22,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  const bool no_by, const bool is_em, const bool add_apardot, const struct gk_geometry *gk_geom, 
+  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -30,7 +30,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, no_by, is_em, add_apardot, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, collless_type, only_apardot, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 85bba2e56f..28bd386614 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -17,8 +17,8 @@
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by, const bool is_em,
-  const bool add_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const double charge, const double mass, enum gkyl_gk_collisionless_type type,
+  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
 {
@@ -40,8 +40,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
-  up->is_em = is_em;
-  up->add_apardot = add_apardot;
+  up->only_apardot = only_apardot;
   up->gk_geom = gkyl_gk_geometry_acquire(gk_geom);
   up->dg_geom = gkyl_dg_geom_acquire(dg_geom);
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
@@ -51,9 +50,8 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   up->flux_surfvpar_add_apardot[0] = get_gk_collisionless_flux_surfvpar_zero_kern();
   
   // Choose appropriate kernels.
-  if (add_apardot){
-    // If we only add Apardot terms to the flux, we set every conf flux_surf kernel to 0 and we cable the vpar one to the
-    // appropriate add Apardot kernel (no conf surf contributions).
+  if (only_apardot){
+    // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
     for (int d=0; d<cdim; ++d) {
       up->flux_surf[d] = get_gk_collisionless_flux_surf_zero_kern();
       up->flux_surf_edge_lo[d] = get_gk_collisionless_flux_surf_zero_kern();
@@ -61,7 +59,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
-    if (no_by) {
+    if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
         up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index 7aea13e2a7..43ec48ee34 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -27,9 +27,8 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param charge Species charge
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
- * @param no_by Whether to neglect the toroidal field (b_y=0)
- * @param is_em Whether the updater only adds EM terms.
- * @param add_apardot Whether to add the AparDot terms only.
+ * @param collless_type Type of collisionless terms.
+ * @param only_apardot Whether we want to only add the apardot term.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -38,9 +37,10 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  const bool no_by, const bool is_em, const bool add_apardot, const struct gk_geometry *gk_geom,
+  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
+
 /**
  * Set the auxiliary fields (e.g. EM fields) needed in computing
  * gyrokinetic updates.
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 0cffbb84a9..3512e87fe7 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -29,9 +29,8 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param charge Species charge
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
- * @param no_by Whether to neglect the toroidal field (b_y=0)
- * @param is_em Whether to add electromagnetic terms
- * @param add_apardot Whether to add the AparDot terms only.
+ * @param collless_type Type of collisionless terms.
+ * @param only_apardot Whether we want to only add the apardot term.
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -42,7 +41,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  const bool no_by, const bool is_em, const bool add_apartdot, const struct gk_geometry *gk_geom,
+  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index fccb1e96d6..43db9539a5 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -17,26 +17,25 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * Create new updater to compute the surface expansion of phase space
  * flux due to the collisionless gyrokinetic terms.
  * 
- * @param phase_grid Phase space grid (for getting cell spacing and cell center).
- * @param conf_basis Configuration space basis functions.
- * @param phase_basis Phase space basis functions.
- * @param charge Species charge.
- * @param mass Species mass.
- * @param no_by Whether to neglect the toroidal field (b_y=0).
- * @param is_em Whether this updater is EM.
- * @param add_apardot Whether this updater is meant to add Apardot terms only.
+ * @param phase_grid Phase space grid (for getting cell spacing and cell center)
+ * @param conf_basis Configuration space basis functions
+ * @param phase_basis Phase space basis functions
+ * @param charge Species charge
+ * @param mass Species mass
+ * @param collless_type Type of collisionless terms.
+ * @param only_apardot Whether to only add Apardot terms to the flux.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
  * @param bctype_conf Type of conf-space BCs.
- * @param use_gpu Whether to use GPU.
+ * @param use_gpu bool to determine if on GPU
  * @return New updater pointer.
  */
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by, const bool is_em,
-  const bool add_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
+  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index e715cfc0e0..1554744832 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -52,7 +52,7 @@ struct gkyl_gk_collisionless_flux {
 
   double charge, mass;
   bool is_em; // Whether it is electromagnetic.
-  bool add_apardot; // Whether it is meant to only add Apardot terms.
+  bool only_apardot; // Whether it is meant to only add Apardot terms.
   const struct gk_geometry *gk_geom; // Pointer to geometry struct.
   const struct gkyl_dg_geom *dg_geom; // Pointer to vol dg geometry struct.
   const struct gkyl_gk_dg_geom *gk_dg_geom; // Pointer to vol gk dg geometry struct.

From 5df88fc8a716dab459f74aad83bf47da3e2d6bae Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 09:59:52 -0500
Subject: [PATCH 031/181] remove unused zero surf vpar kernel and adjust logic
 between EM and EM_BPERP.

---
 gyrokinetic/zero/dg_gyrokinetic.c                  | 2 +-
 gyrokinetic/zero/gk_collisionless_flux.c           | 5 +----
 gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h | 9 ---------
 3 files changed, 2 insertions(+), 14 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 187b3d8d01..5f45cec8b5 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -126,7 +126,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
-  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM  ? 
+  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM || GKYL_GK_COLLISIONLESS_EM_BPERP ? 
     CK(vol_add_apar_kernels,cdim,vdim,poly_order) : kernel_dg_gyrokinetic_vol_return_zero;
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 28bd386614..cf41588173 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -46,9 +46,6 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
-  // Set apardot function to zero by default.
-  up->flux_surfvpar_add_apardot[0] = get_gk_collisionless_flux_surfvpar_zero_kern();
-  
   // Choose appropriate kernels.
   if (only_apardot){
     // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
@@ -69,7 +66,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
           poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
       }
       up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
-    } else {
+    } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
         up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 1554744832..bc22bd4399 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -48,8 +48,6 @@ struct gkyl_gk_collisionless_flux {
                                                         // at upper configuration space edge
   gk_collisionless_flux_surfvpar_t flux_surfvpar[1]; // kernel for computing surface expansion of phase space flux alpha
   
-  gk_collisionless_flux_surfvpar_t flux_surfvpar_add_apardot[1]; // kernel for adding dA_par/dt terms to surface expansion of phase space flux.
-
   double charge, mass;
   bool is_em; // Whether it is electromagnetic.
   bool only_apardot; // Whether it is meant to only add Apardot terms.
@@ -448,13 +446,6 @@ get_gk_collisionless_flux_surf_zero_kern()
   return gk_collisionless_flux_surf_return_zero;
 }
 
-GKYL_CU_D
-static gk_collisionless_flux_surfvpar_t
-get_gk_collisionless_flux_surfvpar_zero_kern()
-{
-  return gk_collisionless_flux_surfvpar_return_zero;
-}
-
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
 choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int poly_order)

From 37799cbd9b1dddebc52b03ecc7925a88f980001d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 10:25:11 -0500
Subject: [PATCH 032/181] Simplification of the field enum table. We do not set
 if we have ES or EM anymore because this is set by the presence of a EM
 species. The is_clopen flag is removed because now it is simply the id
 GK_FIELD_IWL.

---
 core/zero/gkyl_eqn_type.h                     |  6 ++---
 gyrokinetic/apps/gk_field.c                   | 25 +++++++++++--------
 gyrokinetic/apps/gk_multib_field.c            |  2 +-
 gyrokinetic/apps/gk_species_projection.c      |  2 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  1 -
 gyrokinetic/apps/gyrokinetic.c                |  4 +--
 gyrokinetic/apps/gyrokinetic_lw.c             |  6 ++---
 gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c      |  2 +-
 gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c      |  2 +-
 gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c      |  2 +-
 .../creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c |  2 +-
 .../creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c |  2 +-
 12 files changed, 28 insertions(+), 28 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 8fc42b6e36..6e3c43b073 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -34,12 +34,10 @@ enum gkyl_eqn_type {
 
 // Identifiers for specific gyrokinetic field object types.
 enum gkyl_gkfield_id {
-  GKYL_GK_FIELD_ES = 0, // Electrostatic GK. This is default.
+  GKYL_GK_FIELD = 0, // This is default.
   GKYL_GK_FIELD_BOLTZMANN = 1, // GK Boltzmann, isothermal electrons, phi = phi_sheath + (T_e/e)*ln(n_i/n_is).
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
-  GKYL_GK_FIELD_ES_IWL = 3, // Inner-wall limited ES.
-  GKYL_GK_FIELD_EM = 4, // Electromagnetic GK.
-  GKYL_GK_FIELD_EM_IWL = 5, // Inner-wall limited EM.
+  GKYL_GK_FIELD_IWL = 3, // Inner-wall limited ES.
 };
 
 // Identifiers for specific field object types.
diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 35fe662533..dae8d771a8 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -270,11 +270,16 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   f->info = gk->field;
 
-  f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD_ES;
-
-  f->is_clopen = f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL;
-
-  f->is_em = f->gkfield_id == GKYL_GK_FIELD_EM || f->gkfield_id == GKYL_GK_FIELD_EM_IWL;
+  f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD;
+  
+  f->is_em = false;
+  // Ensure that if any species is electromagnetic, the field is electromagnetic.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    f->is_em = f->is_em || s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || 
+                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP ||
+                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPAR;
+  }
 
   f->calc_init_field = !f->info.zero_init_field;
   f->update_field = !f->info.is_static;
@@ -463,7 +468,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
   // Potential smoothing (in z) updater
-  if (f->is_clopen) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
     enum gkyl_fem_parproj_bc_type fem_parproj_bc_core, fem_parproj_bc_sol;
     if (app->cdim == 2) {
       fem_parproj_bc_core = GKYL_FEM_PARPROJ_PERIODIC;
@@ -745,7 +750,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
   f->enforce_parallel_bc = gk_field_enforce_parallel_bc_disabled;
-  if (f->is_clopen) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
     gk_field_add_TSBC_and_SSFG_updaters(app,f);
     f->enforce_parallel_bc = gk_field_enforce_parallel_bc_enabled;
   }
@@ -901,7 +906,7 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
       // Gather charge density into global array.
       // Smooth the charge density. Input is rho_c_global_dg, globally smoothed in z,
       // and then output should be in *local* phi_smooth.
-      if (field->is_clopen) {
+      if (field->gkfield_id == GKYL_GK_FIELD_IWL) {
         gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->rho_c, field->rho_c_global_dg);
         gkyl_fem_parproj_set_rhs(field->fem_parproj_core, field->rho_c_global_dg, field->rho_c_global_dg);
         gkyl_fem_parproj_solve(field->fem_parproj_core, field->rho_c_global_smooth);
@@ -1137,7 +1142,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     }
   }
 
-  if (app->cdim > 1 && f->is_clopen) {
+  if (app->cdim > 1 && f->gkfield_id == GKYL_GK_FIELD_IWL) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
   } else {
@@ -1145,7 +1150,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   }
 
   // Release TS BS and SSFG updater
-  if (f->is_clopen) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
     if(app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_T_LU_lo);
     }
diff --git a/gyrokinetic/apps/gk_multib_field.c b/gyrokinetic/apps/gk_multib_field.c
index fbb68473b1..9ad3fecbbd 100644
--- a/gyrokinetic/apps/gk_multib_field.c
+++ b/gyrokinetic/apps/gk_multib_field.c
@@ -417,7 +417,7 @@ gk_multib_field_new(const struct gkyl_gyrokinetic_multib *mbinp, struct gkyl_gyr
   struct gk_multib_field *mbf = gkyl_malloc(sizeof(struct gk_multib_field));
 
   mbf->info = mbinp->field;
-  mbf->gkfield_id = mbf->info.gkfield_id? mbf->info.gkfield_id : GKYL_GK_FIELD_ES;
+  mbf->gkfield_id = mbf->info.gkfield_id? mbf->info.gkfield_id : GKYL_GK_FIELD;
   mbf->num_local_blocks = mbapp->num_local_blocks;
   mbf->cdim = mbapp->block_topo->ndim;
   mbf->half_domain = mbf->info.half_domain ? mbf->info.half_domain : false;
diff --git a/gyrokinetic/apps/gk_species_projection.c b/gyrokinetic/apps/gk_species_projection.c
index 1a41cb8d9b..bf3cf7a93a 100644
--- a/gyrokinetic/apps/gk_species_projection.c
+++ b/gyrokinetic/apps/gk_species_projection.c
@@ -285,7 +285,7 @@ init_maxwellian_gaussian(struct gkyl_gyrokinetic_app *app, struct gk_species *s,
   // Set periodicity for last dim if we are in IWL, and all other directions defined by the user.
   for (int dir = 0; dir < GKYL_MAX_CDIM; ++dir)
     fg_ctx.is_dir_periodic[dir] = false;
-  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
+  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_IWL;
   for (int i=0; i < app->num_periodic_dir; ++i)
     fg_ctx.is_dir_periodic[app->periodic_dirs[i]] = true;
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 74c82e0b45..20a07b56ed 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1140,7 +1140,6 @@ struct gk_field {
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
   bool is_em; // Whether EM model.
-  bool is_clopen; // Whether we are in a closed + open field line geometry.
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index e8d87e028e..03aee232ea 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1153,7 +1153,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
-    if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+    if (app->field->is_em) {
       const char *fmt = "%s-apar_%d.gkyl";
       int sz = gkyl_calc_strlen(fmt, app->name, frame);
       char fileNm[sz+1]; // ensures no buffer overflow
@@ -1163,7 +1163,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
       }
       gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
     }
-    if (app->field->gkfield_id == GKYL_GK_FIELD_EM || app->field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+    if (app->field->is_em) {
       const char *fmt = "%s-apardot_%d.gkyl";
       int sz = gkyl_calc_strlen(fmt, app->name, frame);
       char fileNm[sz+1]; // ensures no buffer overflow
diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 22512460d9..0b0ffad779 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -66,12 +66,10 @@ static const struct gkyl_str_int_pair gk_collisionless_type[] = {
 
 // Gyrokinetic field type -> enum map.
 static const struct gkyl_str_int_pair gk_field_type[] = {
-  { "Electrostatic", GKYL_GK_FIELD_ES },
+  { "Default", GKYL_GK_FIELD },
   { "Boltzmann", GKYL_GK_FIELD_BOLTZMANN },
   { "Adiabatic", GKYL_GK_FIELD_ADIABATIC },
-  { "ElectrostaticIWL", GKYL_GK_FIELD_ES_IWL },
-  { "Electromagnetic", GKYL_GK_FIELD_EM },
-  { "ElectromagneticIWL", GKYL_GK_FIELD_EM_IWL },
+  { "Inner wall limited", GKYL_GK_FIELD_IWL },
   { 0, 0 }
 };
 
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
index c0dd850001..369e9e2e26 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
@@ -740,7 +740,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
+    .gkfield_id = GKYL_GK_FIELD_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
index d53d8415e3..6d3ac6c818 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
@@ -825,7 +825,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
+    .gkfield_id = GKYL_GK_FIELD_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
index 0debccf7a5..6358a82675 100644
--- a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
@@ -424,7 +424,7 @@ int main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
+    .gkfield_id = GKYL_GK_FIELD_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index 46a66d7af1..f8e325cfb1 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -748,7 +748,7 @@ main(int argc, char **argv)
 
   // Field.
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
+    .gkfield_id = GKYL_GK_FIELD_IWL,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 6e912d8602..7912cb0324 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -781,7 +781,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
+    .gkfield_id = GKYL_GK_FIELD_IWL,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },

From 443531110617410075e7a09243c9c2d67da44c8f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 10:36:47 -0500
Subject: [PATCH 033/181] Add a field_id to activate EM effects regardless of a
 possible EM species (useful for debugging or just checking how EM is
 important). Also I see that the regression test of d3d 2x2v is exaclty runing
 like the main branch right now so this branch is safe in term of not messing
 with ES limit.

---
 core/zero/gkyl_eqn_type.h   | 1 +
 gyrokinetic/apps/gk_field.c | 2 +-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 6e3c43b073..b38c545e75 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -38,6 +38,7 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD_BOLTZMANN = 1, // GK Boltzmann, isothermal electrons, phi = phi_sheath + (T_e/e)*ln(n_i/n_is).
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
   GKYL_GK_FIELD_IWL = 3, // Inner-wall limited ES.
+  GKYL_GK_FIELD_EM = 4, // To force electromagnetic field solve (even if no species is EM).
 };
 
 // Identifiers for specific field object types.
diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index dae8d771a8..3b89578eba 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -272,7 +272,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD;
   
-  f->is_em = false;
+  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM;
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];

From 5989b561a8be7822b5586c9d652a69add3dfdfd1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 10:41:05 -0500
Subject: [PATCH 034/181] need to add a EM_IWL field_id too

---
 core/zero/gkyl_eqn_type.h                |  1 +
 gyrokinetic/apps/gk_field.c              | 12 ++++++------
 gyrokinetic/apps/gk_species_projection.c |  2 +-
 gyrokinetic/apps/gyrokinetic_lw.c        |  2 ++
 4 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index b38c545e75..34ba8a6594 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -39,6 +39,7 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
   GKYL_GK_FIELD_IWL = 3, // Inner-wall limited ES.
   GKYL_GK_FIELD_EM = 4, // To force electromagnetic field solve (even if no species is EM).
+  GKYL_GK_FIELD_EM_IWL = 5, // As above but for IWL.
 };
 
 // Identifiers for specific field object types.
diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 3b89578eba..ac0ca76007 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -272,7 +272,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD;
   
-  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM;
+  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM || f->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
@@ -468,7 +468,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
   // Potential smoothing (in z) updater
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     enum gkyl_fem_parproj_bc_type fem_parproj_bc_core, fem_parproj_bc_sol;
     if (app->cdim == 2) {
       fem_parproj_bc_core = GKYL_FEM_PARPROJ_PERIODIC;
@@ -750,7 +750,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
   f->enforce_parallel_bc = gk_field_enforce_parallel_bc_disabled;
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     gk_field_add_TSBC_and_SSFG_updaters(app,f);
     f->enforce_parallel_bc = gk_field_enforce_parallel_bc_enabled;
   }
@@ -906,7 +906,7 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
       // Gather charge density into global array.
       // Smooth the charge density. Input is rho_c_global_dg, globally smoothed in z,
       // and then output should be in *local* phi_smooth.
-      if (field->gkfield_id == GKYL_GK_FIELD_IWL) {
+      if (field->gkfield_id == GKYL_GK_FIELD_IWL || field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
         gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->rho_c, field->rho_c_global_dg);
         gkyl_fem_parproj_set_rhs(field->fem_parproj_core, field->rho_c_global_dg, field->rho_c_global_dg);
         gkyl_fem_parproj_solve(field->fem_parproj_core, field->rho_c_global_smooth);
@@ -1142,7 +1142,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     }
   }
 
-  if (app->cdim > 1 && f->gkfield_id == GKYL_GK_FIELD_IWL) {
+  if (app->cdim > 1 && (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL)) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
   } else {
@@ -1150,7 +1150,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   }
 
   // Release TS BS and SSFG updater
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     if(app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_T_LU_lo);
     }
diff --git a/gyrokinetic/apps/gk_species_projection.c b/gyrokinetic/apps/gk_species_projection.c
index bf3cf7a93a..d5c0f10db5 100644
--- a/gyrokinetic/apps/gk_species_projection.c
+++ b/gyrokinetic/apps/gk_species_projection.c
@@ -285,7 +285,7 @@ init_maxwellian_gaussian(struct gkyl_gyrokinetic_app *app, struct gk_species *s,
   // Set periodicity for last dim if we are in IWL, and all other directions defined by the user.
   for (int dir = 0; dir < GKYL_MAX_CDIM; ++dir)
     fg_ctx.is_dir_periodic[dir] = false;
-  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_IWL;
+  fg_ctx.is_dir_periodic[app->cdim-1] = app->field->info.gkfield_id == GKYL_GK_FIELD_IWL || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
   for (int i=0; i < app->num_periodic_dir; ++i)
     fg_ctx.is_dir_periodic[app->periodic_dirs[i]] = true;
 
diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 0b0ffad779..61af730b18 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -70,6 +70,8 @@ static const struct gkyl_str_int_pair gk_field_type[] = {
   { "Boltzmann", GKYL_GK_FIELD_BOLTZMANN },
   { "Adiabatic", GKYL_GK_FIELD_ADIABATIC },
   { "Inner wall limited", GKYL_GK_FIELD_IWL },
+  { "Electromagnetic", GKYL_GK_FIELD_EM },
+  { "Electromagnetic Inner wall limited", GKYL_GK_FIELD_EM_IWL },
   { 0, 0 }
 };
 

From 9e35f23bf1fe013eefcafe839c67813244b75835 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 10:54:26 -0500
Subject: [PATCH 035/181] forgot to connect ampere bc input with the field
 initialization.

---
 gyrokinetic/apps/gk_field.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index ac0ca76007..1285dd418d 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -648,14 +648,14 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
       // Translate input file BCs into Ampere BCs.
       for (int d=0; d<app->cdim-1; d++) {
-        struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
+        struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
         if (bc_lo != 0) {
           f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
           for (int i=0; i<3; i++)
             f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
         }
 
-        struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.poisson_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
+        struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
         if (bc_up != 0) {
           f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
           for (int i=0; i<3; i++)

From 46ccfb5c78351c4fbbdbaecb357d643b7d4e02d9 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 14:29:07 -0500
Subject: [PATCH 036/181] Split the collisionless flux kernels between
 electrostatic (es) and electromagnetic (em). The em one are including Apar.
 The split is meant to avoid many steps that are reduced to 0 when using the
 em in the es limit. This commit can run in the ES limit while also compute
 the EM fields.

---
 gyrokinetic/apps/gk_species.c                 |   12 +-
 gyrokinetic/apps/gk_species_collisionless.c   |   34 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |    4 +-
 gyrokinetic/apps/gyrokinetic.c                |   41 +-
 .../gk_collisionless_flux_surf_return_zero.h  |    0
 ...s_flux_add_apardot_surfvpar_1x1v_ser_p1.c} |    2 +-
 ...s_flux_add_apardot_surfvpar_1x2v_ser_p1.c} |    2 +-
 ...s_flux_add_apardot_surfvpar_2x2v_ser_p1.c} |    2 +-
 ...s_flux_add_apardot_surfvpar_3x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfx_1x1v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfx_1x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfx_2x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfx_3x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfy_2x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfy_3x2v_ser_p1.c} |    2 +-
 ...llisionless_flux_edge_surfz_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_1x1v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_1x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfx_1x1v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfx_1x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfx_2x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfx_3x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfy_2x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfy_3x2v_ser_p1.c} |    2 +-
 ..._flux_multib_boundary_surfz_3x2v_ser_p1.c} |    2 +-
 ...nless_flux_no_by_edge_surfx_2x2v_ser_p1.c} |    2 +-
 ...nless_flux_no_by_edge_surfx_3x2v_ser_p1.c} |    2 +-
 ...nless_flux_no_by_edge_surfy_2x2v_ser_p1.c} |    2 +-
 ...nless_flux_no_by_edge_surfy_3x2v_ser_p1.c} |    2 +-
 ...nless_flux_no_by_edge_surfz_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |    2 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |    2 +-
 ...no_by_multib_boundary_surfx_2x2v_ser_p1.c} |    2 +-
 ...no_by_multib_boundary_surfx_3x2v_ser_p1.c} |    2 +-
 ...no_by_multib_boundary_surfy_2x2v_ser_p1.c} |    2 +-
 ...no_by_multib_boundary_surfy_3x2v_ser_p1.c} |    2 +-
 ...no_by_multib_boundary_surfz_3x2v_ser_p1.c} |    2 +-
 ...ionless_flux_no_by_surfvpar_2x2v_ser_p1.c} |   10 +-
 ...ionless_flux_no_by_surfvpar_3x2v_ser_p1.c} |   18 +-
 ...lisionless_flux_no_by_surfx_2x2v_ser_p1.c} |    2 +-
 ...lisionless_flux_no_by_surfx_3x2v_ser_p1.c} |    2 +-
 ...lisionless_flux_no_by_surfy_2x2v_ser_p1.c} |    2 +-
 ...lisionless_flux_no_by_surfy_3x2v_ser_p1.c} |    2 +-
 ...lisionless_flux_no_by_surfz_3x2v_ser_p1.c} |    2 +-
 ...collisionless_flux_surfvpar_1x1v_ser_p1.c} |    4 +-
 ...collisionless_flux_surfvpar_1x2v_ser_p1.c} |    6 +-
 ...collisionless_flux_surfvpar_2x2v_ser_p1.c} |    2 +-
 ...collisionless_flux_surfvpar_3x2v_ser_p1.c} |   18 +-
 ...em_collisionless_flux_surfx_1x1v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfx_1x2v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfx_2x2v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfx_3x2v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfy_2x2v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfy_3x2v_ser_p1.c} |    2 +-
 ...em_collisionless_flux_surfz_3x2v_ser_p1.c} |    2 +-
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |   97 +
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |  125 ++
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |  192 ++
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |  323 +++
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |  192 ++
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |  325 +++
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |  323 +++
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |   99 +
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |  127 ++
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |  206 ++
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c |  349 ++++
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |  206 ++
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c |  351 ++++
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c |  349 ++++
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |   99 +
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |  127 ++
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |  206 ++
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c |  349 ++++
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |  206 ++
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c |  351 ++++
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c |  349 ++++
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |  192 ++
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |  323 +++
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |  192 ++
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |  325 +++
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |  323 +++
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  206 ++
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  349 ++++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  206 ++
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  351 ++++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  349 ++++
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  206 ++
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  349 ++++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  206 ++
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  351 ++++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  349 ++++
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |  185 ++
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |  310 +++
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |  192 ++
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |  323 +++
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |  192 ++
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |  325 +++
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |  323 +++
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |  100 +
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |  120 ++
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  185 ++
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  310 +++
 ..._es_collisionless_flux_surfx_1x1v_ser_p1.c |   97 +
 ..._es_collisionless_flux_surfx_1x2v_ser_p1.c |  125 ++
 ..._es_collisionless_flux_surfx_2x2v_ser_p1.c |  192 ++
 ..._es_collisionless_flux_surfx_3x2v_ser_p1.c |  323 +++
 ..._es_collisionless_flux_surfy_2x2v_ser_p1.c |  192 ++
 ..._es_collisionless_flux_surfy_3x2v_ser_p1.c |  325 +++
 ..._es_collisionless_flux_surfz_3x2v_ser_p1.c |  323 +++
 .../gkyl_gk_collisionless_flux_kernels.h      | 1774 +++++++++++++----
 gyrokinetic/zero/gk_collisionless_flux.c      |   17 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  649 ++++--
 machines/configure.macos.sh                   |    2 +-
 machines/mkdeps.macos.sh                      |    2 +-
 122 files changed, 15304 insertions(+), 763 deletions(-)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c => gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c} (97%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c => gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c => gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c => gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c => gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c} (97%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c} (94%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c} (96%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfvpar_1x1v_ser_p1.c => gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c} (94%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfvpar_1x2v_ser_p1.c => gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c} (94%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfvpar_2x2v_ser_p1.c => gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfvpar_3x2v_ser_p1.c => gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfx_1x1v_ser_p1.c => gk_em_collisionless_flux_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfx_1x2v_ser_p1.c => gk_em_collisionless_flux_surfx_1x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfx_2x2v_ser_p1.c => gk_em_collisionless_flux_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfx_3x2v_ser_p1.c => gk_em_collisionless_flux_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfy_2x2v_ser_p1.c => gk_em_collisionless_flux_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfy_3x2v_ser_p1.c => gk_em_collisionless_flux_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfz_3x2v_ser_p1.c => gk_em_collisionless_flux_surfz_3x2v_ser_p1.c} (99%)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 0fcc38ea28..9852dadecf 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1062,7 +1062,12 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
 
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
-  gks->add_apardot_rhs_func = gks->is_em ? gk_species_add_apardot_dynamic : gk_species_rhs_static;
+
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)
+    gks->add_apardot_rhs_func = gk_species_add_apardot_dynamic;
+  else
+    gks->add_apardot_rhs_func = gk_species_rhs_static;
+
   gks->bflux_update = gk_species_update_bflux_dynamic;
   gks->get_cfl = gk_species_get_cfl_dynamic;
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
@@ -1580,7 +1585,6 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gks->gyro_phi = gkyl_array_acquire(app->field->phi_smooth);
   }
 
-  gks->is_em = app->field->is_em;
   // We do not have FLR effects for EM yet.
   gks->gyro_apar = gkyl_array_acquire(app->field->apar_smooth);
   gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
@@ -1593,7 +1597,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->anom_diff = (struct gk_anomalous_diff) { };
   gk_species_anomalous_diff_init(app, gks, &gks->anom_diff);
 
-  if (gks->collisionless.is_em) {
+  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     // To compute current density for Ampere's law and current dot for Ohm's law.
     gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
   }
@@ -1997,7 +2001,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
 
   gkyl_array_release(s->gyro_apar);
   gkyl_array_release(s->gyro_apardot);
-  if (s->is_em)
+  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL)
     gk_species_moment_release(app, &s->m1);
 
   s->release_func(app, s);
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 67dd8b4a96..f583348e80 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -82,7 +82,6 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
 {
   gkcls->collisionless_id = gks->info.collisionless.type;
   gkcls->no_by = gks->info.collisionless.no_by;
-  gkcls->is_em = app->field->is_em;
   gkcls->write_diagnostics = gks->info.collisionless.write_diagnostics;
 
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
@@ -144,27 +143,28 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
       gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
-    
-    if (gkcls->is_em) {
-      only_apardot = true;
-      // Create a special flux operator that only adds the AparDot contribution.
-      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
-      app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
-      // Create solver that only adds AparDot terms.
-      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
-      &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
-      &aux_inp, app->use_gpu);
-    }
           
     // Methods chosen at runtime.
     gkcls->flux_func = gk_species_collisionless_flux_enabled;
     gkcls->rhs_func = gk_species_collisionless_rhs_enabled;
-    if (gkcls->is_em)
-      gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
     if (gkcls->write_diagnostics) 
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
+
+    // Electromagnetic set up.
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+      only_apardot = true;
+      // Create a special flux operator that only adds the AparDot contribution.
+      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+        gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
+        app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
+      // Create solver that only adds AparDot terms.
+      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+        &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+        gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
+        &aux_inp, app->use_gpu);
+      // Methods chosen at runtime.
+      gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
+    }
   }
 }
 
@@ -206,7 +206,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
-    if (gkcls->is_em) {
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
       gkyl_gk_collisionless_flux_release(gkcls->add_apardot_surf_flux_op);
       gkyl_dg_updater_gyrokinetic_release(gkcls->add_apardot_slvr);
     }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 20a07b56ed..1d20669c52 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -286,7 +286,6 @@ struct gk_rad_drag {
 struct gk_collisionless {
   enum gkyl_gk_collisionless_type collisionless_id; // Type of collisionless terms.
   bool no_by; // Whether to neglect the toroidal field (b_y=0).
-  bool is_em; // Whether we have EM effects.
   bool write_diagnostics; // Whether to write diagnostics out.
 
   // Organization of the different equation objects and the required data and solvers
@@ -870,7 +869,6 @@ struct gk_species {
   struct gkyl_array *gyro_phi; // Gyroaveraged electrostatic potential.
   struct gkyl_array *gyro_apar; // Gyroaveraged parallel vector potential.
   struct gkyl_array *gyro_apardot; // Gyroaveraged parallel vector potential time derivative.
-  bool is_em; // Whether electromagnetic terms are present.
 
   struct gk_species_moment m0; // Computes charge density.
   struct gk_species_moment m1; // Computes current density.
@@ -1139,7 +1137,7 @@ struct gk_field {
 
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
-  bool is_em; // Whether EM model.
+  bool is_em; // Whether we solve the EM field equations.
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 03aee232ea..92d229ec74 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1153,26 +1153,24 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
-    if (app->field->is_em) {
-      const char *fmt = "%s-apar_%d.gkyl";
-      int sz = gkyl_calc_strlen(fmt, app->name, frame);
-      char fileNm[sz+1]; // ensures no buffer overflow
-      snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
-      if (app->use_gpu) {
-        gkyl_array_copy(app->field->apar_host, app->field->apar);
-      }
-      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
+  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+    const char *fmt = "%s-apar_%d.gkyl";
+    int sz = gkyl_calc_strlen(fmt, app->name, frame);
+    char fileNm[sz+1]; // ensures no buffer overflow
+    snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+    if (app->use_gpu) {
+      gkyl_array_copy(app->field->apar_host, app->field->apar);
     }
-    if (app->field->is_em) {
-      const char *fmt = "%s-apardot_%d.gkyl";
-      int sz = gkyl_calc_strlen(fmt, app->name, frame);
-      char fileNm[sz+1]; // ensures no buffer overflow
-      snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
-      if (app->use_gpu) {
-        gkyl_array_copy(app->field->apardot_host, app->field->apardot);
-      }
-      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm);
+    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
+
+    fmt = "%s-apardot_%d.gkyl";
+    sz = gkyl_calc_strlen(fmt, app->name, frame);
+    snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+    if (app->use_gpu) {
+      gkyl_array_copy(app->field->apardot_host, app->field->apardot);
     }
+    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm);
+  }
 
     gk_array_meta_release(mt);
 
@@ -1213,12 +1211,13 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
+    bool write_em = app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
     if (rank == 0) {
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).
         gkyl_dynvec_write(app->field->integ_energy, fileNm0);
 
-        if (app->field->is_em)
+        if (write_em)
           gkyl_dynvec_write(app->field->integ_apar_energy, fileNm0_apar);
 
         app->field->is_first_energy_write_call = false;
@@ -1226,13 +1225,13 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
       else {
         // Append to existing file.
         gkyl_dynvec_awrite(app->field->integ_energy, fileNm0);
-        if (app->field->is_em)
+        if (write_em)
           gkyl_dynvec_awrite(app->field->integ_apar_energy, fileNm0_apar);
       }
       app->stat.n_field_diag_io += 1;
     }
     gkyl_dynvec_clear(app->field->integ_energy);
-    if (app->field->is_em)
+    if (write_em)
       gkyl_dynvec_clear(app->field->integ_apar_energy);
 
     if (app->field->info.time_rate_diagnostics) {
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
similarity index 97%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
index fe8446683c..12e52528d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
index 81f0720ca2..e9c19092a9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
index e0e51c38ad..cc5236dc31 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
index ca88d98d0d..57d3645f56 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index d238da4c5a..90a6185dbe 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 8b28a452a8..abb643af57 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 9525d51831..d481398725 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 62b3bbfb0f..74dab01d37 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 0d3cc97515..3fcfb15e9a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 61775349c6..b53afc39d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index ab2a44e03d..cfa071a002 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
similarity index 97%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 9839938bde..86bf858c8b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 59741c6716..9178775b0d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 7c5f27f3a4..78f56ea7d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 4427f8496b..82f5835ad3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index b46843a5f3..828c96be5f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index fed15e4318..a1d2929177 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 07abcbccac..22ca3cba66 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 3e0e9a58ee..fde3592231 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 57462146c1..cae67f7f34 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 669c837aa1..2a7d13cc5b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 3d6a5ada15..061695ebcb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index ccae8140f5..d145fcb87e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index 661696e018..20b2a9a8c2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index 2cc78a65c5..f708659280 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 6184d536a3..92c1484678 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index a2da499294..236d9d116b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index 4ca93d910c..8a8c643afc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index 43d4ce97f4..d780f7c162 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 403e5afe85..3897256920 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 55a1af88c1..ed70213a63 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index a71b45ec40..a8379b1fee 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index a9079ef2ed..fd55d64a51 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 6646198205..012b22e263 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 6284a429d7..34e8b51d8b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 944529819a..43866b33a1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index b45acf2030..5398b50f5a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 1be9740d4c..8a9f94a5f3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index b2df2b4cc8..5441d7d138 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 9ccf675e30..3c063d47f0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
similarity index 94%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index e600c37586..8e77c3005b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -69,7 +69,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -79,7 +78,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -101,7 +99,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -111,7 +108,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -133,7 +129,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -143,7 +138,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -165,7 +159,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -175,7 +168,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])/q_; 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
similarity index 96%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 4b11599eab..8a4d7783c3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -74,7 +74,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -84,7 +83,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -106,7 +104,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -116,7 +113,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -138,7 +134,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -148,7 +143,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -170,7 +164,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -180,7 +173,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -202,7 +194,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -212,7 +203,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -234,7 +224,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -244,7 +233,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -266,7 +254,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -276,7 +263,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -298,7 +284,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -308,7 +293,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index c6fa855f0b..2a75acf281 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index 8e0df1984a..01f69a0ccf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index a602b33749..3f3ae1c87f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index 8907a70957..5e9589a976 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index a7d42b1e38..f42556cfd1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
similarity index 94%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
index 2aec3997b1..d1d59d4fdb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -62,7 +62,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1])/q_; 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
@@ -85,7 +84,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1])/q_; 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
similarity index 94%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 3701b42301..806566190d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -64,7 +64,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
@@ -75,7 +74,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
@@ -98,7 +96,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
@@ -109,7 +106,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1])/q_; 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 9103273342..b6076faf53 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
index fdda705971..9a79ad5431 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -74,7 +74,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -90,7 +89,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -118,7 +116,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -134,7 +131,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -162,7 +158,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -178,7 +173,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -206,7 +200,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -222,7 +215,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -250,7 +242,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -266,7 +257,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -294,7 +284,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -310,7 +299,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -338,7 +326,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -354,7 +341,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -382,7 +368,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
@@ -398,7 +383,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  mvpar_over_q = ((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])/q_; 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c
index 8351564ace..9529bc93d9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c
index afb03ca1e1..5a925e02bf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c
index 5e8c3cbef7..cf64cd51ba 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c
index da41a35c4e..fd7dc2c76a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c
index 4a910b6a1b..b93ef24d68 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c
index c36a81b5de..19536db253 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c
index b803b6bfb4..d3b9aa1639 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..d7f1f29371
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,97 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..fa28b49982
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,125 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..75e84d9c3b
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..8dc4411306
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..e215d93f53
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..f652909b64
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,325 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..dbd8a403b4
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..5785598e11
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,99 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double JRatfR[3] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..06ca58eb62
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,127 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double JRatfR[6] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..0f2d981a99
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..1b9321b513
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..60bcacccbf
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..b56c6ed521
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,351 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..c3754a76cb
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..7a83dfb7d7
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -0,0 +1,99 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double JRatfL[3] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..8c87e41043
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -0,0 +1,127 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double JRatfL[6] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..269ebb4f13
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..c22156e4a5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..d904ffa7e2
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..b154574b8c
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,351 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..b488afb742
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..06e461b179
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..8b374aa03d
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..d7829367ba
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..c7a64c66af
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,325 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..93fa848cf7
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..6285424c1e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..24221faffb
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..1c708dfcfc
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..78f9967ed0
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,351 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..2a4e2a1571
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..155776e47f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..4ce5e84e81
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..075d642123
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,206 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..534e2bf9e2
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,351 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..1354d3cf3b
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,349 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..ea348fddf8
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,185 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
+  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..3ec5aaba66
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,310 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_; 
+  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[4] = 2.0*vmapSq[1]*m_; 
+  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[6] = 2.0*phi[4]*q_; 
+  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
+  hamil[8] = 2.0*phi[6]*q_; 
+  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 2.0*phi[7]*q_; 
+  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
+  hamil[32] = 2.0*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[72]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[4].bmag; 
+  B3_quad = gkdgv[4].B3; 
+  Jc_quad = dgv[4].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[5].bmag; 
+  B3_quad = gkdgv[5].B3; 
+  Jc_quad = dgv[5].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[6].bmag; 
+  B3_quad = gkdgv[6].B3; 
+  Jc_quad = dgv[6].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[7].bmag; 
+  B3_quad = gkdgv[7].B3; 
+  Jc_quad = dgv[7].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..46a7a88a7f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..4b9a8bb519
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..ded8d71bd9
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..a41d62efb5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -0,0 +1,325 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..c53c21ad48
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..b90e4c516e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,100 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
+  hamil[1] = 1.4142135623730951*phi[1]*q_; 
+  hamil[2] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[3]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..514289668e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,120 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[6]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..30fcac6cbb
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,185 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
+  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..c73cce228a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,310 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_3x2v_ser_p1(
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_; 
+  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[4] = 2.0*vmapSq[1]*m_; 
+  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[6] = 2.0*phi[4]*q_; 
+  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
+  hamil[8] = 2.0*phi[6]*q_; 
+  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 2.0*phi[7]*q_; 
+  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
+  hamil[32] = 2.0*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[72]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[4].bmag; 
+  B3_quad = gkdgv[4].B3; 
+  Jc_quad = dgv[4].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[5].bmag; 
+  B3_quad = gkdgv[5].B3; 
+  Jc_quad = dgv[5].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[6].bmag; 
+  B3_quad = gkdgv[6].B3; 
+  Jc_quad = dgv[6].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[7].bmag; 
+  B3_quad = gkdgv[7].B3; 
+  Jc_quad = dgv[7].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..8852610f72
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -0,0 +1,97 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..afd77e6998
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -0,0 +1,125 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..5603465778
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..35b0e14ae6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..dc2ab8c70a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -0,0 +1,192 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..f2d015a6b2
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -0,0 +1,325 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..6f2c48ea9f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -0,0 +1,323 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_es_collisionless_flux_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index 8719415313..e85e84282d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -7,438 +7,1326 @@
 
 EXTERN_C_BEG
 
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_es_collisionless_flux_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_3x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+                    const double *w, const double *dxv,
+                    
+                    const double *vmap, const double *vmapSq, const double q_, const double m_,
+                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+                const double *w, const double *dxv,
+                const double *vmap_prime_l, const double *vmap_prime_r, 
+                const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                double* GKYL_RESTRICT flux_surf); 
+
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p2(
             const double *w, const double *dxv,
             const double *vmap_prime_l, const double *vmap_prime_r, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -446,7 +1334,14 @@ GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
             const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
             double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p2(
             const double *w, const double *dxv,
             const double *vmap_prime_l, const double *vmap_prime_r, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -454,7 +1349,14 @@ GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
             const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
             double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
+            const double *w, const double *dxv,
+            const double *vmap_prime_l, const double *vmap_prime_r, 
+            const double *vmap, const double *vmapSq, const double q_, const double m_, 
+            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
+            double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p2(
             const double *w, const double *dxv,
             const double *vmap_prime_l, const double *vmap_prime_r, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -462,7 +1364,7 @@ GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
             const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
             double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
             const double *w, const double *dxv,
             const double *vmap_prime_l, const double *vmap_prime_r, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -479,11 +1381,11 @@ GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf);
 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
-    const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_r, 
-    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-    const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-    double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv, 
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf);
 
 EXTERN_C_END
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index cf41588173..5b0e93295b 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -56,26 +56,27 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
+    int em = (type == GKYL_GK_COLLISIONLESS_EM || type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 1 : 0;
     if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
+        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
           poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
           poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
       }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
     } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
+        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
           poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
           poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
       }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
     }
   }
 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index bc22bd4399..b00c8183f2 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -36,7 +36,10 @@ static struct { int vdim[3]; } cv_index[] = {
 
 // for use in kernel tables
 typedef struct { gk_collisionless_flux_surf_t kernels[3]; } gkyl_gk_collisionless_flux_surf_kern_list;
+typedef struct { gkyl_gk_collisionless_flux_surf_kern_list kernels_list[4]; } gkyl_gk_collisionless_flux_surf_kern_table;
+
 typedef struct { gk_collisionless_flux_surfvpar_t kernels[3]; } gkyl_gk_collisionless_flux_surfvpar_kern_list;
+typedef struct { gkyl_gk_collisionless_flux_surfvpar_kern_list kernels_list[4]; } gkyl_gk_collisionless_flux_surfvpar_kern_table;
 
 struct gkyl_gk_collisionless_flux {
   struct gkyl_rect_grid phase_grid; // Phase space grid for cell spacing and cell center
@@ -65,123 +68,278 @@ struct gkyl_gk_collisionless_flux {
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_surfvpar_kernels[] = {
-  { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_surfvpar_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
-
 //
 // Kernels used at multiblock boundaries.
 //
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[] = {
+  {
+    .kernels_list= {
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list= {
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[] = {
+  {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfz_kernels[] = {
+  { 
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 
@@ -190,146 +348,301 @@ static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+    },  
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_no_by_surfvpar_kernels[] = {
-  { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_no_by_surfvpar_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
-
 //
 // Kernels used at multiblock boundaries.
 //
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[] = {
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[] = {
+  { 
+    .kernels_list = {
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[] = {
-  { NULL, NULL, NULL }, // 0
-  { NULL, NULL, NULL }, // 1
-  { NULL, NULL, NULL }, // 2
-  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[] = {
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  }
 };
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -337,25 +650,25 @@ choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int pol
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_edge_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -363,32 +676,32 @@ choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, in
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_surf_vpar_kern(int cdim, int vdim, int poly_order)
+choose_gk_collisionless_flux_surf_vpar_kern(int em, int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_surfvpar_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_no_by_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -396,25 +709,25 @@ choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, i
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -422,9 +735,9 @@ choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vd
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
+choose_gk_collisionless_flux_no_by_surf_vpar_kern(int em, int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 
@@ -433,10 +746,10 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_o
 // Parallel electric field term.
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_apardot_surfvpar_kernels[] = {
-  { NULL, gk_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1, NULL }, // 3
+  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
 GKYL_CU_D
diff --git a/machines/configure.macos.sh b/machines/configure.macos.sh
index 5f5158a7a2..32baebfe92 100755
--- a/machines/configure.macos.sh
+++ b/machines/configure.macos.sh
@@ -1,2 +1,2 @@
-: "${PREFIX:=$HOME/gkylsoft}"
+: "${PREFIX:=$HOME/gkeyll_dev/gkylsoft}"
 ./configure --prefix=$PREFIX --use-lua=yes
diff --git a/machines/mkdeps.macos.sh b/machines/mkdeps.macos.sh
index 948f370d7a..d026ea1798 100755
--- a/machines/mkdeps.macos.sh
+++ b/machines/mkdeps.macos.sh
@@ -1,4 +1,4 @@
 cd install-deps
-: "${PREFIX:=$HOME/gkylsoft}"
+: "${PREFIX:=$HOME/gkeyll_dev/gkylsoft}"
 export MACOSX_DEPLOYMENT_TARGET=14.7
 ./mkdeps.sh --build-openblas=no --build-superlu=yes --build-luajit=yes --prefix=$PREFIX

From bc0b6d6b815bbd0f708c8cdaae310471fd11307f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 6 Nov 2025 14:44:46 -0500
Subject: [PATCH 037/181] restore the config and mkdeps

---
 machines/configure.macos.sh | 2 +-
 machines/mkdeps.macos.sh    | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/machines/configure.macos.sh b/machines/configure.macos.sh
index 32baebfe92..5f5158a7a2 100755
--- a/machines/configure.macos.sh
+++ b/machines/configure.macos.sh
@@ -1,2 +1,2 @@
-: "${PREFIX:=$HOME/gkeyll_dev/gkylsoft}"
+: "${PREFIX:=$HOME/gkylsoft}"
 ./configure --prefix=$PREFIX --use-lua=yes
diff --git a/machines/mkdeps.macos.sh b/machines/mkdeps.macos.sh
index d026ea1798..948f370d7a 100755
--- a/machines/mkdeps.macos.sh
+++ b/machines/mkdeps.macos.sh
@@ -1,4 +1,4 @@
 cd install-deps
-: "${PREFIX:=$HOME/gkeyll_dev/gkylsoft}"
+: "${PREFIX:=$HOME/gkylsoft}"
 export MACOSX_DEPLOYMENT_TARGET=14.7
 ./mkdeps.sh --build-openblas=no --build-superlu=yes --build-luajit=yes --prefix=$PREFIX

From 7eb79c3fcf239987f86abfe3e96fd2fa277ee082 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 7 Nov 2025 10:22:16 -0500
Subject: [PATCH 038/181] Clean a bit the interface with return 0 kernels

---
 gyrokinetic/zero/dg_gyrokinetic.c             |  6 +---
 gyrokinetic/zero/gk_collisionless_flux.c      |  6 ++--
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   | 29 ++++++++++++++++++-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  7 -----
 4 files changed, 32 insertions(+), 16 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 5f45cec8b5..9eaa0b9903 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -51,10 +51,6 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 
-  // gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
-  // const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
-  // const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
-  // const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
@@ -127,7 +123,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   }
 
   gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM || GKYL_GK_COLLISIONLESS_EM_BPERP ? 
-    CK(vol_add_apar_kernels,cdim,vdim,poly_order) : kernel_dg_gyrokinetic_vol_return_zero;
+    CK(vol_add_apar_kernels,cdim,vdim,poly_order) : dg_gyrokinetic_vol_return_zero;
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
   if (cdim>1)
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 5b0e93295b..120323e373 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -50,9 +50,9 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   if (only_apardot){
     // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
     for (int d=0; d<cdim; ++d) {
-      up->flux_surf[d] = get_gk_collisionless_flux_surf_zero_kern();
-      up->flux_surf_edge_lo[d] = get_gk_collisionless_flux_surf_zero_kern();
-      up->flux_surf_edge_up[d] = get_gk_collisionless_flux_surf_zero_kern();
+      up->flux_surf[d] = gk_collisionless_flux_surf_return_zero;
+      up->flux_surf_edge_lo[d] = gk_collisionless_flux_surf_return_zero;
+      up->flux_surf_edge_up[d] = gk_collisionless_flux_surf_return_zero;
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 4b65faa4c4..40f820463c 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -418,13 +418,40 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_apardot_vol_kernels[] = {
 
 // To turn off EM effects:
 #include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double kernel_dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+GKYL_CU_DH double dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
     const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   return 0.; 
 } 
 
+GKYL_CU_DH
+static double
+kernel_dg_gyrokinetic_vol_return_zero(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
+{
+  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+
+  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
+    return 0.;
+  }
+  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
+
+  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
+  return dg_gyrokinetic_vol_return_zero(xc, dx,
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
+    gyrokinetic->charge, gyrokinetic->mass,
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
+    qIn, qRhsOut);
+}
 
 //
 // Serendipity surface kernels general geometry
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index b00c8183f2..a8717a6062 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -752,13 +752,6 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_
   { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
-GKYL_CU_D
-static gk_collisionless_flux_surf_t
-get_gk_collisionless_flux_surf_zero_kern()
-{
-  return gk_collisionless_flux_surf_return_zero;
-}
-
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
 choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int poly_order)

From 314530e87bd3fbf56269dedd76da63132c756023 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 7 Nov 2025 11:24:29 -0500
Subject: [PATCH 039/181] fix an error were apardot was expanded on bP and not
 bC

---
 ..._gyrokinetic_add_apardot_vol_1x1v_ser_p1.c |  16 +--
 ..._gyrokinetic_add_apardot_vol_1x2v_ser_p1.c |  30 ++---
 ..._gyrokinetic_add_apardot_vol_2x2v_ser_p1.c |  60 +++------
 ..._gyrokinetic_add_apardot_vol_3x2v_ser_p1.c | 120 ++++++------------
 4 files changed, 76 insertions(+), 150 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
index 9c26ddd0c7..3bb8a2ec69 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
@@ -8,18 +8,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[6] = {0.}; 
-  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
-  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
-  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
-  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
+  alphavpar[0] = -((1.4142135623730951*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((1.4142135623730951*apardot[1]*q_)/m_); 
 
 
-  out[2] += 0.8660254037844386*(alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[3] += 0.8660254037844387*(alphavpar[4]*fin[5]+fin[4]*alphavpar[5])+0.8660254037844386*(alphavpar[2]*fin[3]+fin[2]*alphavpar[3]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[4] += 1.7320508075688774*(alphavpar[3]*fin[5]+fin[3]*alphavpar[5])+1.7320508075688772*(alphavpar[2]*fin[4]+fin[2]*alphavpar[4])+1.9364916731037085*(alphavpar[1]*fin[3]+fin[1]*alphavpar[3]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
-  out[5] += 1.7320508075688772*(alphavpar[2]*fin[5]+fin[2]*alphavpar[5])+1.7320508075688774*(alphavpar[3]*fin[4]+fin[3]*alphavpar[4])+1.9364916731037085*(alphavpar[0]*fin[3]+fin[0]*alphavpar[3]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[2] += 0.8660254037844386*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[3] += 0.8660254037844386*(alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[4] += 1.9364916731037085*(alphavpar[1]*fin[3]+alphavpar[0]*fin[2]); 
+  out[5] += 1.9364916731037085*(alphavpar[0]*fin[3]+alphavpar[1]*fin[2]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
index 500c925030..7185f94cc0 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
@@ -8,28 +8,18 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[12] = {0.}; 
-  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
-  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
-  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
-  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
-  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
-  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
-  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
-  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
-  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
-  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
+  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
 
 
-  out[2] += 0.6123724356957944*(alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[4] += 0.6123724356957944*(alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[6] += 0.6123724356957944*(alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
-  out[7] += 0.6123724356957944*(alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
-  out[8] += 1.224744871391589*(alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8])+1.369306393762915*(alphavpar[5]*fin[7]+fin[5]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
-  out[9] += 1.224744871391589*(alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8])+1.369306393762915*(alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
-  out[10] += 1.224744871391589*(alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8])+1.369306393762915*(alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
-  out[11] += 1.224744871391589*(alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8])+1.369306393762915*(alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
+  out[2] += 0.6123724356957944*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[4] += 0.6123724356957944*(alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[6] += 0.6123724356957944*(alphavpar[1]*fin[5]+alphavpar[0]*fin[3]); 
+  out[7] += 0.6123724356957944*(alphavpar[0]*fin[5]+alphavpar[1]*fin[3]); 
+  out[8] += 1.369306393762915*(alphavpar[1]*fin[4]+alphavpar[0]*fin[2]); 
+  out[9] += 1.369306393762915*(alphavpar[0]*fin[4]+alphavpar[1]*fin[2]); 
+  out[10] += 1.369306393762915*(alphavpar[1]*fin[7]+alphavpar[0]*fin[6]); 
+  out[11] += 1.369306393762915*(alphavpar[0]*fin[7]+alphavpar[1]*fin[6]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
index 856faccde1..03e7f95feb 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
@@ -8,48 +8,28 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
-  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
-  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
-  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
-  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
-  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
-  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
-  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
-  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
-  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
-  alphavpar[12] = -((1.0*apardot[12]*q_)/m_); 
-  alphavpar[13] = -((1.0*apardot[13]*q_)/m_); 
-  alphavpar[14] = -((1.0*apardot[14]*q_)/m_); 
-  alphavpar[15] = -((1.0*apardot[15]*q_)/m_); 
-  alphavpar[16] = -((1.0*apardot[16]*q_)/m_); 
-  alphavpar[17] = -((1.0*apardot[17]*q_)/m_); 
-  alphavpar[18] = -((1.0*apardot[18]*q_)/m_); 
-  alphavpar[19] = -((1.0*apardot[19]*q_)/m_); 
-  alphavpar[20] = -((1.0*apardot[20]*q_)/m_); 
-  alphavpar[21] = -((1.0*apardot[21]*q_)/m_); 
-  alphavpar[22] = -((1.0*apardot[22]*q_)/m_); 
-  alphavpar[23] = -((1.0*apardot[23]*q_)/m_); 
+  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((2.0*apardot[2]*q_)/m_); 
+  alphavpar[5] = -((2.0*apardot[3]*q_)/m_); 
 
 
-  out[3] += 0.4330127018922193*(alphavpar[23]*fin[23]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[19]*fin[19]+alphavpar[18]*fin[18]+alphavpar[17]*fin[17]+alphavpar[16]*fin[16]+alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[6] += 0.43301270189221935*(alphavpar[22]*fin[23]+fin[22]*alphavpar[23]+alphavpar[19]*fin[21]+fin[19]*alphavpar[21]+alphavpar[18]*fin[20]+fin[18]*alphavpar[20]+alphavpar[16]*fin[17]+fin[16]*alphavpar[17])+0.4330127018922193*(alphavpar[14]*fin[15]+fin[14]*alphavpar[15]+alphavpar[10]*fin[13]+fin[10]*alphavpar[13]+alphavpar[9]*fin[12]+fin[9]*alphavpar[12]+alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[7] += 0.43301270189221935*(alphavpar[21]*fin[23]+fin[21]*alphavpar[23]+alphavpar[19]*fin[22]+fin[19]*alphavpar[22]+alphavpar[17]*fin[20]+fin[17]*alphavpar[20]+alphavpar[16]*fin[18]+fin[16]*alphavpar[18])+0.4330127018922193*(alphavpar[13]*fin[15]+fin[13]*alphavpar[15]+alphavpar[10]*fin[14]+fin[10]*alphavpar[14]+alphavpar[8]*fin[12]+fin[8]*alphavpar[12]+alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
-  out[10] += 0.43301270189221935*(alphavpar[20]*fin[23]+fin[20]*alphavpar[23]+alphavpar[18]*fin[22]+fin[18]*alphavpar[22]+alphavpar[17]*fin[21]+fin[17]*alphavpar[21]+alphavpar[16]*fin[19]+fin[16]*alphavpar[19])+0.4330127018922193*(alphavpar[11]*fin[15]+fin[11]*alphavpar[15]+alphavpar[7]*fin[14]+fin[7]*alphavpar[14]+alphavpar[6]*fin[13]+fin[6]*alphavpar[13]+alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[3]*fin[10]+fin[3]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]); 
-  out[11] += 0.4330127018922193*(alphavpar[19]*fin[23]+fin[19]*alphavpar[23]+alphavpar[21]*fin[22]+fin[21]*alphavpar[22]+alphavpar[16]*fin[20]+fin[16]*alphavpar[20]+alphavpar[17]*fin[18]+fin[17]*alphavpar[18]+alphavpar[10]*fin[15]+fin[10]*alphavpar[15]+alphavpar[13]*fin[14]+fin[13]*alphavpar[14]+alphavpar[4]*fin[12]+fin[4]*alphavpar[12]+alphavpar[3]*fin[11]+fin[3]*alphavpar[11]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
-  out[13] += 0.4330127018922193*(alphavpar[18]*fin[23]+fin[18]*alphavpar[23]+alphavpar[20]*fin[22]+fin[20]*alphavpar[22]+alphavpar[16]*fin[21]+fin[16]*alphavpar[21]+alphavpar[17]*fin[19]+fin[17]*alphavpar[19]+alphavpar[7]*fin[15]+fin[7]*alphavpar[15]+alphavpar[11]*fin[14]+fin[11]*alphavpar[14]+alphavpar[3]*fin[13]+fin[3]*alphavpar[13]+alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[5]*fin[9]+fin[5]*alphavpar[9]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]); 
-  out[14] += 0.4330127018922193*(alphavpar[17]*fin[23]+fin[17]*alphavpar[23]+alphavpar[16]*fin[22]+fin[16]*alphavpar[22]+alphavpar[20]*fin[21]+fin[20]*alphavpar[21]+alphavpar[18]*fin[19]+fin[18]*alphavpar[19]+alphavpar[6]*fin[15]+fin[6]*alphavpar[15]+alphavpar[3]*fin[14]+fin[3]*alphavpar[14]+alphavpar[11]*fin[13]+fin[11]*alphavpar[13]+alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[0]*fin[9]+fin[0]*alphavpar[9]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]); 
-  out[15] += 0.43301270189221935*(alphavpar[16]*fin[23]+fin[16]*alphavpar[23]+alphavpar[17]*fin[22]+fin[17]*alphavpar[22]+alphavpar[18]*fin[21]+fin[18]*alphavpar[21]+alphavpar[19]*fin[20]+fin[19]*alphavpar[20])+0.4330127018922193*(alphavpar[3]*fin[15]+fin[3]*alphavpar[15]+alphavpar[6]*fin[14]+fin[6]*alphavpar[14]+alphavpar[7]*fin[13]+fin[7]*alphavpar[13]+alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[1]*fin[9]+fin[1]*alphavpar[9]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]); 
-  out[16] += 0.8660254037844387*(alphavpar[15]*fin[23]+fin[15]*alphavpar[23])+0.8660254037844386*(alphavpar[14]*fin[22]+fin[14]*alphavpar[22]+alphavpar[13]*fin[21]+fin[13]*alphavpar[21]+alphavpar[11]*fin[20]+fin[11]*alphavpar[20])+0.8660254037844387*(alphavpar[10]*fin[19]+fin[10]*alphavpar[19]+alphavpar[7]*fin[18]+fin[7]*alphavpar[18]+alphavpar[6]*fin[17]+fin[6]*alphavpar[17])+0.8660254037844386*(alphavpar[3]*fin[16]+fin[3]*alphavpar[16])+0.9682458365518543*(alphavpar[12]*fin[15]+fin[12]*alphavpar[15]+alphavpar[9]*fin[14]+fin[9]*alphavpar[14]+alphavpar[8]*fin[13]+fin[8]*alphavpar[13]+alphavpar[5]*fin[11]+fin[5]*alphavpar[11]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
-  out[17] += 0.8660254037844386*(alphavpar[14]*fin[23]+fin[14]*alphavpar[23])+0.8660254037844387*(alphavpar[15]*fin[22]+fin[15]*alphavpar[22]+alphavpar[10]*fin[21]+fin[10]*alphavpar[21]+alphavpar[7]*fin[20]+fin[7]*alphavpar[20])+0.8660254037844386*(alphavpar[13]*fin[19]+fin[13]*alphavpar[19]+alphavpar[11]*fin[18]+fin[11]*alphavpar[18]+alphavpar[3]*fin[17]+fin[3]*alphavpar[17])+0.8660254037844387*(alphavpar[6]*fin[16]+fin[6]*alphavpar[16])+0.9682458365518543*(alphavpar[9]*fin[15]+fin[9]*alphavpar[15]+alphavpar[12]*fin[14]+fin[12]*alphavpar[14]+alphavpar[4]*fin[13]+fin[4]*alphavpar[13]+alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[5]*fin[7]+fin[5]*alphavpar[7]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
-  out[18] += 0.8660254037844386*(alphavpar[13]*fin[23]+fin[13]*alphavpar[23])+0.8660254037844387*(alphavpar[10]*fin[22]+fin[10]*alphavpar[22]+alphavpar[15]*fin[21]+fin[15]*alphavpar[21]+alphavpar[6]*fin[20]+fin[6]*alphavpar[20])+0.8660254037844386*(alphavpar[14]*fin[19]+fin[14]*alphavpar[19]+alphavpar[3]*fin[18]+fin[3]*alphavpar[18]+alphavpar[11]*fin[17]+fin[11]*alphavpar[17])+0.8660254037844387*(alphavpar[7]*fin[16]+fin[7]*alphavpar[16])+0.9682458365518543*(alphavpar[8]*fin[15]+fin[8]*alphavpar[15]+alphavpar[4]*fin[14]+fin[4]*alphavpar[14]+alphavpar[12]*fin[13]+fin[12]*alphavpar[13]+alphavpar[1]*fin[11]+fin[1]*alphavpar[11]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
-  out[19] += 0.8660254037844386*(alphavpar[11]*fin[23]+fin[11]*alphavpar[23])+0.8660254037844387*(alphavpar[7]*fin[22]+fin[7]*alphavpar[22]+alphavpar[6]*fin[21]+fin[6]*alphavpar[21]+alphavpar[15]*fin[20]+fin[15]*alphavpar[20])+0.8660254037844386*(alphavpar[3]*fin[19]+fin[3]*alphavpar[19]+alphavpar[14]*fin[18]+fin[14]*alphavpar[18]+alphavpar[13]*fin[17]+fin[13]*alphavpar[17])+0.8660254037844387*(alphavpar[10]*fin[16]+fin[10]*alphavpar[16])+0.9682458365518543*(alphavpar[5]*fin[15]+fin[5]*alphavpar[15]+alphavpar[2]*fin[14]+fin[2]*alphavpar[14]+alphavpar[1]*fin[13]+fin[1]*alphavpar[13]+alphavpar[11]*fin[12]+fin[11]*alphavpar[12]+alphavpar[0]*fin[10]+fin[0]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
-  out[20] += 0.8660254037844387*(alphavpar[10]*fin[23]+fin[10]*alphavpar[23])+0.8660254037844386*(alphavpar[13]*fin[22]+fin[13]*alphavpar[22]+alphavpar[14]*fin[21]+fin[14]*alphavpar[21]+alphavpar[3]*fin[20]+fin[3]*alphavpar[20])+0.8660254037844387*(alphavpar[15]*fin[19]+fin[15]*alphavpar[19]+alphavpar[6]*fin[18]+fin[6]*alphavpar[18]+alphavpar[7]*fin[17]+fin[7]*alphavpar[17])+0.8660254037844386*(alphavpar[11]*fin[16]+fin[11]*alphavpar[16])+0.9682458365518543*(alphavpar[4]*fin[15]+fin[4]*alphavpar[15]+alphavpar[8]*fin[14]+fin[8]*alphavpar[14]+alphavpar[9]*fin[13]+fin[9]*alphavpar[13]+alphavpar[10]*fin[12]+fin[10]*alphavpar[12]+alphavpar[0]*fin[11]+fin[0]*alphavpar[11]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]); 
-  out[21] += 0.8660254037844387*(alphavpar[7]*fin[23]+fin[7]*alphavpar[23])+0.8660254037844386*(alphavpar[11]*fin[22]+fin[11]*alphavpar[22]+alphavpar[3]*fin[21]+fin[3]*alphavpar[21]+alphavpar[14]*fin[20]+fin[14]*alphavpar[20])+0.8660254037844387*(alphavpar[6]*fin[19]+fin[6]*alphavpar[19]+alphavpar[15]*fin[18]+fin[15]*alphavpar[18]+alphavpar[10]*fin[17]+fin[10]*alphavpar[17])+0.8660254037844386*(alphavpar[13]*fin[16]+fin[13]*alphavpar[16])+0.9682458365518543*(alphavpar[2]*fin[15]+fin[2]*alphavpar[15]+alphavpar[5]*fin[14]+fin[5]*alphavpar[14]+alphavpar[0]*fin[13]+fin[0]*alphavpar[13]+alphavpar[7]*fin[12]+fin[7]*alphavpar[12]+alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[1]*fin[10]+fin[1]*alphavpar[10]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]); 
-  out[22] += 0.8660254037844387*(alphavpar[6]*fin[23]+fin[6]*alphavpar[23])+0.8660254037844386*(alphavpar[3]*fin[22]+fin[3]*alphavpar[22]+alphavpar[11]*fin[21]+fin[11]*alphavpar[21]+alphavpar[13]*fin[20]+fin[13]*alphavpar[20])+0.8660254037844387*(alphavpar[7]*fin[19]+fin[7]*alphavpar[19]+alphavpar[10]*fin[18]+fin[10]*alphavpar[18]+alphavpar[15]*fin[17]+fin[15]*alphavpar[17])+0.8660254037844386*(alphavpar[14]*fin[16]+fin[14]*alphavpar[16])+0.9682458365518543*(alphavpar[1]*fin[15]+fin[1]*alphavpar[15]+alphavpar[0]*fin[14]+fin[0]*alphavpar[14]+alphavpar[5]*fin[13]+fin[5]*alphavpar[13]+alphavpar[6]*fin[12]+fin[6]*alphavpar[12]+alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[3]*fin[9]+fin[3]*alphavpar[9]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]); 
-  out[23] += 0.8660254037844386*(alphavpar[3]*fin[23]+fin[3]*alphavpar[23])+0.8660254037844387*(alphavpar[6]*fin[22]+fin[6]*alphavpar[22]+alphavpar[7]*fin[21]+fin[7]*alphavpar[21]+alphavpar[10]*fin[20]+fin[10]*alphavpar[20])+0.8660254037844386*(alphavpar[11]*fin[19]+fin[11]*alphavpar[19]+alphavpar[13]*fin[18]+fin[13]*alphavpar[18]+alphavpar[14]*fin[17]+fin[14]*alphavpar[17])+0.8660254037844387*(alphavpar[15]*fin[16]+fin[15]*alphavpar[16])+0.9682458365518543*(alphavpar[0]*fin[15]+fin[0]*alphavpar[15]+alphavpar[1]*fin[14]+fin[1]*alphavpar[14]+alphavpar[2]*fin[13]+fin[2]*alphavpar[13]+alphavpar[3]*fin[12]+fin[3]*alphavpar[12]+alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[5]*fin[10]+fin[5]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]); 
+  out[3] += 0.4330127018922193*(alphavpar[5]*fin[5]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[6] += 0.4330127018922193*(alphavpar[2]*fin[5]+fin[2]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[7] += 0.4330127018922193*(alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[10] += 0.4330127018922193*(alphavpar[5]*fin[12]+alphavpar[2]*fin[9]+alphavpar[1]*fin[8]+alphavpar[0]*fin[4]); 
+  out[11] += 0.4330127018922193*(alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[13] += 0.4330127018922193*(alphavpar[2]*fin[12]+alphavpar[5]*fin[9]+alphavpar[0]*fin[8]+alphavpar[1]*fin[4]); 
+  out[14] += 0.4330127018922193*(alphavpar[1]*fin[12]+alphavpar[0]*fin[9]+alphavpar[5]*fin[8]+alphavpar[2]*fin[4]); 
+  out[15] += 0.4330127018922193*(alphavpar[0]*fin[12]+alphavpar[1]*fin[9]+alphavpar[2]*fin[8]+fin[4]*alphavpar[5]); 
+  out[16] += 0.9682458365518543*(alphavpar[5]*fin[11]+alphavpar[2]*fin[7]+alphavpar[1]*fin[6]+alphavpar[0]*fin[3]); 
+  out[17] += 0.9682458365518543*(alphavpar[2]*fin[11]+alphavpar[5]*fin[7]+alphavpar[0]*fin[6]+alphavpar[1]*fin[3]); 
+  out[18] += 0.9682458365518543*(alphavpar[1]*fin[11]+alphavpar[0]*fin[7]+alphavpar[5]*fin[6]+alphavpar[2]*fin[3]); 
+  out[19] += 0.9682458365518543*(alphavpar[5]*fin[15]+alphavpar[2]*fin[14]+alphavpar[1]*fin[13]+alphavpar[0]*fin[10]); 
+  out[20] += 0.9682458365518543*(alphavpar[0]*fin[11]+alphavpar[1]*fin[7]+alphavpar[2]*fin[6]+fin[3]*alphavpar[5]); 
+  out[21] += 0.9682458365518543*(alphavpar[2]*fin[15]+alphavpar[5]*fin[14]+alphavpar[0]*fin[13]+alphavpar[1]*fin[10]); 
+  out[22] += 0.9682458365518543*(alphavpar[1]*fin[15]+alphavpar[0]*fin[14]+alphavpar[5]*fin[13]+alphavpar[2]*fin[10]); 
+  out[23] += 0.9682458365518543*(alphavpar[0]*fin[15]+alphavpar[1]*fin[14]+alphavpar[2]*fin[13]+alphavpar[5]*fin[10]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
index 805c88b9b2..ba187efefa 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
@@ -8,88 +8,48 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = -((1.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((1.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((1.0*apardot[2]*q_)/m_); 
-  alphavpar[3] = -((1.0*apardot[3]*q_)/m_); 
-  alphavpar[4] = -((1.0*apardot[4]*q_)/m_); 
-  alphavpar[5] = -((1.0*apardot[5]*q_)/m_); 
-  alphavpar[6] = -((1.0*apardot[6]*q_)/m_); 
-  alphavpar[7] = -((1.0*apardot[7]*q_)/m_); 
-  alphavpar[8] = -((1.0*apardot[8]*q_)/m_); 
-  alphavpar[9] = -((1.0*apardot[9]*q_)/m_); 
-  alphavpar[10] = -((1.0*apardot[10]*q_)/m_); 
-  alphavpar[11] = -((1.0*apardot[11]*q_)/m_); 
-  alphavpar[12] = -((1.0*apardot[12]*q_)/m_); 
-  alphavpar[13] = -((1.0*apardot[13]*q_)/m_); 
-  alphavpar[14] = -((1.0*apardot[14]*q_)/m_); 
-  alphavpar[15] = -((1.0*apardot[15]*q_)/m_); 
-  alphavpar[16] = -((1.0*apardot[16]*q_)/m_); 
-  alphavpar[17] = -((1.0*apardot[17]*q_)/m_); 
-  alphavpar[18] = -((1.0*apardot[18]*q_)/m_); 
-  alphavpar[19] = -((1.0*apardot[19]*q_)/m_); 
-  alphavpar[20] = -((1.0*apardot[20]*q_)/m_); 
-  alphavpar[21] = -((1.0*apardot[21]*q_)/m_); 
-  alphavpar[22] = -((1.0*apardot[22]*q_)/m_); 
-  alphavpar[23] = -((1.0*apardot[23]*q_)/m_); 
-  alphavpar[24] = -((1.0*apardot[24]*q_)/m_); 
-  alphavpar[25] = -((1.0*apardot[25]*q_)/m_); 
-  alphavpar[26] = -((1.0*apardot[26]*q_)/m_); 
-  alphavpar[27] = -((1.0*apardot[27]*q_)/m_); 
-  alphavpar[28] = -((1.0*apardot[28]*q_)/m_); 
-  alphavpar[29] = -((1.0*apardot[29]*q_)/m_); 
-  alphavpar[30] = -((1.0*apardot[30]*q_)/m_); 
-  alphavpar[31] = -((1.0*apardot[31]*q_)/m_); 
-  alphavpar[32] = -((1.0*apardot[32]*q_)/m_); 
-  alphavpar[33] = -((1.0*apardot[33]*q_)/m_); 
-  alphavpar[34] = -((1.0*apardot[34]*q_)/m_); 
-  alphavpar[35] = -((1.0*apardot[35]*q_)/m_); 
-  alphavpar[36] = -((1.0*apardot[36]*q_)/m_); 
-  alphavpar[37] = -((1.0*apardot[37]*q_)/m_); 
-  alphavpar[38] = -((1.0*apardot[38]*q_)/m_); 
-  alphavpar[39] = -((1.0*apardot[39]*q_)/m_); 
-  alphavpar[40] = -((1.0*apardot[40]*q_)/m_); 
-  alphavpar[41] = -((1.0*apardot[41]*q_)/m_); 
-  alphavpar[42] = -((1.0*apardot[42]*q_)/m_); 
-  alphavpar[43] = -((1.0*apardot[43]*q_)/m_); 
-  alphavpar[44] = -((1.0*apardot[44]*q_)/m_); 
-  alphavpar[45] = -((1.0*apardot[45]*q_)/m_); 
-  alphavpar[46] = -((1.0*apardot[46]*q_)/m_); 
-  alphavpar[47] = -((1.0*apardot[47]*q_)/m_); 
+  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
+  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
+  alphavpar[2] = -((2.0*apardot[2]*q_)/m_); 
+  alphavpar[3] = -((2.0*apardot[3]*q_)/m_); 
+  alphavpar[6] = -((2.0*apardot[4]*q_)/m_); 
+  alphavpar[7] = -((2.0*apardot[5]*q_)/m_); 
+  alphavpar[8] = -((2.0*apardot[6]*q_)/m_); 
+  alphavpar[16] = -((2.0*apardot[7]*q_)/m_); 
 
 
-  out[4] += 0.3061862178478971*(alphavpar[47]*fin[47]+alphavpar[46]*fin[46]+alphavpar[45]*fin[45]+alphavpar[44]*fin[44]+alphavpar[43]*fin[43]+alphavpar[42]*fin[42]+alphavpar[41]*fin[41]+alphavpar[40]*fin[40]+alphavpar[39]*fin[39]+alphavpar[38]*fin[38]+alphavpar[37]*fin[37]+alphavpar[36]*fin[36]+alphavpar[35]*fin[35]+alphavpar[34]*fin[34]+alphavpar[33]*fin[33]+alphavpar[32]*fin[32]+alphavpar[31]*fin[31]+alphavpar[30]*fin[30]+alphavpar[29]*fin[29]+alphavpar[28]*fin[28]+alphavpar[27]*fin[27]+alphavpar[26]*fin[26]+alphavpar[25]*fin[25]+alphavpar[24]*fin[24]+alphavpar[23]*fin[23]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[19]*fin[19]+alphavpar[18]*fin[18]+alphavpar[17]*fin[17]+alphavpar[16]*fin[16]+alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[9] += 0.3061862178478971*(alphavpar[46]*fin[47]+fin[46]*alphavpar[47]+alphavpar[42]*fin[45]+fin[42]*alphavpar[45]+alphavpar[41]*fin[44]+fin[41]*alphavpar[44]+alphavpar[39]*fin[43]+fin[39]*alphavpar[43]+alphavpar[36]*fin[40]+fin[36]*alphavpar[40]+alphavpar[35]*fin[38]+fin[35]*alphavpar[38]+alphavpar[34]*fin[37]+fin[34]*alphavpar[37]+alphavpar[32]*fin[33]+fin[32]*alphavpar[33]+alphavpar[30]*fin[31]+fin[30]*alphavpar[31]+alphavpar[25]*fin[29]+fin[25]*alphavpar[29]+alphavpar[24]*fin[28]+fin[24]*alphavpar[28]+alphavpar[22]*fin[27]+fin[22]*alphavpar[27]+alphavpar[19]*fin[26]+fin[19]*alphavpar[26]+alphavpar[15]*fin[23]+fin[15]*alphavpar[23]+alphavpar[14]*fin[21]+fin[14]*alphavpar[21]+alphavpar[13]*fin[20]+fin[13]*alphavpar[20]+alphavpar[11]*fin[18]+fin[11]*alphavpar[18]+alphavpar[10]*fin[17]+fin[10]*alphavpar[17]+alphavpar[8]*fin[16]+fin[8]*alphavpar[16]+alphavpar[5]*fin[12]+fin[5]*alphavpar[12]+alphavpar[4]*fin[9]+fin[4]*alphavpar[9]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[10] += 0.3061862178478971*(alphavpar[45]*fin[47]+fin[45]*alphavpar[47]+alphavpar[42]*fin[46]+fin[42]*alphavpar[46]+alphavpar[40]*fin[44]+fin[40]*alphavpar[44]+alphavpar[38]*fin[43]+fin[38]*alphavpar[43]+alphavpar[36]*fin[41]+fin[36]*alphavpar[41]+alphavpar[35]*fin[39]+fin[35]*alphavpar[39]+alphavpar[33]*fin[37]+fin[33]*alphavpar[37]+alphavpar[32]*fin[34]+fin[32]*alphavpar[34]+alphavpar[29]*fin[31]+fin[29]*alphavpar[31]+alphavpar[25]*fin[30]+fin[25]*alphavpar[30]+alphavpar[23]*fin[28]+fin[23]*alphavpar[28]+alphavpar[21]*fin[27]+fin[21]*alphavpar[27]+alphavpar[18]*fin[26]+fin[18]*alphavpar[26]+alphavpar[15]*fin[24]+fin[15]*alphavpar[24]+alphavpar[14]*fin[22]+fin[14]*alphavpar[22]+alphavpar[12]*fin[20]+fin[12]*alphavpar[20]+alphavpar[11]*fin[19]+fin[11]*alphavpar[19]+alphavpar[9]*fin[17]+fin[9]*alphavpar[17]+alphavpar[7]*fin[16]+fin[7]*alphavpar[16]+alphavpar[5]*fin[13]+fin[5]*alphavpar[13]+alphavpar[4]*fin[10]+fin[4]*alphavpar[10]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
-  out[11] += 0.3061862178478971*(alphavpar[44]*fin[47]+fin[44]*alphavpar[47]+alphavpar[41]*fin[46]+fin[41]*alphavpar[46]+alphavpar[40]*fin[45]+fin[40]*alphavpar[45]+alphavpar[37]*fin[43]+fin[37]*alphavpar[43]+alphavpar[36]*fin[42]+fin[36]*alphavpar[42]+alphavpar[34]*fin[39]+fin[34]*alphavpar[39]+alphavpar[33]*fin[38]+fin[33]*alphavpar[38]+alphavpar[32]*fin[35]+fin[32]*alphavpar[35]+alphavpar[28]*fin[31]+fin[28]*alphavpar[31]+alphavpar[24]*fin[30]+fin[24]*alphavpar[30]+alphavpar[23]*fin[29]+fin[23]*alphavpar[29]+alphavpar[20]*fin[27]+fin[20]*alphavpar[27]+alphavpar[17]*fin[26]+fin[17]*alphavpar[26]+alphavpar[15]*fin[25]+fin[15]*alphavpar[25]+alphavpar[13]*fin[22]+fin[13]*alphavpar[22]+alphavpar[12]*fin[21]+fin[12]*alphavpar[21]+alphavpar[10]*fin[19]+fin[10]*alphavpar[19]+alphavpar[9]*fin[18]+fin[9]*alphavpar[18]+alphavpar[6]*fin[16]+fin[6]*alphavpar[16]+alphavpar[5]*fin[14]+fin[5]*alphavpar[14]+alphavpar[4]*fin[11]+fin[4]*alphavpar[11]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
-  out[15] += 0.3061862178478971*(alphavpar[43]*fin[47]+fin[43]*alphavpar[47]+alphavpar[39]*fin[46]+fin[39]*alphavpar[46]+alphavpar[38]*fin[45]+fin[38]*alphavpar[45]+alphavpar[37]*fin[44]+fin[37]*alphavpar[44]+alphavpar[35]*fin[42]+fin[35]*alphavpar[42]+alphavpar[34]*fin[41]+fin[34]*alphavpar[41]+alphavpar[33]*fin[40]+fin[33]*alphavpar[40]+alphavpar[32]*fin[36]+fin[32]*alphavpar[36]+alphavpar[26]*fin[31]+fin[26]*alphavpar[31]+alphavpar[19]*fin[30]+fin[19]*alphavpar[30]+alphavpar[18]*fin[29]+fin[18]*alphavpar[29]+alphavpar[17]*fin[28]+fin[17]*alphavpar[28]+alphavpar[16]*fin[27]+fin[16]*alphavpar[27]+alphavpar[11]*fin[25]+fin[11]*alphavpar[25]+alphavpar[10]*fin[24]+fin[10]*alphavpar[24]+alphavpar[9]*fin[23]+fin[9]*alphavpar[23]+alphavpar[8]*fin[22]+fin[8]*alphavpar[22]+alphavpar[7]*fin[21]+fin[7]*alphavpar[21]+alphavpar[6]*fin[20]+fin[6]*alphavpar[20]+alphavpar[4]*fin[15]+fin[4]*alphavpar[15]+alphavpar[3]*fin[14]+fin[3]*alphavpar[14]+alphavpar[2]*fin[13]+fin[2]*alphavpar[13]+alphavpar[1]*fin[12]+fin[1]*alphavpar[12]+alphavpar[0]*fin[5]+fin[0]*alphavpar[5]); 
-  out[17] += 0.3061862178478971*(alphavpar[42]*fin[47]+fin[42]*alphavpar[47]+alphavpar[45]*fin[46]+fin[45]*alphavpar[46]+alphavpar[36]*fin[44]+fin[36]*alphavpar[44]+alphavpar[35]*fin[43]+fin[35]*alphavpar[43]+alphavpar[40]*fin[41]+fin[40]*alphavpar[41]+alphavpar[38]*fin[39]+fin[38]*alphavpar[39]+alphavpar[32]*fin[37]+fin[32]*alphavpar[37]+alphavpar[33]*fin[34]+fin[33]*alphavpar[34]+alphavpar[25]*fin[31]+fin[25]*alphavpar[31]+alphavpar[29]*fin[30]+fin[29]*alphavpar[30]+alphavpar[15]*fin[28]+fin[15]*alphavpar[28]+alphavpar[14]*fin[27]+fin[14]*alphavpar[27]+alphavpar[11]*fin[26]+fin[11]*alphavpar[26]+alphavpar[23]*fin[24]+fin[23]*alphavpar[24]+alphavpar[21]*fin[22]+fin[21]*alphavpar[22]+alphavpar[5]*fin[20]+fin[5]*alphavpar[20]+alphavpar[18]*fin[19]+fin[18]*alphavpar[19]+alphavpar[4]*fin[17]+fin[4]*alphavpar[17]+alphavpar[3]*fin[16]+fin[3]*alphavpar[16]+alphavpar[12]*fin[13]+fin[12]*alphavpar[13]+alphavpar[9]*fin[10]+fin[9]*alphavpar[10]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
-  out[18] += 0.3061862178478971*(alphavpar[41]*fin[47]+fin[41]*alphavpar[47]+alphavpar[44]*fin[46]+fin[44]*alphavpar[46]+alphavpar[36]*fin[45]+fin[36]*alphavpar[45]+alphavpar[34]*fin[43]+fin[34]*alphavpar[43]+alphavpar[40]*fin[42]+fin[40]*alphavpar[42]+alphavpar[37]*fin[39]+fin[37]*alphavpar[39]+alphavpar[32]*fin[38]+fin[32]*alphavpar[38]+alphavpar[33]*fin[35]+fin[33]*alphavpar[35]+alphavpar[24]*fin[31]+fin[24]*alphavpar[31]+alphavpar[28]*fin[30]+fin[28]*alphavpar[30]+alphavpar[15]*fin[29]+fin[15]*alphavpar[29]+alphavpar[13]*fin[27]+fin[13]*alphavpar[27]+alphavpar[10]*fin[26]+fin[10]*alphavpar[26]+alphavpar[23]*fin[25]+fin[23]*alphavpar[25]+alphavpar[20]*fin[22]+fin[20]*alphavpar[22]+alphavpar[5]*fin[21]+fin[5]*alphavpar[21]+alphavpar[17]*fin[19]+fin[17]*alphavpar[19]+alphavpar[4]*fin[18]+fin[4]*alphavpar[18]+alphavpar[2]*fin[16]+fin[2]*alphavpar[16]+alphavpar[12]*fin[14]+fin[12]*alphavpar[14]+alphavpar[9]*fin[11]+fin[9]*alphavpar[11]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
-  out[19] += 0.3061862178478971*(alphavpar[40]*fin[47]+fin[40]*alphavpar[47]+alphavpar[36]*fin[46]+fin[36]*alphavpar[46]+alphavpar[44]*fin[45]+fin[44]*alphavpar[45]+alphavpar[33]*fin[43]+fin[33]*alphavpar[43]+alphavpar[41]*fin[42]+fin[41]*alphavpar[42]+alphavpar[32]*fin[39]+fin[32]*alphavpar[39]+alphavpar[37]*fin[38]+fin[37]*alphavpar[38]+alphavpar[34]*fin[35]+fin[34]*alphavpar[35]+alphavpar[23]*fin[31]+fin[23]*alphavpar[31]+alphavpar[15]*fin[30]+fin[15]*alphavpar[30]+alphavpar[28]*fin[29]+fin[28]*alphavpar[29]+alphavpar[12]*fin[27]+fin[12]*alphavpar[27]+alphavpar[9]*fin[26]+fin[9]*alphavpar[26]+alphavpar[24]*fin[25]+fin[24]*alphavpar[25]+alphavpar[5]*fin[22]+fin[5]*alphavpar[22]+alphavpar[20]*fin[21]+fin[20]*alphavpar[21]+alphavpar[4]*fin[19]+fin[4]*alphavpar[19]+alphavpar[17]*fin[18]+fin[17]*alphavpar[18]+alphavpar[1]*fin[16]+fin[1]*alphavpar[16]+alphavpar[13]*fin[14]+fin[13]*alphavpar[14]+alphavpar[10]*fin[11]+fin[10]*alphavpar[11]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
-  out[23] += 0.3061862178478971*(alphavpar[39]*fin[47]+fin[39]*alphavpar[47]+alphavpar[43]*fin[46]+fin[43]*alphavpar[46]+alphavpar[35]*fin[45]+fin[35]*alphavpar[45]+alphavpar[34]*fin[44]+fin[34]*alphavpar[44]+alphavpar[38]*fin[42]+fin[38]*alphavpar[42]+alphavpar[37]*fin[41]+fin[37]*alphavpar[41]+alphavpar[32]*fin[40]+fin[32]*alphavpar[40]+alphavpar[33]*fin[36]+fin[33]*alphavpar[36]+alphavpar[19]*fin[31]+fin[19]*alphavpar[31]+alphavpar[26]*fin[30]+fin[26]*alphavpar[30]+alphavpar[11]*fin[29]+fin[11]*alphavpar[29]+alphavpar[10]*fin[28]+fin[10]*alphavpar[28]+alphavpar[8]*fin[27]+fin[8]*alphavpar[27]+alphavpar[18]*fin[25]+fin[18]*alphavpar[25]+alphavpar[17]*fin[24]+fin[17]*alphavpar[24]+alphavpar[4]*fin[23]+fin[4]*alphavpar[23]+alphavpar[16]*fin[22]+fin[16]*alphavpar[22]+alphavpar[3]*fin[21]+fin[3]*alphavpar[21]+alphavpar[2]*fin[20]+fin[2]*alphavpar[20]+alphavpar[9]*fin[15]+fin[9]*alphavpar[15]+alphavpar[7]*fin[14]+fin[7]*alphavpar[14]+alphavpar[6]*fin[13]+fin[6]*alphavpar[13]+alphavpar[0]*fin[12]+fin[0]*alphavpar[12]+alphavpar[1]*fin[5]+fin[1]*alphavpar[5]); 
-  out[24] += 0.3061862178478971*(alphavpar[38]*fin[47]+fin[38]*alphavpar[47]+alphavpar[35]*fin[46]+fin[35]*alphavpar[46]+alphavpar[43]*fin[45]+fin[43]*alphavpar[45]+alphavpar[33]*fin[44]+fin[33]*alphavpar[44]+alphavpar[39]*fin[42]+fin[39]*alphavpar[42]+alphavpar[32]*fin[41]+fin[32]*alphavpar[41]+alphavpar[37]*fin[40]+fin[37]*alphavpar[40]+alphavpar[34]*fin[36]+fin[34]*alphavpar[36]+alphavpar[18]*fin[31]+fin[18]*alphavpar[31]+alphavpar[11]*fin[30]+fin[11]*alphavpar[30]+alphavpar[26]*fin[29]+fin[26]*alphavpar[29]+alphavpar[9]*fin[28]+fin[9]*alphavpar[28]+alphavpar[7]*fin[27]+fin[7]*alphavpar[27]+alphavpar[19]*fin[25]+fin[19]*alphavpar[25]+alphavpar[4]*fin[24]+fin[4]*alphavpar[24]+alphavpar[17]*fin[23]+fin[17]*alphavpar[23]+alphavpar[3]*fin[22]+fin[3]*alphavpar[22]+alphavpar[16]*fin[21]+fin[16]*alphavpar[21]+alphavpar[1]*fin[20]+fin[1]*alphavpar[20]+alphavpar[10]*fin[15]+fin[10]*alphavpar[15]+alphavpar[8]*fin[14]+fin[8]*alphavpar[14]+alphavpar[0]*fin[13]+fin[0]*alphavpar[13]+alphavpar[6]*fin[12]+fin[6]*alphavpar[12]+alphavpar[2]*fin[5]+fin[2]*alphavpar[5]); 
-  out[25] += 0.3061862178478971*(alphavpar[37]*fin[47]+fin[37]*alphavpar[47]+alphavpar[34]*fin[46]+fin[34]*alphavpar[46]+alphavpar[33]*fin[45]+fin[33]*alphavpar[45]+alphavpar[43]*fin[44]+fin[43]*alphavpar[44]+alphavpar[32]*fin[42]+fin[32]*alphavpar[42]+alphavpar[39]*fin[41]+fin[39]*alphavpar[41]+alphavpar[38]*fin[40]+fin[38]*alphavpar[40]+alphavpar[35]*fin[36]+fin[35]*alphavpar[36]+alphavpar[17]*fin[31]+fin[17]*alphavpar[31]+alphavpar[10]*fin[30]+fin[10]*alphavpar[30]+alphavpar[9]*fin[29]+fin[9]*alphavpar[29]+alphavpar[26]*fin[28]+fin[26]*alphavpar[28]+alphavpar[6]*fin[27]+fin[6]*alphavpar[27]+alphavpar[4]*fin[25]+fin[4]*alphavpar[25]+alphavpar[19]*fin[24]+fin[19]*alphavpar[24]+alphavpar[18]*fin[23]+fin[18]*alphavpar[23]+alphavpar[2]*fin[22]+fin[2]*alphavpar[22]+alphavpar[1]*fin[21]+fin[1]*alphavpar[21]+alphavpar[16]*fin[20]+fin[16]*alphavpar[20]+alphavpar[11]*fin[15]+fin[11]*alphavpar[15]+alphavpar[0]*fin[14]+fin[0]*alphavpar[14]+alphavpar[8]*fin[13]+fin[8]*alphavpar[13]+alphavpar[7]*fin[12]+fin[7]*alphavpar[12]+alphavpar[3]*fin[5]+fin[3]*alphavpar[5]); 
-  out[26] += 0.3061862178478971*(alphavpar[36]*fin[47]+fin[36]*alphavpar[47]+alphavpar[40]*fin[46]+fin[40]*alphavpar[46]+alphavpar[41]*fin[45]+fin[41]*alphavpar[45]+alphavpar[42]*fin[44]+fin[42]*alphavpar[44]+alphavpar[32]*fin[43]+fin[32]*alphavpar[43]+alphavpar[33]*fin[39]+fin[33]*alphavpar[39]+alphavpar[34]*fin[38]+fin[34]*alphavpar[38]+alphavpar[35]*fin[37]+fin[35]*alphavpar[37]+alphavpar[15]*fin[31]+fin[15]*alphavpar[31]+alphavpar[23]*fin[30]+fin[23]*alphavpar[30]+alphavpar[24]*fin[29]+fin[24]*alphavpar[29]+alphavpar[25]*fin[28]+fin[25]*alphavpar[28]+alphavpar[5]*fin[27]+fin[5]*alphavpar[27]+alphavpar[4]*fin[26]+fin[4]*alphavpar[26]+alphavpar[12]*fin[22]+fin[12]*alphavpar[22]+alphavpar[13]*fin[21]+fin[13]*alphavpar[21]+alphavpar[14]*fin[20]+fin[14]*alphavpar[20]+alphavpar[9]*fin[19]+fin[9]*alphavpar[19]+alphavpar[10]*fin[18]+fin[10]*alphavpar[18]+alphavpar[11]*fin[17]+fin[11]*alphavpar[17]+alphavpar[0]*fin[16]+fin[0]*alphavpar[16]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]); 
-  out[28] += 0.3061862178478971*(alphavpar[35]*fin[47]+fin[35]*alphavpar[47]+alphavpar[38]*fin[46]+fin[38]*alphavpar[46]+alphavpar[39]*fin[45]+fin[39]*alphavpar[45]+alphavpar[32]*fin[44]+fin[32]*alphavpar[44]+alphavpar[42]*fin[43]+fin[42]*alphavpar[43]+alphavpar[33]*fin[41]+fin[33]*alphavpar[41]+alphavpar[34]*fin[40]+fin[34]*alphavpar[40]+alphavpar[36]*fin[37]+fin[36]*alphavpar[37]+alphavpar[11]*fin[31]+fin[11]*alphavpar[31]+alphavpar[18]*fin[30]+fin[18]*alphavpar[30]+alphavpar[19]*fin[29]+fin[19]*alphavpar[29]+alphavpar[4]*fin[28]+fin[4]*alphavpar[28]+alphavpar[3]*fin[27]+fin[3]*alphavpar[27]+alphavpar[25]*fin[26]+fin[25]*alphavpar[26]+alphavpar[9]*fin[24]+fin[9]*alphavpar[24]+alphavpar[10]*fin[23]+fin[10]*alphavpar[23]+alphavpar[7]*fin[22]+fin[7]*alphavpar[22]+alphavpar[8]*fin[21]+fin[8]*alphavpar[21]+alphavpar[0]*fin[20]+fin[0]*alphavpar[20]+alphavpar[15]*fin[17]+fin[15]*alphavpar[17]+alphavpar[14]*fin[16]+fin[14]*alphavpar[16]+alphavpar[1]*fin[13]+fin[1]*alphavpar[13]+alphavpar[2]*fin[12]+fin[2]*alphavpar[12]+alphavpar[5]*fin[6]+fin[5]*alphavpar[6]); 
-  out[29] += 0.3061862178478971*(alphavpar[34]*fin[47]+fin[34]*alphavpar[47]+alphavpar[37]*fin[46]+fin[37]*alphavpar[46]+alphavpar[32]*fin[45]+fin[32]*alphavpar[45]+alphavpar[39]*fin[44]+fin[39]*alphavpar[44]+alphavpar[41]*fin[43]+fin[41]*alphavpar[43]+alphavpar[33]*fin[42]+fin[33]*alphavpar[42]+alphavpar[35]*fin[40]+fin[35]*alphavpar[40]+alphavpar[36]*fin[38]+fin[36]*alphavpar[38]+alphavpar[10]*fin[31]+fin[10]*alphavpar[31]+alphavpar[17]*fin[30]+fin[17]*alphavpar[30]+alphavpar[4]*fin[29]+fin[4]*alphavpar[29]+alphavpar[19]*fin[28]+fin[19]*alphavpar[28]+alphavpar[2]*fin[27]+fin[2]*alphavpar[27]+alphavpar[24]*fin[26]+fin[24]*alphavpar[26]+alphavpar[9]*fin[25]+fin[9]*alphavpar[25]+alphavpar[11]*fin[23]+fin[11]*alphavpar[23]+alphavpar[6]*fin[22]+fin[6]*alphavpar[22]+alphavpar[0]*fin[21]+fin[0]*alphavpar[21]+alphavpar[8]*fin[20]+fin[8]*alphavpar[20]+alphavpar[15]*fin[18]+fin[15]*alphavpar[18]+alphavpar[13]*fin[16]+fin[13]*alphavpar[16]+alphavpar[1]*fin[14]+fin[1]*alphavpar[14]+alphavpar[3]*fin[12]+fin[3]*alphavpar[12]+alphavpar[5]*fin[7]+fin[5]*alphavpar[7]); 
-  out[30] += 0.3061862178478971*(alphavpar[33]*fin[47]+fin[33]*alphavpar[47]+alphavpar[32]*fin[46]+fin[32]*alphavpar[46]+alphavpar[37]*fin[45]+fin[37]*alphavpar[45]+alphavpar[38]*fin[44]+fin[38]*alphavpar[44]+alphavpar[40]*fin[43]+fin[40]*alphavpar[43]+alphavpar[34]*fin[42]+fin[34]*alphavpar[42]+alphavpar[35]*fin[41]+fin[35]*alphavpar[41]+alphavpar[36]*fin[39]+fin[36]*alphavpar[39]+alphavpar[9]*fin[31]+fin[9]*alphavpar[31]+alphavpar[4]*fin[30]+fin[4]*alphavpar[30]+alphavpar[17]*fin[29]+fin[17]*alphavpar[29]+alphavpar[18]*fin[28]+fin[18]*alphavpar[28]+alphavpar[1]*fin[27]+fin[1]*alphavpar[27]+alphavpar[23]*fin[26]+fin[23]*alphavpar[26]+alphavpar[10]*fin[25]+fin[10]*alphavpar[25]+alphavpar[11]*fin[24]+fin[11]*alphavpar[24]+alphavpar[0]*fin[22]+fin[0]*alphavpar[22]+alphavpar[6]*fin[21]+fin[6]*alphavpar[21]+alphavpar[7]*fin[20]+fin[7]*alphavpar[20]+alphavpar[15]*fin[19]+fin[15]*alphavpar[19]+alphavpar[12]*fin[16]+fin[12]*alphavpar[16]+alphavpar[2]*fin[14]+fin[2]*alphavpar[14]+alphavpar[3]*fin[13]+fin[3]*alphavpar[13]+alphavpar[5]*fin[8]+fin[5]*alphavpar[8]); 
-  out[31] += 0.3061862178478971*(alphavpar[32]*fin[47]+fin[32]*alphavpar[47]+alphavpar[33]*fin[46]+fin[33]*alphavpar[46]+alphavpar[34]*fin[45]+fin[34]*alphavpar[45]+alphavpar[35]*fin[44]+fin[35]*alphavpar[44]+alphavpar[36]*fin[43]+fin[36]*alphavpar[43]+alphavpar[37]*fin[42]+fin[37]*alphavpar[42]+alphavpar[38]*fin[41]+fin[38]*alphavpar[41]+alphavpar[39]*fin[40]+fin[39]*alphavpar[40]+alphavpar[4]*fin[31]+fin[4]*alphavpar[31]+alphavpar[9]*fin[30]+fin[9]*alphavpar[30]+alphavpar[10]*fin[29]+fin[10]*alphavpar[29]+alphavpar[11]*fin[28]+fin[11]*alphavpar[28]+alphavpar[0]*fin[27]+fin[0]*alphavpar[27]+alphavpar[15]*fin[26]+fin[15]*alphavpar[26]+alphavpar[17]*fin[25]+fin[17]*alphavpar[25]+alphavpar[18]*fin[24]+fin[18]*alphavpar[24]+alphavpar[19]*fin[23]+fin[19]*alphavpar[23]+alphavpar[1]*fin[22]+fin[1]*alphavpar[22]+alphavpar[2]*fin[21]+fin[2]*alphavpar[21]+alphavpar[3]*fin[20]+fin[3]*alphavpar[20]+alphavpar[5]*fin[16]+fin[5]*alphavpar[16]+alphavpar[6]*fin[14]+fin[6]*alphavpar[14]+alphavpar[7]*fin[13]+fin[7]*alphavpar[13]+alphavpar[8]*fin[12]+fin[8]*alphavpar[12]); 
-  out[32] += 0.6123724356957944*(alphavpar[31]*fin[47]+fin[31]*alphavpar[47]+alphavpar[30]*fin[46]+fin[30]*alphavpar[46]+alphavpar[29]*fin[45]+fin[29]*alphavpar[45]+alphavpar[28]*fin[44]+fin[28]*alphavpar[44]+alphavpar[26]*fin[43]+fin[26]*alphavpar[43]+alphavpar[25]*fin[42]+fin[25]*alphavpar[42]+alphavpar[24]*fin[41]+fin[24]*alphavpar[41]+alphavpar[23]*fin[40]+fin[23]*alphavpar[40]+alphavpar[19]*fin[39]+fin[19]*alphavpar[39]+alphavpar[18]*fin[38]+fin[18]*alphavpar[38]+alphavpar[17]*fin[37]+fin[17]*alphavpar[37]+alphavpar[15]*fin[36]+fin[15]*alphavpar[36]+alphavpar[11]*fin[35]+fin[11]*alphavpar[35]+alphavpar[10]*fin[34]+fin[10]*alphavpar[34]+alphavpar[9]*fin[33]+fin[9]*alphavpar[33]+alphavpar[4]*fin[32]+fin[4]*alphavpar[32])+0.6846531968814573*(alphavpar[27]*fin[31]+fin[27]*alphavpar[31]+alphavpar[22]*fin[30]+fin[22]*alphavpar[30]+alphavpar[21]*fin[29]+fin[21]*alphavpar[29]+alphavpar[20]*fin[28]+fin[20]*alphavpar[28]+alphavpar[16]*fin[26]+fin[16]*alphavpar[26]+alphavpar[14]*fin[25]+fin[14]*alphavpar[25]+alphavpar[13]*fin[24]+fin[13]*alphavpar[24]+alphavpar[12]*fin[23]+fin[12]*alphavpar[23]+alphavpar[8]*fin[19]+fin[8]*alphavpar[19]+alphavpar[7]*fin[18]+fin[7]*alphavpar[18]+alphavpar[6]*fin[17]+fin[6]*alphavpar[17]+alphavpar[5]*fin[15]+fin[5]*alphavpar[15]+alphavpar[3]*fin[11]+fin[3]*alphavpar[11]+alphavpar[2]*fin[10]+fin[2]*alphavpar[10]+alphavpar[1]*fin[9]+fin[1]*alphavpar[9]+alphavpar[0]*fin[4]+fin[0]*alphavpar[4]); 
-  out[33] += 0.6123724356957944*(alphavpar[30]*fin[47]+fin[30]*alphavpar[47]+alphavpar[31]*fin[46]+fin[31]*alphavpar[46]+alphavpar[25]*fin[45]+fin[25]*alphavpar[45]+alphavpar[24]*fin[44]+fin[24]*alphavpar[44]+alphavpar[19]*fin[43]+fin[19]*alphavpar[43]+alphavpar[29]*fin[42]+fin[29]*alphavpar[42]+alphavpar[28]*fin[41]+fin[28]*alphavpar[41]+alphavpar[15]*fin[40]+fin[15]*alphavpar[40]+alphavpar[26]*fin[39]+fin[26]*alphavpar[39]+alphavpar[11]*fin[38]+fin[11]*alphavpar[38]+alphavpar[10]*fin[37]+fin[10]*alphavpar[37]+alphavpar[23]*fin[36]+fin[23]*alphavpar[36]+alphavpar[18]*fin[35]+fin[18]*alphavpar[35]+alphavpar[17]*fin[34]+fin[17]*alphavpar[34]+alphavpar[4]*fin[33]+fin[4]*alphavpar[33]+alphavpar[9]*fin[32]+fin[9]*alphavpar[32])+0.6846531968814574*(alphavpar[22]*fin[31]+fin[22]*alphavpar[31]+alphavpar[27]*fin[30]+fin[27]*alphavpar[30]+alphavpar[14]*fin[29]+fin[14]*alphavpar[29]+alphavpar[13]*fin[28]+fin[13]*alphavpar[28]+alphavpar[8]*fin[26]+fin[8]*alphavpar[26]+alphavpar[21]*fin[25]+fin[21]*alphavpar[25]+alphavpar[20]*fin[24]+fin[20]*alphavpar[24]+alphavpar[5]*fin[23]+fin[5]*alphavpar[23]+alphavpar[16]*fin[19]+fin[16]*alphavpar[19]+alphavpar[3]*fin[18]+fin[3]*alphavpar[18]+alphavpar[2]*fin[17]+fin[2]*alphavpar[17]+alphavpar[12]*fin[15]+fin[12]*alphavpar[15]+alphavpar[7]*fin[11]+fin[7]*alphavpar[11]+alphavpar[6]*fin[10]+fin[6]*alphavpar[10]+alphavpar[0]*fin[9]+fin[0]*alphavpar[9]+alphavpar[1]*fin[4]+fin[1]*alphavpar[4]); 
-  out[34] += 0.6123724356957944*(alphavpar[29]*fin[47]+fin[29]*alphavpar[47]+alphavpar[25]*fin[46]+fin[25]*alphavpar[46]+alphavpar[31]*fin[45]+fin[31]*alphavpar[45]+alphavpar[23]*fin[44]+fin[23]*alphavpar[44]+alphavpar[18]*fin[43]+fin[18]*alphavpar[43]+alphavpar[30]*fin[42]+fin[30]*alphavpar[42]+alphavpar[15]*fin[41]+fin[15]*alphavpar[41]+alphavpar[28]*fin[40]+fin[28]*alphavpar[40]+alphavpar[11]*fin[39]+fin[11]*alphavpar[39]+alphavpar[26]*fin[38]+fin[26]*alphavpar[38]+alphavpar[9]*fin[37]+fin[9]*alphavpar[37]+alphavpar[24]*fin[36]+fin[24]*alphavpar[36]+alphavpar[19]*fin[35]+fin[19]*alphavpar[35]+alphavpar[4]*fin[34]+fin[4]*alphavpar[34]+alphavpar[17]*fin[33]+fin[17]*alphavpar[33]+alphavpar[10]*fin[32]+fin[10]*alphavpar[32])+0.6846531968814574*(alphavpar[21]*fin[31]+fin[21]*alphavpar[31]+alphavpar[14]*fin[30]+fin[14]*alphavpar[30]+alphavpar[27]*fin[29]+fin[27]*alphavpar[29]+alphavpar[12]*fin[28]+fin[12]*alphavpar[28]+alphavpar[7]*fin[26]+fin[7]*alphavpar[26]+alphavpar[22]*fin[25]+fin[22]*alphavpar[25]+alphavpar[5]*fin[24]+fin[5]*alphavpar[24]+alphavpar[20]*fin[23]+fin[20]*alphavpar[23]+alphavpar[3]*fin[19]+fin[3]*alphavpar[19]+alphavpar[16]*fin[18]+fin[16]*alphavpar[18]+alphavpar[1]*fin[17]+fin[1]*alphavpar[17]+alphavpar[13]*fin[15]+fin[13]*alphavpar[15]+alphavpar[8]*fin[11]+fin[8]*alphavpar[11]+alphavpar[0]*fin[10]+fin[0]*alphavpar[10]+alphavpar[6]*fin[9]+fin[6]*alphavpar[9]+alphavpar[2]*fin[4]+fin[2]*alphavpar[4]); 
-  out[35] += 0.6123724356957944*(alphavpar[28]*fin[47]+fin[28]*alphavpar[47]+alphavpar[24]*fin[46]+fin[24]*alphavpar[46]+alphavpar[23]*fin[45]+fin[23]*alphavpar[45]+alphavpar[31]*fin[44]+fin[31]*alphavpar[44]+alphavpar[17]*fin[43]+fin[17]*alphavpar[43]+alphavpar[15]*fin[42]+fin[15]*alphavpar[42]+alphavpar[30]*fin[41]+fin[30]*alphavpar[41]+alphavpar[29]*fin[40]+fin[29]*alphavpar[40]+alphavpar[10]*fin[39]+fin[10]*alphavpar[39]+alphavpar[9]*fin[38]+fin[9]*alphavpar[38]+alphavpar[26]*fin[37]+fin[26]*alphavpar[37]+alphavpar[25]*fin[36]+fin[25]*alphavpar[36]+alphavpar[4]*fin[35]+fin[4]*alphavpar[35]+alphavpar[19]*fin[34]+fin[19]*alphavpar[34]+alphavpar[18]*fin[33]+fin[18]*alphavpar[33]+alphavpar[11]*fin[32]+fin[11]*alphavpar[32])+0.6846531968814574*(alphavpar[20]*fin[31]+fin[20]*alphavpar[31]+alphavpar[13]*fin[30]+fin[13]*alphavpar[30]+alphavpar[12]*fin[29]+fin[12]*alphavpar[29]+alphavpar[27]*fin[28]+fin[27]*alphavpar[28]+alphavpar[6]*fin[26]+fin[6]*alphavpar[26]+alphavpar[5]*fin[25]+fin[5]*alphavpar[25]+alphavpar[22]*fin[24]+fin[22]*alphavpar[24]+alphavpar[21]*fin[23]+fin[21]*alphavpar[23]+alphavpar[2]*fin[19]+fin[2]*alphavpar[19]+alphavpar[1]*fin[18]+fin[1]*alphavpar[18]+alphavpar[16]*fin[17]+fin[16]*alphavpar[17]+alphavpar[14]*fin[15]+fin[14]*alphavpar[15]+alphavpar[0]*fin[11]+fin[0]*alphavpar[11]+alphavpar[8]*fin[10]+fin[8]*alphavpar[10]+alphavpar[7]*fin[9]+fin[7]*alphavpar[9]+alphavpar[3]*fin[4]+fin[3]*alphavpar[4]); 
-  out[36] += 0.6123724356957944*(alphavpar[26]*fin[47]+fin[26]*alphavpar[47]+alphavpar[19]*fin[46]+fin[19]*alphavpar[46]+alphavpar[18]*fin[45]+fin[18]*alphavpar[45]+alphavpar[17]*fin[44]+fin[17]*alphavpar[44]+alphavpar[31]*fin[43]+fin[31]*alphavpar[43]+alphavpar[11]*fin[42]+fin[11]*alphavpar[42]+alphavpar[10]*fin[41]+fin[10]*alphavpar[41]+alphavpar[9]*fin[40]+fin[9]*alphavpar[40]+alphavpar[30]*fin[39]+fin[30]*alphavpar[39]+alphavpar[29]*fin[38]+fin[29]*alphavpar[38]+alphavpar[28]*fin[37]+fin[28]*alphavpar[37]+alphavpar[4]*fin[36]+fin[4]*alphavpar[36]+alphavpar[25]*fin[35]+fin[25]*alphavpar[35]+alphavpar[24]*fin[34]+fin[24]*alphavpar[34]+alphavpar[23]*fin[33]+fin[23]*alphavpar[33]+alphavpar[15]*fin[32]+fin[15]*alphavpar[32])+0.6846531968814574*(alphavpar[16]*fin[31]+fin[16]*alphavpar[31]+alphavpar[8]*fin[30]+fin[8]*alphavpar[30]+alphavpar[7]*fin[29]+fin[7]*alphavpar[29]+alphavpar[6]*fin[28]+fin[6]*alphavpar[28]+alphavpar[26]*fin[27]+fin[26]*alphavpar[27]+alphavpar[3]*fin[25]+fin[3]*alphavpar[25]+alphavpar[2]*fin[24]+fin[2]*alphavpar[24]+alphavpar[1]*fin[23]+fin[1]*alphavpar[23]+alphavpar[19]*fin[22]+fin[19]*alphavpar[22]+alphavpar[18]*fin[21]+fin[18]*alphavpar[21]+alphavpar[17]*fin[20]+fin[17]*alphavpar[20]+alphavpar[0]*fin[15]+fin[0]*alphavpar[15]+alphavpar[11]*fin[14]+fin[11]*alphavpar[14]+alphavpar[10]*fin[13]+fin[10]*alphavpar[13]+alphavpar[9]*fin[12]+fin[9]*alphavpar[12]+alphavpar[4]*fin[5]+fin[4]*alphavpar[5]); 
-  out[37] += 0.6123724356957944*(alphavpar[25]*fin[47]+fin[25]*alphavpar[47]+alphavpar[29]*fin[46]+fin[29]*alphavpar[46]+alphavpar[30]*fin[45]+fin[30]*alphavpar[45]+alphavpar[15]*fin[44]+fin[15]*alphavpar[44]+alphavpar[11]*fin[43]+fin[11]*alphavpar[43]+alphavpar[31]*fin[42]+fin[31]*alphavpar[42]+alphavpar[23]*fin[41]+fin[23]*alphavpar[41]+alphavpar[24]*fin[40]+fin[24]*alphavpar[40]+alphavpar[18]*fin[39]+fin[18]*alphavpar[39]+alphavpar[19]*fin[38]+fin[19]*alphavpar[38]+alphavpar[4]*fin[37]+fin[4]*alphavpar[37]+alphavpar[28]*fin[36]+fin[28]*alphavpar[36]+alphavpar[26]*fin[35]+fin[26]*alphavpar[35]+alphavpar[9]*fin[34]+fin[9]*alphavpar[34]+alphavpar[10]*fin[33]+fin[10]*alphavpar[33]+alphavpar[17]*fin[32]+fin[17]*alphavpar[32])+0.6846531968814573*(alphavpar[14]*fin[31]+fin[14]*alphavpar[31]+alphavpar[21]*fin[30]+fin[21]*alphavpar[30]+alphavpar[22]*fin[29]+fin[22]*alphavpar[29]+alphavpar[5]*fin[28]+fin[5]*alphavpar[28]+alphavpar[25]*fin[27]+fin[25]*alphavpar[27]+alphavpar[3]*fin[26]+fin[3]*alphavpar[26]+alphavpar[12]*fin[24]+fin[12]*alphavpar[24]+alphavpar[13]*fin[23]+fin[13]*alphavpar[23]+alphavpar[15]*fin[20]+fin[15]*alphavpar[20]+alphavpar[7]*fin[19]+fin[7]*alphavpar[19]+alphavpar[8]*fin[18]+fin[8]*alphavpar[18]+alphavpar[0]*fin[17]+fin[0]*alphavpar[17]+alphavpar[11]*fin[16]+fin[11]*alphavpar[16]+alphavpar[1]*fin[10]+fin[1]*alphavpar[10]+alphavpar[2]*fin[9]+fin[2]*alphavpar[9]+alphavpar[4]*fin[6]+fin[4]*alphavpar[6]); 
-  out[38] += 0.6123724356957944*(alphavpar[24]*fin[47]+fin[24]*alphavpar[47]+alphavpar[28]*fin[46]+fin[28]*alphavpar[46]+alphavpar[15]*fin[45]+fin[15]*alphavpar[45]+alphavpar[30]*fin[44]+fin[30]*alphavpar[44]+alphavpar[10]*fin[43]+fin[10]*alphavpar[43]+alphavpar[23]*fin[42]+fin[23]*alphavpar[42]+alphavpar[31]*fin[41]+fin[31]*alphavpar[41]+alphavpar[25]*fin[40]+fin[25]*alphavpar[40]+alphavpar[17]*fin[39]+fin[17]*alphavpar[39]+alphavpar[4]*fin[38]+fin[4]*alphavpar[38]+alphavpar[19]*fin[37]+fin[19]*alphavpar[37]+alphavpar[29]*fin[36]+fin[29]*alphavpar[36]+alphavpar[9]*fin[35]+fin[9]*alphavpar[35]+alphavpar[26]*fin[34]+fin[26]*alphavpar[34]+alphavpar[11]*fin[33]+fin[11]*alphavpar[33]+alphavpar[18]*fin[32]+fin[18]*alphavpar[32])+0.6846531968814573*(alphavpar[13]*fin[31]+fin[13]*alphavpar[31]+alphavpar[20]*fin[30]+fin[20]*alphavpar[30]+alphavpar[5]*fin[29]+fin[5]*alphavpar[29]+alphavpar[22]*fin[28]+fin[22]*alphavpar[28]+alphavpar[24]*fin[27]+fin[24]*alphavpar[27]+alphavpar[2]*fin[26]+fin[2]*alphavpar[26]+alphavpar[12]*fin[25]+fin[12]*alphavpar[25]+alphavpar[14]*fin[23]+fin[14]*alphavpar[23]+alphavpar[15]*fin[21]+fin[15]*alphavpar[21]+alphavpar[6]*fin[19]+fin[6]*alphavpar[19]+alphavpar[0]*fin[18]+fin[0]*alphavpar[18]+alphavpar[8]*fin[17]+fin[8]*alphavpar[17]+alphavpar[10]*fin[16]+fin[10]*alphavpar[16]+alphavpar[1]*fin[11]+fin[1]*alphavpar[11]+alphavpar[3]*fin[9]+fin[3]*alphavpar[9]+alphavpar[4]*fin[7]+fin[4]*alphavpar[7]); 
-  out[39] += 0.6123724356957944*(alphavpar[23]*fin[47]+fin[23]*alphavpar[47]+alphavpar[15]*fin[46]+fin[15]*alphavpar[46]+alphavpar[28]*fin[45]+fin[28]*alphavpar[45]+alphavpar[29]*fin[44]+fin[29]*alphavpar[44]+alphavpar[9]*fin[43]+fin[9]*alphavpar[43]+alphavpar[24]*fin[42]+fin[24]*alphavpar[42]+alphavpar[25]*fin[41]+fin[25]*alphavpar[41]+alphavpar[31]*fin[40]+fin[31]*alphavpar[40]+alphavpar[4]*fin[39]+fin[4]*alphavpar[39]+alphavpar[17]*fin[38]+fin[17]*alphavpar[38]+alphavpar[18]*fin[37]+fin[18]*alphavpar[37]+alphavpar[30]*fin[36]+fin[30]*alphavpar[36]+alphavpar[10]*fin[35]+fin[10]*alphavpar[35]+alphavpar[11]*fin[34]+fin[11]*alphavpar[34]+alphavpar[26]*fin[33]+fin[26]*alphavpar[33]+alphavpar[19]*fin[32]+fin[19]*alphavpar[32])+0.6846531968814573*(alphavpar[12]*fin[31]+fin[12]*alphavpar[31]+alphavpar[5]*fin[30]+fin[5]*alphavpar[30]+alphavpar[20]*fin[29]+fin[20]*alphavpar[29]+alphavpar[21]*fin[28]+fin[21]*alphavpar[28]+alphavpar[23]*fin[27]+fin[23]*alphavpar[27]+alphavpar[1]*fin[26]+fin[1]*alphavpar[26]+alphavpar[13]*fin[25]+fin[13]*alphavpar[25]+alphavpar[14]*fin[24]+fin[14]*alphavpar[24]+alphavpar[15]*fin[22]+fin[15]*alphavpar[22]+alphavpar[0]*fin[19]+fin[0]*alphavpar[19]+alphavpar[6]*fin[18]+fin[6]*alphavpar[18]+alphavpar[7]*fin[17]+fin[7]*alphavpar[17]+alphavpar[9]*fin[16]+fin[9]*alphavpar[16]+alphavpar[2]*fin[11]+fin[2]*alphavpar[11]+alphavpar[3]*fin[10]+fin[3]*alphavpar[10]+alphavpar[4]*fin[8]+fin[4]*alphavpar[8]); 
-  out[40] += 0.6123724356957944*(alphavpar[19]*fin[47]+fin[19]*alphavpar[47]+alphavpar[26]*fin[46]+fin[26]*alphavpar[46]+alphavpar[11]*fin[45]+fin[11]*alphavpar[45]+alphavpar[10]*fin[44]+fin[10]*alphavpar[44]+alphavpar[30]*fin[43]+fin[30]*alphavpar[43]+alphavpar[18]*fin[42]+fin[18]*alphavpar[42]+alphavpar[17]*fin[41]+fin[17]*alphavpar[41]+alphavpar[4]*fin[40]+fin[4]*alphavpar[40]+alphavpar[31]*fin[39]+fin[31]*alphavpar[39]+alphavpar[25]*fin[38]+fin[25]*alphavpar[38]+alphavpar[24]*fin[37]+fin[24]*alphavpar[37]+alphavpar[9]*fin[36]+fin[9]*alphavpar[36]+alphavpar[29]*fin[35]+fin[29]*alphavpar[35]+alphavpar[28]*fin[34]+fin[28]*alphavpar[34]+alphavpar[15]*fin[33]+fin[15]*alphavpar[33]+alphavpar[23]*fin[32]+fin[23]*alphavpar[32])+0.6846531968814573*(alphavpar[8]*fin[31]+fin[8]*alphavpar[31]+alphavpar[16]*fin[30]+fin[16]*alphavpar[30]+alphavpar[3]*fin[29]+fin[3]*alphavpar[29]+alphavpar[2]*fin[28]+fin[2]*alphavpar[28]+alphavpar[19]*fin[27]+fin[19]*alphavpar[27]+alphavpar[22]*fin[26]+fin[22]*alphavpar[26]+alphavpar[7]*fin[25]+fin[7]*alphavpar[25]+alphavpar[6]*fin[24]+fin[6]*alphavpar[24]+alphavpar[0]*fin[23]+fin[0]*alphavpar[23]+alphavpar[11]*fin[21]+fin[11]*alphavpar[21]+alphavpar[10]*fin[20]+fin[10]*alphavpar[20]+alphavpar[14]*fin[18]+fin[14]*alphavpar[18]+alphavpar[13]*fin[17]+fin[13]*alphavpar[17]+alphavpar[1]*fin[15]+fin[1]*alphavpar[15]+alphavpar[4]*fin[12]+fin[4]*alphavpar[12]+alphavpar[5]*fin[9]+fin[5]*alphavpar[9]); 
-  out[41] += 0.6123724356957944*(alphavpar[18]*fin[47]+fin[18]*alphavpar[47]+alphavpar[11]*fin[46]+fin[11]*alphavpar[46]+alphavpar[26]*fin[45]+fin[26]*alphavpar[45]+alphavpar[9]*fin[44]+fin[9]*alphavpar[44]+alphavpar[29]*fin[43]+fin[29]*alphavpar[43]+alphavpar[19]*fin[42]+fin[19]*alphavpar[42]+alphavpar[4]*fin[41]+fin[4]*alphavpar[41]+alphavpar[17]*fin[40]+fin[17]*alphavpar[40]+alphavpar[25]*fin[39]+fin[25]*alphavpar[39]+alphavpar[31]*fin[38]+fin[31]*alphavpar[38]+alphavpar[23]*fin[37]+fin[23]*alphavpar[37]+alphavpar[10]*fin[36]+fin[10]*alphavpar[36]+alphavpar[30]*fin[35]+fin[30]*alphavpar[35]+alphavpar[15]*fin[34]+fin[15]*alphavpar[34]+alphavpar[28]*fin[33]+fin[28]*alphavpar[33]+alphavpar[24]*fin[32]+fin[24]*alphavpar[32])+0.6846531968814573*(alphavpar[7]*fin[31]+fin[7]*alphavpar[31]+alphavpar[3]*fin[30]+fin[3]*alphavpar[30]+alphavpar[16]*fin[29]+fin[16]*alphavpar[29]+alphavpar[1]*fin[28]+fin[1]*alphavpar[28]+alphavpar[18]*fin[27]+fin[18]*alphavpar[27]+alphavpar[21]*fin[26]+fin[21]*alphavpar[26]+alphavpar[8]*fin[25]+fin[8]*alphavpar[25]+alphavpar[0]*fin[24]+fin[0]*alphavpar[24]+alphavpar[6]*fin[23]+fin[6]*alphavpar[23]+alphavpar[11]*fin[22]+fin[11]*alphavpar[22]+alphavpar[9]*fin[20]+fin[9]*alphavpar[20]+alphavpar[14]*fin[19]+fin[14]*alphavpar[19]+alphavpar[12]*fin[17]+fin[12]*alphavpar[17]+alphavpar[2]*fin[15]+fin[2]*alphavpar[15]+alphavpar[4]*fin[13]+fin[4]*alphavpar[13]+alphavpar[5]*fin[10]+fin[5]*alphavpar[10]); 
-  out[42] += 0.6123724356957944*(alphavpar[17]*fin[47]+fin[17]*alphavpar[47]+alphavpar[10]*fin[46]+fin[10]*alphavpar[46]+alphavpar[9]*fin[45]+fin[9]*alphavpar[45]+alphavpar[26]*fin[44]+fin[26]*alphavpar[44]+alphavpar[28]*fin[43]+fin[28]*alphavpar[43]+alphavpar[4]*fin[42]+fin[4]*alphavpar[42]+alphavpar[19]*fin[41]+fin[19]*alphavpar[41]+alphavpar[18]*fin[40]+fin[18]*alphavpar[40]+alphavpar[24]*fin[39]+fin[24]*alphavpar[39]+alphavpar[23]*fin[38]+fin[23]*alphavpar[38]+alphavpar[31]*fin[37]+fin[31]*alphavpar[37]+alphavpar[11]*fin[36]+fin[11]*alphavpar[36]+alphavpar[15]*fin[35]+fin[15]*alphavpar[35]+alphavpar[30]*fin[34]+fin[30]*alphavpar[34]+alphavpar[29]*fin[33]+fin[29]*alphavpar[33]+alphavpar[25]*fin[32]+fin[25]*alphavpar[32])+0.6846531968814573*(alphavpar[6]*fin[31]+fin[6]*alphavpar[31]+alphavpar[2]*fin[30]+fin[2]*alphavpar[30]+alphavpar[1]*fin[29]+fin[1]*alphavpar[29]+alphavpar[16]*fin[28]+fin[16]*alphavpar[28]+alphavpar[17]*fin[27]+fin[17]*alphavpar[27]+alphavpar[20]*fin[26]+fin[20]*alphavpar[26]+alphavpar[0]*fin[25]+fin[0]*alphavpar[25]+alphavpar[8]*fin[24]+fin[8]*alphavpar[24]+alphavpar[7]*fin[23]+fin[7]*alphavpar[23]+alphavpar[10]*fin[22]+fin[10]*alphavpar[22]+alphavpar[9]*fin[21]+fin[9]*alphavpar[21]+alphavpar[13]*fin[19]+fin[13]*alphavpar[19]+alphavpar[12]*fin[18]+fin[12]*alphavpar[18]+alphavpar[3]*fin[15]+fin[3]*alphavpar[15]+alphavpar[4]*fin[14]+fin[4]*alphavpar[14]+alphavpar[5]*fin[11]+fin[5]*alphavpar[11]); 
-  out[43] += 0.6123724356957944*(alphavpar[15]*fin[47]+fin[15]*alphavpar[47]+alphavpar[23]*fin[46]+fin[23]*alphavpar[46]+alphavpar[24]*fin[45]+fin[24]*alphavpar[45]+alphavpar[25]*fin[44]+fin[25]*alphavpar[44]+alphavpar[4]*fin[43]+fin[4]*alphavpar[43]+alphavpar[28]*fin[42]+fin[28]*alphavpar[42]+alphavpar[29]*fin[41]+fin[29]*alphavpar[41]+alphavpar[30]*fin[40]+fin[30]*alphavpar[40]+alphavpar[9]*fin[39]+fin[9]*alphavpar[39]+alphavpar[10]*fin[38]+fin[10]*alphavpar[38]+alphavpar[11]*fin[37]+fin[11]*alphavpar[37]+alphavpar[31]*fin[36]+fin[31]*alphavpar[36]+alphavpar[17]*fin[35]+fin[17]*alphavpar[35]+alphavpar[18]*fin[34]+fin[18]*alphavpar[34]+alphavpar[19]*fin[33]+fin[19]*alphavpar[33]+alphavpar[26]*fin[32]+fin[26]*alphavpar[32])+0.6846531968814574*(alphavpar[5]*fin[31]+fin[5]*alphavpar[31]+alphavpar[12]*fin[30]+fin[12]*alphavpar[30]+alphavpar[13]*fin[29]+fin[13]*alphavpar[29]+alphavpar[14]*fin[28]+fin[14]*alphavpar[28]+alphavpar[15]*fin[27]+fin[15]*alphavpar[27]+alphavpar[0]*fin[26]+fin[0]*alphavpar[26]+alphavpar[20]*fin[25]+fin[20]*alphavpar[25]+alphavpar[21]*fin[24]+fin[21]*alphavpar[24]+alphavpar[22]*fin[23]+fin[22]*alphavpar[23]+alphavpar[1]*fin[19]+fin[1]*alphavpar[19]+alphavpar[2]*fin[18]+fin[2]*alphavpar[18]+alphavpar[3]*fin[17]+fin[3]*alphavpar[17]+alphavpar[4]*fin[16]+fin[4]*alphavpar[16]+alphavpar[6]*fin[11]+fin[6]*alphavpar[11]+alphavpar[7]*fin[10]+fin[7]*alphavpar[10]+alphavpar[8]*fin[9]+fin[8]*alphavpar[9]); 
-  out[44] += 0.6123724356957944*(alphavpar[11]*fin[47]+fin[11]*alphavpar[47]+alphavpar[18]*fin[46]+fin[18]*alphavpar[46]+alphavpar[19]*fin[45]+fin[19]*alphavpar[45]+alphavpar[4]*fin[44]+fin[4]*alphavpar[44]+alphavpar[25]*fin[43]+fin[25]*alphavpar[43]+alphavpar[26]*fin[42]+fin[26]*alphavpar[42]+alphavpar[9]*fin[41]+fin[9]*alphavpar[41]+alphavpar[10]*fin[40]+fin[10]*alphavpar[40]+alphavpar[29]*fin[39]+fin[29]*alphavpar[39]+alphavpar[30]*fin[38]+fin[30]*alphavpar[38]+alphavpar[15]*fin[37]+fin[15]*alphavpar[37]+alphavpar[17]*fin[36]+fin[17]*alphavpar[36]+alphavpar[31]*fin[35]+fin[31]*alphavpar[35]+alphavpar[23]*fin[34]+fin[23]*alphavpar[34]+alphavpar[24]*fin[33]+fin[24]*alphavpar[33]+alphavpar[28]*fin[32]+fin[28]*alphavpar[32])+0.6846531968814574*(alphavpar[3]*fin[31]+fin[3]*alphavpar[31]+alphavpar[7]*fin[30]+fin[7]*alphavpar[30]+alphavpar[8]*fin[29]+fin[8]*alphavpar[29]+alphavpar[0]*fin[28]+fin[0]*alphavpar[28]+alphavpar[11]*fin[27]+fin[11]*alphavpar[27]+alphavpar[14]*fin[26]+fin[14]*alphavpar[26]+alphavpar[16]*fin[25]+fin[16]*alphavpar[25]+alphavpar[1]*fin[24]+fin[1]*alphavpar[24]+alphavpar[2]*fin[23]+fin[2]*alphavpar[23]+alphavpar[18]*fin[22]+fin[18]*alphavpar[22]+alphavpar[19]*fin[21]+fin[19]*alphavpar[21]+alphavpar[4]*fin[20]+fin[4]*alphavpar[20]+alphavpar[5]*fin[17]+fin[5]*alphavpar[17]+alphavpar[6]*fin[15]+fin[6]*alphavpar[15]+alphavpar[9]*fin[13]+fin[9]*alphavpar[13]+alphavpar[10]*fin[12]+fin[10]*alphavpar[12]); 
-  out[45] += 0.6123724356957944*(alphavpar[10]*fin[47]+fin[10]*alphavpar[47]+alphavpar[17]*fin[46]+fin[17]*alphavpar[46]+alphavpar[4]*fin[45]+fin[4]*alphavpar[45]+alphavpar[19]*fin[44]+fin[19]*alphavpar[44]+alphavpar[24]*fin[43]+fin[24]*alphavpar[43]+alphavpar[9]*fin[42]+fin[9]*alphavpar[42]+alphavpar[26]*fin[41]+fin[26]*alphavpar[41]+alphavpar[11]*fin[40]+fin[11]*alphavpar[40]+alphavpar[28]*fin[39]+fin[28]*alphavpar[39]+alphavpar[15]*fin[38]+fin[15]*alphavpar[38]+alphavpar[30]*fin[37]+fin[30]*alphavpar[37]+alphavpar[18]*fin[36]+fin[18]*alphavpar[36]+alphavpar[23]*fin[35]+fin[23]*alphavpar[35]+alphavpar[31]*fin[34]+fin[31]*alphavpar[34]+alphavpar[25]*fin[33]+fin[25]*alphavpar[33]+alphavpar[29]*fin[32]+fin[29]*alphavpar[32])+0.6846531968814574*(alphavpar[2]*fin[31]+fin[2]*alphavpar[31]+alphavpar[6]*fin[30]+fin[6]*alphavpar[30]+alphavpar[0]*fin[29]+fin[0]*alphavpar[29]+alphavpar[8]*fin[28]+fin[8]*alphavpar[28]+alphavpar[10]*fin[27]+fin[10]*alphavpar[27]+alphavpar[13]*fin[26]+fin[13]*alphavpar[26]+alphavpar[1]*fin[25]+fin[1]*alphavpar[25]+alphavpar[16]*fin[24]+fin[16]*alphavpar[24]+alphavpar[3]*fin[23]+fin[3]*alphavpar[23]+alphavpar[17]*fin[22]+fin[17]*alphavpar[22]+alphavpar[4]*fin[21]+fin[4]*alphavpar[21]+alphavpar[19]*fin[20]+fin[19]*alphavpar[20]+alphavpar[5]*fin[18]+fin[5]*alphavpar[18]+alphavpar[7]*fin[15]+fin[7]*alphavpar[15]+alphavpar[9]*fin[14]+fin[9]*alphavpar[14]+alphavpar[11]*fin[12]+fin[11]*alphavpar[12]); 
-  out[46] += 0.6123724356957944*(alphavpar[9]*fin[47]+fin[9]*alphavpar[47]+alphavpar[4]*fin[46]+fin[4]*alphavpar[46]+alphavpar[17]*fin[45]+fin[17]*alphavpar[45]+alphavpar[18]*fin[44]+fin[18]*alphavpar[44]+alphavpar[23]*fin[43]+fin[23]*alphavpar[43]+alphavpar[10]*fin[42]+fin[10]*alphavpar[42]+alphavpar[11]*fin[41]+fin[11]*alphavpar[41]+alphavpar[26]*fin[40]+fin[26]*alphavpar[40]+alphavpar[15]*fin[39]+fin[15]*alphavpar[39]+alphavpar[28]*fin[38]+fin[28]*alphavpar[38]+alphavpar[29]*fin[37]+fin[29]*alphavpar[37]+alphavpar[19]*fin[36]+fin[19]*alphavpar[36]+alphavpar[24]*fin[35]+fin[24]*alphavpar[35]+alphavpar[25]*fin[34]+fin[25]*alphavpar[34]+alphavpar[31]*fin[33]+fin[31]*alphavpar[33]+alphavpar[30]*fin[32]+fin[30]*alphavpar[32])+0.6846531968814574*(alphavpar[1]*fin[31]+fin[1]*alphavpar[31]+alphavpar[0]*fin[30]+fin[0]*alphavpar[30]+alphavpar[6]*fin[29]+fin[6]*alphavpar[29]+alphavpar[7]*fin[28]+fin[7]*alphavpar[28]+alphavpar[9]*fin[27]+fin[9]*alphavpar[27]+alphavpar[12]*fin[26]+fin[12]*alphavpar[26]+alphavpar[2]*fin[25]+fin[2]*alphavpar[25]+alphavpar[3]*fin[24]+fin[3]*alphavpar[24]+alphavpar[16]*fin[23]+fin[16]*alphavpar[23]+alphavpar[4]*fin[22]+fin[4]*alphavpar[22]+alphavpar[17]*fin[21]+fin[17]*alphavpar[21]+alphavpar[18]*fin[20]+fin[18]*alphavpar[20]+alphavpar[5]*fin[19]+fin[5]*alphavpar[19]+alphavpar[8]*fin[15]+fin[8]*alphavpar[15]+alphavpar[10]*fin[14]+fin[10]*alphavpar[14]+alphavpar[11]*fin[13]+fin[11]*alphavpar[13]); 
-  out[47] += 0.6123724356957944*(alphavpar[4]*fin[47]+fin[4]*alphavpar[47]+alphavpar[9]*fin[46]+fin[9]*alphavpar[46]+alphavpar[10]*fin[45]+fin[10]*alphavpar[45]+alphavpar[11]*fin[44]+fin[11]*alphavpar[44]+alphavpar[15]*fin[43]+fin[15]*alphavpar[43]+alphavpar[17]*fin[42]+fin[17]*alphavpar[42]+alphavpar[18]*fin[41]+fin[18]*alphavpar[41]+alphavpar[19]*fin[40]+fin[19]*alphavpar[40]+alphavpar[23]*fin[39]+fin[23]*alphavpar[39]+alphavpar[24]*fin[38]+fin[24]*alphavpar[38]+alphavpar[25]*fin[37]+fin[25]*alphavpar[37]+alphavpar[26]*fin[36]+fin[26]*alphavpar[36]+alphavpar[28]*fin[35]+fin[28]*alphavpar[35]+alphavpar[29]*fin[34]+fin[29]*alphavpar[34]+alphavpar[30]*fin[33]+fin[30]*alphavpar[33]+alphavpar[31]*fin[32]+fin[31]*alphavpar[32])+0.6846531968814573*(alphavpar[0]*fin[31]+fin[0]*alphavpar[31]+alphavpar[1]*fin[30]+fin[1]*alphavpar[30]+alphavpar[2]*fin[29]+fin[2]*alphavpar[29]+alphavpar[3]*fin[28]+fin[3]*alphavpar[28]+alphavpar[4]*fin[27]+fin[4]*alphavpar[27]+alphavpar[5]*fin[26]+fin[5]*alphavpar[26]+alphavpar[6]*fin[25]+fin[6]*alphavpar[25]+alphavpar[7]*fin[24]+fin[7]*alphavpar[24]+alphavpar[8]*fin[23]+fin[8]*alphavpar[23]+alphavpar[9]*fin[22]+fin[9]*alphavpar[22]+alphavpar[10]*fin[21]+fin[10]*alphavpar[21]+alphavpar[11]*fin[20]+fin[11]*alphavpar[20]+alphavpar[12]*fin[19]+fin[12]*alphavpar[19]+alphavpar[13]*fin[18]+fin[13]*alphavpar[18]+alphavpar[14]*fin[17]+fin[14]*alphavpar[17]+alphavpar[15]*fin[16]+fin[15]*alphavpar[16]); 
+  out[4] += 0.3061862178478971*(alphavpar[16]*fin[16]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[9] += 0.3061862178478971*(alphavpar[8]*fin[16]+fin[8]*alphavpar[16]+alphavpar[3]*fin[7]+fin[3]*alphavpar[7]+alphavpar[2]*fin[6]+fin[2]*alphavpar[6]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[10] += 0.3061862178478971*(alphavpar[7]*fin[16]+fin[7]*alphavpar[16]+alphavpar[3]*fin[8]+fin[3]*alphavpar[8]+alphavpar[1]*fin[6]+fin[1]*alphavpar[6]+alphavpar[0]*fin[2]+fin[0]*alphavpar[2]); 
+  out[11] += 0.3061862178478971*(alphavpar[6]*fin[16]+fin[6]*alphavpar[16]+alphavpar[2]*fin[8]+fin[2]*alphavpar[8]+alphavpar[1]*fin[7]+fin[1]*alphavpar[7]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[15] += 0.3061862178478971*(alphavpar[16]*fin[27]+alphavpar[8]*fin[22]+alphavpar[7]*fin[21]+alphavpar[6]*fin[20]+alphavpar[3]*fin[14]+alphavpar[2]*fin[13]+alphavpar[1]*fin[12]+alphavpar[0]*fin[5]); 
+  out[17] += 0.3061862178478971*(alphavpar[3]*fin[16]+fin[3]*alphavpar[16]+alphavpar[7]*fin[8]+fin[7]*alphavpar[8]+alphavpar[0]*fin[6]+fin[0]*alphavpar[6]+alphavpar[1]*fin[2]+fin[1]*alphavpar[2]); 
+  out[18] += 0.3061862178478971*(alphavpar[2]*fin[16]+fin[2]*alphavpar[16]+alphavpar[6]*fin[8]+fin[6]*alphavpar[8]+alphavpar[0]*fin[7]+fin[0]*alphavpar[7]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[19] += 0.3061862178478971*(alphavpar[1]*fin[16]+fin[1]*alphavpar[16]+alphavpar[0]*fin[8]+fin[0]*alphavpar[8]+alphavpar[6]*fin[7]+fin[6]*alphavpar[7]+alphavpar[2]*fin[3]+fin[2]*alphavpar[3]); 
+  out[23] += 0.3061862178478971*(alphavpar[8]*fin[27]+alphavpar[16]*fin[22]+alphavpar[3]*fin[21]+alphavpar[2]*fin[20]+alphavpar[7]*fin[14]+alphavpar[6]*fin[13]+alphavpar[0]*fin[12]+alphavpar[1]*fin[5]); 
+  out[24] += 0.3061862178478971*(alphavpar[7]*fin[27]+alphavpar[3]*fin[22]+alphavpar[16]*fin[21]+alphavpar[1]*fin[20]+alphavpar[8]*fin[14]+alphavpar[0]*fin[13]+alphavpar[6]*fin[12]+alphavpar[2]*fin[5]); 
+  out[25] += 0.3061862178478971*(alphavpar[6]*fin[27]+alphavpar[2]*fin[22]+alphavpar[1]*fin[21]+alphavpar[16]*fin[20]+alphavpar[0]*fin[14]+alphavpar[8]*fin[13]+alphavpar[7]*fin[12]+alphavpar[3]*fin[5]); 
+  out[26] += 0.3061862178478971*(alphavpar[0]*fin[16]+fin[0]*alphavpar[16]+alphavpar[1]*fin[8]+fin[1]*alphavpar[8]+alphavpar[2]*fin[7]+fin[2]*alphavpar[7]+alphavpar[3]*fin[6]+fin[3]*alphavpar[6]); 
+  out[28] += 0.3061862178478971*(alphavpar[3]*fin[27]+alphavpar[7]*fin[22]+alphavpar[8]*fin[21]+alphavpar[0]*fin[20]+fin[14]*alphavpar[16]+alphavpar[1]*fin[13]+alphavpar[2]*fin[12]+fin[5]*alphavpar[6]); 
+  out[29] += 0.3061862178478971*(alphavpar[2]*fin[27]+alphavpar[6]*fin[22]+alphavpar[0]*fin[21]+alphavpar[8]*fin[20]+fin[13]*alphavpar[16]+alphavpar[1]*fin[14]+alphavpar[3]*fin[12]+fin[5]*alphavpar[7]); 
+  out[30] += 0.3061862178478971*(alphavpar[1]*fin[27]+alphavpar[0]*fin[22]+alphavpar[6]*fin[21]+alphavpar[7]*fin[20]+fin[12]*alphavpar[16]+alphavpar[2]*fin[14]+alphavpar[3]*fin[13]+fin[5]*alphavpar[8]); 
+  out[31] += 0.3061862178478971*(alphavpar[0]*fin[27]+alphavpar[1]*fin[22]+alphavpar[2]*fin[21]+alphavpar[3]*fin[20]+fin[5]*alphavpar[16]+alphavpar[6]*fin[14]+alphavpar[7]*fin[13]+alphavpar[8]*fin[12]); 
+  out[32] += 0.6846531968814573*(alphavpar[16]*fin[26]+alphavpar[8]*fin[19]+alphavpar[7]*fin[18]+alphavpar[6]*fin[17]+alphavpar[3]*fin[11]+alphavpar[2]*fin[10]+alphavpar[1]*fin[9]+alphavpar[0]*fin[4]); 
+  out[33] += 0.6846531968814574*(alphavpar[8]*fin[26]+alphavpar[16]*fin[19]+alphavpar[3]*fin[18]+alphavpar[2]*fin[17]+alphavpar[7]*fin[11]+alphavpar[6]*fin[10]+alphavpar[0]*fin[9]+alphavpar[1]*fin[4]); 
+  out[34] += 0.6846531968814574*(alphavpar[7]*fin[26]+alphavpar[3]*fin[19]+alphavpar[16]*fin[18]+alphavpar[1]*fin[17]+alphavpar[8]*fin[11]+alphavpar[0]*fin[10]+alphavpar[6]*fin[9]+alphavpar[2]*fin[4]); 
+  out[35] += 0.6846531968814574*(alphavpar[6]*fin[26]+alphavpar[2]*fin[19]+alphavpar[1]*fin[18]+alphavpar[16]*fin[17]+alphavpar[0]*fin[11]+alphavpar[8]*fin[10]+alphavpar[7]*fin[9]+alphavpar[3]*fin[4]); 
+  out[36] += 0.6846531968814574*(alphavpar[16]*fin[31]+alphavpar[8]*fin[30]+alphavpar[7]*fin[29]+alphavpar[6]*fin[28]+alphavpar[3]*fin[25]+alphavpar[2]*fin[24]+alphavpar[1]*fin[23]+alphavpar[0]*fin[15]); 
+  out[37] += 0.6846531968814573*(alphavpar[3]*fin[26]+alphavpar[7]*fin[19]+alphavpar[8]*fin[18]+alphavpar[0]*fin[17]+fin[11]*alphavpar[16]+alphavpar[1]*fin[10]+alphavpar[2]*fin[9]+fin[4]*alphavpar[6]); 
+  out[38] += 0.6846531968814573*(alphavpar[2]*fin[26]+alphavpar[6]*fin[19]+alphavpar[0]*fin[18]+alphavpar[8]*fin[17]+fin[10]*alphavpar[16]+alphavpar[1]*fin[11]+alphavpar[3]*fin[9]+fin[4]*alphavpar[7]); 
+  out[39] += 0.6846531968814573*(alphavpar[1]*fin[26]+alphavpar[0]*fin[19]+alphavpar[6]*fin[18]+alphavpar[7]*fin[17]+fin[9]*alphavpar[16]+alphavpar[2]*fin[11]+alphavpar[3]*fin[10]+fin[4]*alphavpar[8]); 
+  out[40] += 0.6846531968814573*(alphavpar[8]*fin[31]+alphavpar[16]*fin[30]+alphavpar[3]*fin[29]+alphavpar[2]*fin[28]+alphavpar[7]*fin[25]+alphavpar[6]*fin[24]+alphavpar[0]*fin[23]+alphavpar[1]*fin[15]); 
+  out[41] += 0.6846531968814573*(alphavpar[7]*fin[31]+alphavpar[3]*fin[30]+alphavpar[16]*fin[29]+alphavpar[1]*fin[28]+alphavpar[8]*fin[25]+alphavpar[0]*fin[24]+alphavpar[6]*fin[23]+alphavpar[2]*fin[15]); 
+  out[42] += 0.6846531968814573*(alphavpar[6]*fin[31]+alphavpar[2]*fin[30]+alphavpar[1]*fin[29]+alphavpar[16]*fin[28]+alphavpar[0]*fin[25]+alphavpar[8]*fin[24]+alphavpar[7]*fin[23]+alphavpar[3]*fin[15]); 
+  out[43] += 0.6846531968814574*(alphavpar[0]*fin[26]+alphavpar[1]*fin[19]+alphavpar[2]*fin[18]+alphavpar[3]*fin[17]+fin[4]*alphavpar[16]+alphavpar[6]*fin[11]+alphavpar[7]*fin[10]+alphavpar[8]*fin[9]); 
+  out[44] += 0.6846531968814574*(alphavpar[3]*fin[31]+alphavpar[7]*fin[30]+alphavpar[8]*fin[29]+alphavpar[0]*fin[28]+alphavpar[16]*fin[25]+alphavpar[1]*fin[24]+alphavpar[2]*fin[23]+alphavpar[6]*fin[15]); 
+  out[45] += 0.6846531968814574*(alphavpar[2]*fin[31]+alphavpar[6]*fin[30]+alphavpar[0]*fin[29]+alphavpar[8]*fin[28]+alphavpar[1]*fin[25]+alphavpar[16]*fin[24]+alphavpar[3]*fin[23]+alphavpar[7]*fin[15]); 
+  out[46] += 0.6846531968814574*(alphavpar[1]*fin[31]+alphavpar[0]*fin[30]+alphavpar[6]*fin[29]+alphavpar[7]*fin[28]+alphavpar[2]*fin[25]+alphavpar[3]*fin[24]+alphavpar[16]*fin[23]+alphavpar[8]*fin[15]); 
+  out[47] += 0.6846531968814573*(alphavpar[0]*fin[31]+alphavpar[1]*fin[30]+alphavpar[2]*fin[29]+alphavpar[3]*fin[28]+alphavpar[6]*fin[25]+alphavpar[7]*fin[24]+alphavpar[8]*fin[23]+fin[15]*alphavpar[16]); 
 
   return 0.; 
 } 

From a37c0756b8ece2273b306b8ee8bc86b285c39036 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 7 Nov 2025 11:39:29 -0500
Subject: [PATCH 040/181] =?UTF-8?q?the=20d3d=20rt=20gk=202x2v=20test=20is?=
 =?UTF-8?q?=20running=20with=20the=20EM=20activated=20now=20=F0=9F=A5=81?=
 =?UTF-8?q?=20It=20does=20not=20change=20anything,=20takes=20111=20steps?=
 =?UTF-8?q?=20to=20complete=20as=20in=20the=20ES=20limit.=20The=20code=20i?=
 =?UTF-8?q?s=20ready=20to=20have=20real=20EM=20testcase=20now=20?=
 =?UTF-8?q?=F0=9F=99=82=E2=80=8D=E2=86=95=EF=B8=8F?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 ..._gyrokinetic_add_apardot_vol_1x1v_ser_p1.c |  2 +-
 ..._gyrokinetic_add_apardot_vol_1x2v_ser_p1.c |  6 +--
 ..._gyrokinetic_add_apardot_vol_2x2v_ser_p1.c | 10 ++---
 ..._gyrokinetic_add_apardot_vol_3x2v_ser_p1.c | 18 ++++-----
 .../gkyl_dg_gyrokinetic_kernels.h             | 40 ++++---------------
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   | 20 ++++++++--
 6 files changed, 42 insertions(+), 54 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
index 3bb8a2ec69..ab4e2f0517 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double q_, const double m_, const double *apardot,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double *vmap, const double q_, const double m_, const double *apardot,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // q_,m_: species charge and mass.
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
index 7185f94cc0..15f1dcc074 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, const double m_, const double *apardot,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double *vmap, const double q_, const double m_, const double *apardot,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // q_,m_: species charge and mass.
@@ -8,8 +8,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[12] = {0.}; 
-  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
+  alphavpar[0] = -((1.6329931618554527*apardot[0]*q_)/(vmap[1]*m_)); 
+  alphavpar[1] = -((1.6329931618554527*apardot[1]*q_)/(vmap[1]*m_)); 
 
 
   out[2] += 0.6123724356957944*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
index 03e7f95feb..3ea2ccf2e2 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, const double m_, const double *apardot,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double *vmap, const double q_, const double m_, const double *apardot,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // q_,m_: species charge and mass.
@@ -8,10 +8,10 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((2.0*apardot[2]*q_)/m_); 
-  alphavpar[5] = -((2.0*apardot[3]*q_)/m_); 
+  alphavpar[0] = -((1.6329931618554527*apardot[0]*q_)/(vmap[1]*m_)); 
+  alphavpar[1] = -((1.6329931618554527*apardot[1]*q_)/(vmap[1]*m_)); 
+  alphavpar[2] = -((1.6329931618554527*apardot[2]*q_)/(vmap[1]*m_)); 
+  alphavpar[5] = -((1.6329931618554527*apardot[3]*q_)/(vmap[1]*m_)); 
 
 
   out[3] += 0.4330127018922193*(alphavpar[5]*fin[5]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
index ba187efefa..9f55bf3a8e 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, const double m_, const double *apardot,
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double *vmap, const double q_, const double m_, const double *apardot,
     const double *fin, double* GKYL_RESTRICT out) 
 { 
   // q_,m_: species charge and mass.
@@ -8,14 +8,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, co
   // out: output increment.
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = -((2.0*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((2.0*apardot[1]*q_)/m_); 
-  alphavpar[2] = -((2.0*apardot[2]*q_)/m_); 
-  alphavpar[3] = -((2.0*apardot[3]*q_)/m_); 
-  alphavpar[6] = -((2.0*apardot[4]*q_)/m_); 
-  alphavpar[7] = -((2.0*apardot[5]*q_)/m_); 
-  alphavpar[8] = -((2.0*apardot[6]*q_)/m_); 
-  alphavpar[16] = -((2.0*apardot[7]*q_)/m_); 
+  alphavpar[0] = -((1.6329931618554527*apardot[0]*q_)/(vmap[1]*m_)); 
+  alphavpar[1] = -((1.6329931618554527*apardot[1]*q_)/(vmap[1]*m_)); 
+  alphavpar[2] = -((1.6329931618554527*apardot[2]*q_)/(vmap[1]*m_)); 
+  alphavpar[3] = -((1.6329931618554527*apardot[3]*q_)/(vmap[1]*m_)); 
+  alphavpar[6] = -((1.6329931618554527*apardot[4]*q_)/(vmap[1]*m_)); 
+  alphavpar[7] = -((1.6329931618554527*apardot[5]*q_)/(vmap[1]*m_)); 
+  alphavpar[8] = -((1.6329931618554527*apardot[6]*q_)/(vmap[1]*m_)); 
+  alphavpar[16] = -((1.6329931618554527*apardot[7]*q_)/(vmap[1]*m_)); 
 
 
   out[4] += 0.3061862178478971*(alphavpar[16]*fin[16]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
index 3a54018e34..e8225e1740 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
+++ b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
@@ -233,56 +233,32 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
             const double *bmag, const double *jacobtot_inv,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
-
-GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p2(const double *w, const double *dxv, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
-            const double *b_i, const double *phi, const double *apar,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p2(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double *vmap, const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out); 
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
             const double *bmag, const double *jacobtot_inv,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
-
-GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p2(const double *w, const double *dxv, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
-            const double *b_i, const double *phi, const double *apar,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p2(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double *vmap, const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out); 
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
             const double *bmag, const double *jacobtot_inv,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
-
-GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p2(const double *w, const double *dxv, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
-            const double *b_i, const double *phi, const double *apar,
-            const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p2(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double *vmap, const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out); 
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
             const double *bmag, const double *jacobtot_inv,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
-GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double q_, const double m_,
-            const double *apardot, const double *fin, double* GKYL_RESTRICT out) ; 
+GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double *vmap, const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out); 
 
 
 EXTERN_C_END
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 40f820463c..0f6497ee7e 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -342,9 +342,12 @@ kernel_dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn,
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   return dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
@@ -360,9 +363,12 @@ kernel_dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn,
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   return dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
@@ -378,9 +384,12 @@ kernel_dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn,
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   return dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
@@ -396,9 +405,12 @@ kernel_dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn,
   if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
     return 0.;
   }
-  
+  int vel_idx[2];
+  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
   long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
+  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   return dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(
+    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);

From 99e785f96ee4c25461c76a4f793ab0828b80b8d0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 7 Nov 2025 14:36:30 -0500
Subject: [PATCH 041/181] always init m1 moment because we want to use it even
 if we do not set gk_field_id to be EM.

---
 gyrokinetic/apps/gk_species.c | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 9852dadecf..73a45f8738 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1597,10 +1597,8 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   gks->anom_diff = (struct gk_anomalous_diff) { };
   gk_species_anomalous_diff_init(app, gks, &gks->anom_diff);
 
-  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL) {
-    // To compute current density for Ampere's law and current dot for Ohm's law.
-    gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
-  }
+  // To compute current density for Ampere's law and current dot for Ohm's law.
+  gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
 
   // Allocate data for diagnostic moments.
   int ndm = gks->info.num_diag_moments;
@@ -2001,8 +1999,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
 
   gkyl_array_release(s->gyro_apar);
   gkyl_array_release(s->gyro_apardot);
-  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL)
-    gk_species_moment_release(app, &s->m1);
+  gk_species_moment_release(app, &s->m1);
 
   s->release_func(app, s);
 }

From a6e7cfbbac19d9d021e6764372c72d0c71ac880f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 8 Nov 2025 16:14:49 -0500
Subject: [PATCH 042/181] fix the output of Apar and Apardot, we still have to
 figure how to handle optimally the flag system and the interaction between
 the gk_collisionless_id and the gk_field_id...

---
 core/zero/gkyl_eqn_type.h      |  7 ++++---
 gyrokinetic/apps/gyrokinetic.c | 23 ++++++++++++-----------
 2 files changed, 16 insertions(+), 14 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 34ba8a6594..a3f0702158 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -37,9 +37,10 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD = 0, // This is default.
   GKYL_GK_FIELD_BOLTZMANN = 1, // GK Boltzmann, isothermal electrons, phi = phi_sheath + (T_e/e)*ln(n_i/n_is).
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
-  GKYL_GK_FIELD_IWL = 3, // Inner-wall limited ES.
-  GKYL_GK_FIELD_EM = 4, // To force electromagnetic field solve (even if no species is EM).
-  GKYL_GK_FIELD_EM_IWL = 5, // As above but for IWL.
+  GKYL_GK_FIELD_IWL = 3, // Inner-wall limited.
+  GKYL_GK_FIELD_ES = 4, // Electrostatic field.
+  GKYL_GK_FIELD_EM = 5, // To force electromagnetic field solve (even if no species is EM).
+  GKYL_GK_FIELD_EM_IWL = 6, // As above but for IWL.
 };
 
 // Identifiers for specific field object types.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 33c75b328a..63f8d3ecac 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1153,23 +1153,24 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
-  if (app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL) {
-    const char *fmt = "%s-apar_%d.gkyl";
-    int sz = gkyl_calc_strlen(fmt, app->name, frame);
-    char fileNm[sz+1]; // ensures no buffer overflow
-    snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+  if (!(app->field->info.gkfield_id == GKYL_GK_FIELD_ES)) {
+    const char *fmt1 = "%s-apar_%d.gkyl";
+    int sz = gkyl_calc_strlen(fmt1, app->name, frame);
+    char fileNm1[sz+1]; // ensures no buffer overflow
+    snprintf(fileNm1, sizeof fileNm1, fmt1, app->name, frame);
     if (app->use_gpu) {
       gkyl_array_copy(app->field->apar_host, app->field->apar);
     }
-    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm);
+    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm1);
 
-    fmt = "%s-apardot_%d.gkyl";
-    sz = gkyl_calc_strlen(fmt, app->name, frame);
-    snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
+    const char *fmt2 = "%s-apardot_%d.gkyl";
+    sz = gkyl_calc_strlen(fmt2, app->name, frame);
+    char fileNm2[sz+1]; // ensures no buffer overflow
+    snprintf(fileNm2, sizeof fileNm2, fmt2, app->name, frame);
     if (app->use_gpu) {
       gkyl_array_copy(app->field->apardot_host, app->field->apardot);
     }
-    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm);
+    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm2);
   }
 
     gk_array_meta_release(mt);
@@ -1211,7 +1212,7 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
-    bool write_em = app->field->info.gkfield_id == GKYL_GK_FIELD_EM || app->field->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
+    bool write_em = !(app->field->info.gkfield_id == GKYL_GK_FIELD_ES);
     if (rank == 0) {
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).

From a644c6f62bd5154f866afa59437a1464a6dcb0af Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 10 Nov 2025 16:43:17 -0500
Subject: [PATCH 043/181] Rstore the GKYL_GK_FIELD_ES_IWL enum because
 GKYL_GK_FIELD_ES is not sufficient as we ES option is merged with IWL...

---
 core/zero/gkyl_eqn_type.h      | 5 +++--
 gyrokinetic/apps/gyrokinetic.c | 4 ++--
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index a3f0702158..18225fc117 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -39,8 +39,9 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD_ADIABATIC = 2, // GK field with an adiabatic species.
   GKYL_GK_FIELD_IWL = 3, // Inner-wall limited.
   GKYL_GK_FIELD_ES = 4, // Electrostatic field.
-  GKYL_GK_FIELD_EM = 5, // To force electromagnetic field solve (even if no species is EM).
-  GKYL_GK_FIELD_EM_IWL = 6, // As above but for IWL.
+  GKYL_GK_FIELD_ES_IWL = 5, // Electromagnetic field with inner-wall limited BCs.
+  GKYL_GK_FIELD_EM = 6, // To force electromagnetic field solve (even if no species is EM).
+  GKYL_GK_FIELD_EM_IWL = 7, // As above but for IWL.
 };
 
 // Identifiers for specific field object types.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 63f8d3ecac..6a862ecbd7 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1153,7 +1153,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
-  if (!(app->field->info.gkfield_id == GKYL_GK_FIELD_ES)) {
+  if (!(app->field->info.gkfield_id == GKYL_GK_FIELD_ES || app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
     const char *fmt1 = "%s-apar_%d.gkyl";
     int sz = gkyl_calc_strlen(fmt1, app->name, frame);
     char fileNm1[sz+1]; // ensures no buffer overflow
@@ -1212,7 +1212,7 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
-    bool write_em = !(app->field->info.gkfield_id == GKYL_GK_FIELD_ES);
+    bool write_em = !(app->field->info.gkfield_id == GKYL_GK_FIELD_ES || app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL);
     if (rank == 0) {
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).

From e1009f96c880f88ec30b28a63158e94085da8ac8 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 10 Nov 2025 17:01:35 -0500
Subject: [PATCH 044/181] Include the new GKYL_GK_FIELD_ES_IWL to the logic in
 field.c and update the regression test accordingly

---
 gyrokinetic/apps/gk_field.c                     | 17 ++++++++++++-----
 gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c        |  2 +-
 gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c        |  2 +-
 gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c        |  2 +-
 .../creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c   |  2 +-
 .../creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c   |  2 +-
 6 files changed, 17 insertions(+), 10 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 1285dd418d..f6b064d666 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -271,6 +271,8 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->info = gk->field;
 
   f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD;
+
+  bool is_iwl = f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL;
   
   f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM || f->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
@@ -468,7 +470,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
   // Potential smoothing (in z) updater
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+  if (is_iwl) {
     enum gkyl_fem_parproj_bc_type fem_parproj_bc_core, fem_parproj_bc_sol;
     if (app->cdim == 2) {
       fem_parproj_bc_core = GKYL_FEM_PARPROJ_PERIODIC;
@@ -750,7 +752,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
   f->enforce_parallel_bc = gk_field_enforce_parallel_bc_disabled;
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+  if (is_iwl) {
     gk_field_add_TSBC_and_SSFG_updaters(app,f);
     f->enforce_parallel_bc = gk_field_enforce_parallel_bc_enabled;
   }
@@ -906,7 +908,11 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
       // Gather charge density into global array.
       // Smooth the charge density. Input is rho_c_global_dg, globally smoothed in z,
       // and then output should be in *local* phi_smooth.
-      if (field->gkfield_id == GKYL_GK_FIELD_IWL || field->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+      if (
+        field->gkfield_id == GKYL_GK_FIELD_IWL ||
+        field->gkfield_id == GKYL_GK_FIELD_ES_IWL ||
+        field->gkfield_id == GKYL_GK_FIELD_EM_IWL
+      ) {
         gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->rho_c, field->rho_c_global_dg);
         gkyl_fem_parproj_set_rhs(field->fem_parproj_core, field->rho_c_global_dg, field->rho_c_global_dg);
         gkyl_fem_parproj_solve(field->fem_parproj_core, field->rho_c_global_smooth);
@@ -1142,7 +1148,8 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     }
   }
 
-  if (app->cdim > 1 && (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL)) {
+  bool is_iwl = (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL);
+  if (app->cdim > 1 && is_iwl) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
   } else {
@@ -1150,7 +1157,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   }
 
   // Release TS BS and SSFG updater
-  if (f->gkfield_id == GKYL_GK_FIELD_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
+  if (is_iwl) {
     if(app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_T_LU_lo);
     }
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
index 369e9e2e26..c0dd850001 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
@@ -740,7 +740,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_IWL,
+    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
index 6d3ac6c818..d53d8415e3 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
@@ -825,7 +825,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_IWL,
+    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
index 6358a82675..0debccf7a5 100644
--- a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
@@ -424,7 +424,7 @@ int main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_IWL,
+    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index f8e325cfb1..46a66d7af1 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -748,7 +748,7 @@ main(int argc, char **argv)
 
   // Field.
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_IWL,
+    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 7912cb0324..6e912d8602 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -781,7 +781,7 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_IWL,
+    .gkfield_id = GKYL_GK_FIELD_ES_IWL,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },

From 1fd7b560a03a7f0861d15707194f4feb8001f747 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 11 Nov 2025 09:07:21 -0500
Subject: [PATCH 045/181] add a new regression test for alfven wave that tries
 to imitate the g2 lua test 1x1v. It is however 1x2v and nonlinear so we have
 to figure out still if the results are consistent.

---
 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c | 351 +++++++++++++++++++++
 1 file changed, 351 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
new file mode 100644
index 0000000000..2856df023f
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
@@ -0,0 +1,351 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  double mu0;
+
+  // Geometry and magnetic field.
+  double R; // Major radius of the simulation box [m].
+  double a; // Minor radius at outboard midplane [m].
+  double r; // Minor radius of the simulation box [m].
+  double B; // Magnetic field magnitude in the simulation box [T].
+  double z_min;  double z_max;
+
+  double kperp;  // Perpendicular wavenumber.
+
+  // Plasma parameters.
+  double me;  double qe;
+  double mi;  double qi;
+  double n0;  double Te0;  double Ti0; 
+
+  // Grid parameters.
+  double kz_min;
+  int Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc;  double mu_max_elc;
+  double vpar_max_ion;  double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Ion initial conditions.
+void density_init_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->n0;
+}
+void upar_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Ti0;
+}
+
+// Electron initial conditions.
+void density_init_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double z = xn[0];
+  fout[0] = app->n0 * (1 + 1e-6*cos(app->kz_min*z));
+}
+void upar_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Te0;
+}
+
+// Slab magnetic equilibrium.
+static inline void
+mapc2p(double t, const double* xc, double* GKYL_RESTRICT xp, void* ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xc[0], y = xc[1], z = xc[2];
+  xp[0] = x; xp[1] = y; xp[2] = z;
+}
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = 0.0;
+  fout[1] = 0.0;
+  fout[2] = app->B;
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 1, vdim = 2; // Dimensionality.
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+  double me = GKYL_ELECTRON_MASS;
+  double mp = GKYL_PROTON_MASS;
+  double mu0 = GKYL_MU0;
+  // Geometry, magnetic field and gradients.
+  double R0 = 1.313; // Major radius of the simulation box [m].
+  double a = 0.4701; // Minor radius at outboard midplane [m].
+  double B0 = 1.91; // Magnetic field magnitude in the simulation box [T].
+  double Ti0 = 2072*eV;
+  double eps_n = 0.2;
+  // double eta_e = 2.0; // Comes from rt-alfven-p1.lua but unused.
+  // double eta_i = 2.5; // Comes from rt-alfven-p1.lua but unused.
+  double ky_rhos = 0.01;
+  double kz_Ln = 1.0;
+  double beta_hat = 10.0; // beta_e/2*m_p/m_e.
+  double beta_e = beta_hat*2.0*me/mp;
+  double tau = 1.0; // Ti/Te.
+  // Derived paramters.
+  double r0 = 0.5*a; // Minor radius of the simulation box [m].
+  double R = R0 + r0; // Major radius at center of simulation box [m].
+  double B = B0 * R0/R; // Magnetic field at center of simulation box [T].
+  double Te0 = Ti0/tau; // Electron temperature [J].
+  double n0 = beta_e*B*B/(2*mu0*Te0); // Density [m^-3].
+  double vte = sqrt(Te0/me); // Electron thermal speed [m/s].
+  double vti = sqrt(Ti0/mp); // Ion thermal speed [m/s].
+  double c_s = sqrt(Te0/mp); // Sound speed [m/s].
+  double omega_ci = fabs(qi*B/mp); // Ion cyclotron frequency [rad/s].
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius [m
+  double ky_min = ky_rhos/rho_s; // Minimum perpendicular wavenumber [1/m].
+  double L_n = R*eps_n; // Density gradient scale length [m].
+  double kz_min = kz_Ln/L_n; // Minimum parallel wavenumber [1/m].
+  double L_parallel = 2*M_PI/kz_min; // Domain size in z [m].
+  // Expected frequency from dispersion relation:
+  double omega = kz_min*c_s*sqrt(2/beta_e/(1+beta_hat*pow(ky_rhos,2)));
+
+  // Velocity grid parameters.
+  double vpar_max_elc = 6.0*vte; // Max electron parallel velocity [m/s].
+  double vpar_min_elc = -vpar_max_elc; // Min electron parallel velocity [m/s].
+  double vpar_max_ion = 6.0*vti; // Max ion parallel velocity [m/s].
+  double vpar_min_ion = -vpar_max_ion; // Min ion parallel
+  double mu_max_elc = me*pow(4*vte,2)/(2*B); // Max electron mu [J/T].
+  double mu_max_ion = mp*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
+
+  // Grid parameters
+  int Nz = 8;
+  int Nvpar = 8;
+  int Nmu = 6;
+  int poly_order = 1;
+
+  double t_end = 2*M_PI/omega; // End time [s].
+  int num_frames = 1;
+  double write_phase_freq = 0.1; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*100;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .mu0 = mu0,
+    .R = R,
+    .B = B,
+    .z_min = -M_PI/kz_min,  .z_max = M_PI/kz_min,
+  
+    .kperp = ky_min,
+    .kz_min = kz_min,
+  
+    .me = me,  .qe = qe,
+    .mi = mp,  .qi = qi,
+    .n0 = n0,  .Te0 = Te0,  .Ti0 = Ti0,
+    
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .cells = {Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+    .vpar_max_elc = vpar_max_elc,  .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion,  .mu_max_ion = mu_max_ion,
+
+    .t_end = t_end,  .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+
+int main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // Electrons.
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_elc, 0.0},
+    .upper = {  ctx.vpar_max_elc, ctx.mu_max_elc}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_elc,
+      .ctx_upar = &ctx,
+      .upar= upar_elc,
+      .ctx_temp = &ctx,
+      .temp = temp_elc,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+  };
+
+  // Ions.
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = {  ctx.vpar_max_ion, ctx.mu_max_ion}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_ion,
+      .ctx_upar = &ctx,
+      .upar= upar_ion,
+      .ctx_temp = &ctx,
+      .temp = temp_ion,      
+    },
+
+    .is_static = true,
+    
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+  };
+
+  // field
+  struct gkyl_gyrokinetic_field field = {
+    .kperpSq = ctx.kperp * ctx.kperp,
+    .mu0 = ctx.mu0,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .name = "gk_em_alfven_1x2v_p1",
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.z_min },
+    .upper = { ctx.z_max },
+    .cells = { cells_x[0] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_MAPC2P,
+      .world = {0., 0.},
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx
+    },
+
+    .num_periodic_dir = 1,
+    .periodic_dirs = { 0 },
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .cuts = { app_args.cuts[0] },
+      .comm = comm,
+    },
+  };
+
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+  return 0;
+}

From 2ad20e535874cf54a88868ef26266d311a3c7114 Mon Sep 17 00:00:00 2001
From: Antoine <antoine.hoffmann@epfl.ch>
Date: Wed, 12 Nov 2025 16:11:59 -0500
Subject: [PATCH 046/181] this commit is shady but it has ideas on how to step
 Apar correctly

---
 gyrokinetic/apps/gk_field.c                   | 68 +++++++++++++++++--
 gyrokinetic/apps/gk_species.c                 |  2 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      | 36 +++++++++-
 gyrokinetic/apps/gyrokinetic.c                | 10 +--
 .../apps/gyrokinetic_multib_update_ssp_rk3.c  | 14 ++--
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c | 25 +++++--
 6 files changed, 132 insertions(+), 23 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index f6b064d666..b3d65eaacf 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -246,13 +246,13 @@ static void
 gk_field_step_apar_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
-  gkyl_array_accumulate(out, dt, inp);
+  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
 
   // Update the smooth version of Apar (out).
-  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
-  gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
-  gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
-  gkyl_array_copy_range_to_range(field->apar_smooth, field->apar_fem, &app->local, &field->global_sub_range);
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
+  // gkyl_array_copy_range_to_range(field->apar_smooth, field->apar_fem, &app->local, &field->global_sub_range);
 }
 
 static void
@@ -262,6 +262,37 @@ gk_field_step_apar_none(gkyl_gyrokinetic_app *app, struct gk_field *field, struc
   // do nothing
 }
 
+static void
+gk_field_combine_dynamic(struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  gkyl_array_accumulate_range(gkyl_array_set_range(out, c1, arr1, rng),
+    c2, arr2, rng);
+}
+
+static void
+gk_field_combine_static(struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  // do nothing
+}
+
+static void
+gk_field_copy_range_dynamic(struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  gkyl_array_copy_range(out, inp, range);
+}
+
+static void
+gk_field_copy_range_static(struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  // do nothing
+}
+
 // Initialize field object.
 struct gk_field* 
 gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
@@ -598,11 +629,15 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->accumulate_current = gk_field_accumulate_current_dens_none;
   f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_none;
   f->step_apar = gk_field_step_apar_none;
+  f->combine_func = gk_field_combine_static;
+  f->copy_func = gk_field_copy_range_static;
   f->apar_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   if (f->is_em) {
     f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar_old = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar_curr = f->apar;
+    f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
     
     f->apar_host = f->apar;
@@ -682,6 +717,8 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->accumulate_current = gk_field_accumulate_current_dens_dyn;
     f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_dyn;
     f->step_apar = gk_field_step_apar_dyn;
+    f->combine_func = gk_field_combine_dynamic;
+    f->copy_func = gk_field_copy_range_dynamic;
     
     // Factor for EM energy.
     f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
@@ -953,6 +990,21 @@ void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struc
   field->step_apar(app, field, out, a, inp);
 }
 
+void
+gk_field_combine(struct gk_field *field, struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  field->combine_func(out, c1, arr1, c2, arr2, rng);
+}
+
+void
+gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  field->copy_func(out, inp, range);
+}
+
 void
 gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[])
 {
@@ -1101,7 +1153,9 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   gkyl_array_release(f->apardot);
   if (f->is_em) {
     gkyl_array_release(f->apar);
-    gkyl_array_release(f->apar_old);
+    gkyl_array_release(f->apar_curr);
+    gkyl_array_release(f->apar1);
+    gkyl_array_release(f->aparnew);
     gkyl_array_release(f->apar_fem);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 73a45f8738..91822b6b5f 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1586,7 +1586,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   }
 
   // We do not have FLR effects for EM yet.
-  gks->gyro_apar = gkyl_array_acquire(app->field->apar_smooth);
+  gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);
   gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
 
   // Initialize the collisionless solver.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 1d20669c52..f80d0b9148 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1162,8 +1162,8 @@ struct gk_field {
     };
     // EM GK model
     struct {
-      struct gkyl_array *apar; // Array for A_parallel (solved only in ic).
-      struct gkyl_array *apar_old; // Previous state of A_parallel (for update with apardot).
+      struct gkyl_array *apar, *apar1, *aparnew; // Array for A_parallel and RK stages.
+      struct gkyl_array *apar_curr; // A_parallel at current RK stage.
       struct gkyl_array *apar_fem; // FEM A_parallel. 
       struct gkyl_array *apar_smooth; // Smoothed A_parallel.
       struct gkyl_array *apar_host; // Host copy for use IO.
@@ -1253,6 +1253,8 @@ struct gk_field {
   void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*step_apar) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
+  void (*combine_func) (struct gkyl_array *out, double c1, const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,const struct gkyl_range *rng);
+  void (*copy_func) (struct gkyl_array *out, const struct gkyl_array *inp, const struct gkyl_range *range);
 };
 
 // Gyrokinetic object: used as opaque pointer in user code.
@@ -3709,6 +3711,33 @@ void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field);
 void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp);
 
+/**
+ * Combine for rk3 method.
+ *
+ * @param field Pointer to field.
+ * @param out Output array.
+ * @param c1 Scaling factor.
+ * @param arr1 Input array.
+ * @param c2 Scaling factor.
+ * @param arr2 Input array.
+ * @param rng Range.
+ */
+void gk_field_combine(struct gk_field *field, struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng);
+
+/**
+ * Copy for rk3 method.
+ *
+ * @param field Pointer to field.
+ * @param out Output array.
+ * @param inp Input array.
+ * @param range Range.
+ */
+void gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range);
+
+
 /**
  * Compute electrostatic potential, phi, from charge density and
  * time derivative of the parallel component of the vector potential, apardot,
@@ -3809,11 +3838,14 @@ void gyrokinetic_calc_field_and_apply_bc(gkyl_gyrokinetic_app* app, double tcurr
  * @param fin_neut Input array of neutral-species distribution functions.
  * @param fout_neut Output array of neutral-species distribution functions.
  * @param bflux_out_neut Output array of neutral-species boundary fluxes.
+ * @param aparin Input array for parallel component of magnetic vector potential.
+ * @param aparout Output array for parallel component of magnetic vector potential.
  * @param st Time stepping status object.
  */
 void gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   const struct gkyl_array *fin[], struct gkyl_array *fout[], struct gkyl_array **bflux_out[], 
   const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], struct gkyl_array **bflux_out_neut[],
+  const struct gkyl_array *aparin, struct gkyl_array *aparout,
   struct gkyl_update_status *st); 
 
 /**
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 6a862ecbd7..8dd96a4118 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1721,7 +1721,8 @@ gkyl_gyrokinetic_app_write(gkyl_gyrokinetic_app* app, double tm, int frame)
 void
 gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   const struct gkyl_array *fin[], struct gkyl_array *fout[], struct gkyl_array **bflux_out[], 
-  const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], struct gkyl_array **bflux_out_neut[], 
+  const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], struct gkyl_array **bflux_out_neut[],
+  const struct gkyl_array *aparin, struct gkyl_array *aparout,
   struct gkyl_update_status *st)
 {
   double dtmin = DBL_MAX;
@@ -1783,11 +1784,12 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
-  // Compute the electromagnetic field RHS (solves Ohm's law using the full ES RHS).
+  // Compute Apardot (solves Ohm's law using the previously built RHS).
   gk_field_em_rhs(app, app->field, fout);
+  // Update aparout.
+  gk_field_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
 
-  // Add electromagnetic contributions to the collisionless update of charged species.
-  // This is done after all ES+Apar terms since we need to compute M1 of fdot.
+  // Add Apardot contributions to the collisionless update of charged species.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
     gk_species_add_apardot_rhs(app, s, fin[i], fout[i], bflux_out[i]);
diff --git a/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
index 477e200cb6..2aa91e5e86 100644
--- a/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
@@ -3,6 +3,7 @@
 static void
 gyrokinetic_multib_forward_euler(struct gkyl_gyrokinetic_multib_app* app, double tcurr, double dt,
   const struct gkyl_array *fin[], struct gkyl_array *fout[], 
+  const struct gkyl_array *aparin, struct gkyl_array *aparout,
   struct gkyl_array **bflux_in[], struct gkyl_array **bflux_out[], 
   const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], 
   struct gkyl_array **bflux_in_neut[], struct gkyl_array **bflux_out_neut[], 
@@ -23,7 +24,8 @@ gyrokinetic_multib_forward_euler(struct gkyl_gyrokinetic_multib_app* app, double
     int li_charged = b * app->num_species;
     int li_neut = b * app->num_neut_species;
     gyrokinetic_rhs(app->singleb_apps[b], tcurr, dt, &fin[li_charged], &fout[li_charged],
-      &bflux_out[li_charged], &fin_neut[li_neut], &fout_neut[li_neut], &bflux_out_neut[li_neut], st);
+      &bflux_out[li_charged], &fin_neut[li_neut], &fout_neut[li_neut], &bflux_out_neut[li_neut], 
+      aparin, aparout, st);
     dtmin = fmin(dtmin, st->dt_actual);
   }
 
@@ -69,6 +71,8 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
 
   const struct gkyl_array *fin[ns_charged * nblocks_local];
   struct gkyl_array *fout[ns_charged * nblocks_local];
+  const struct gkyl_array *aparin;
+  struct gkyl_array *aparout;
   struct gkyl_array **bflux_in[ns_charged * nblocks_local];
   struct gkyl_array **bflux_out[ns_charged * nblocks_local];
 
@@ -98,6 +102,8 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
             bflux_in[li_charged+i] = gks->bflux.f;
             bflux_out[li_charged+i] = gks->bflux.f1;
           }
+          aparin = NULL;
+          aparout = NULL;
           for (int i=0; i<ns_neut; ++i) {
             struct gk_neut_species *gkns = &sbapp->neut_species[i];
             fin_neut[li_neut+i] = gkns->f;
@@ -109,7 +115,7 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
         }
 
         gyrokinetic_multib_forward_euler(app, tcurr, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
+          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
         dt = st.dt_actual;
 
         // Subtract boundary flux f from f1 so that we only step boundary
@@ -174,7 +180,7 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
         }
 
         gyrokinetic_multib_forward_euler(app, tcurr+dt, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
+          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
 
         if (st.dt_actual < dt) {
 
@@ -263,7 +269,7 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
         }
 
         gyrokinetic_multib_forward_euler(app, tcurr+dt/2, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
+          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
 
         if (st.dt_actual < dt) {
           // Recalculate the field.
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index 0d4d04bbdd..8698f624ef 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -3,6 +3,7 @@
 static void
 gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   const struct gkyl_array *fin[], struct gkyl_array *fout[], 
+  const struct gkyl_array *aparin, struct gkyl_array *aparout,
   struct gkyl_array **bflux_in[], struct gkyl_array **bflux_out[], 
   const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], 
   struct gkyl_array **bflux_in_neut[], struct gkyl_array **bflux_out_neut[], 
@@ -18,7 +19,8 @@ gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   app->stat.nfeuler += 1;
 
   // Compute the time rate of change of the distributions, df/dt.
-  gyrokinetic_rhs(app, tcurr, dt, fin, fout, bflux_out, fin_neut, fout_neut, bflux_out_neut, st);
+  gyrokinetic_rhs(app, tcurr, dt, fin, fout, bflux_out, fin_neut, fout_neut, bflux_out_neut, 
+    aparin, aparout, st);
 
   struct timespec wst = gkyl_wall_clock();
   // Complete update of distribution functions.
@@ -33,7 +35,8 @@ gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_step_f(gkns, fout_neut[i], dta, fin_neut[i]);
     gk_neut_species_bflux_accumulate(app, &gkns->bflux, bflux_out_neut[i], 1.0, bflux_in_neut[i]);
   }
-  gk_field_step_apar(app, app->field, app->field->apar, dta, app->field->apardot);
+  gk_field_step_apar(app, app->field, aparout, dta, aparin);
+  app->field->apar_curr = aparout; // Update current A_parallel.
 
   app->stat.fwd_euler_step_f_tm += gkyl_time_diff_now_sec(wst);
   app->stat.fwd_euler_tm += gkyl_time_diff_now_sec(wst_fe);
@@ -48,6 +51,8 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
   // from the actual time-step.
   const struct gkyl_array *fin[app->num_species];
   struct gkyl_array *fout[app->num_species];
+  const struct gkyl_array *aparin;
+  struct gkyl_array *aparout;
   struct gkyl_array **bflux_in[app->num_species];
   struct gkyl_array **bflux_out[app->num_species];
 
@@ -73,6 +78,8 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
           bflux_in[i] = gks->bflux.f;
           bflux_out[i] = gks->bflux.f1;
         }
+        aparin = app->field->apar;
+        aparout = app->field->apar1;
         for (int i=0; i<app->num_neut_species; ++i) {
           struct gk_neut_species *gkns = &app->neut_species[i];
           fin_neut[i] = gkns->f;
@@ -88,7 +95,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
           gk_species_source_adapt(app, gks, &gks->src, gks->lte.f_lte, bflux_in, tcurr);
         }
 
-        gyrokinetic_forward_euler(app, tcurr, dt, fin, fout, bflux_in, bflux_out,
+        gyrokinetic_forward_euler(app, tcurr, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
         dt = st.dt_actual;
 
@@ -139,8 +146,10 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
           bflux_in_neut[i] = gkns->bflux.f1;
           bflux_out_neut[i] = gkns->bflux.fnew;
         }
+        aparin = app->field->apar1;
+        aparout = app->field->aparnew;
 
-        gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, bflux_in, bflux_out,
+        gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
 
         if (st.dt_actual < dt) {
@@ -211,8 +220,10 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
           bflux_in_neut[i] = gkns->bflux.f1;
           bflux_out_neut[i] = gkns->bflux.fnew;
         }
+        aparin = app->field->apar1;
+        aparout = app->field->aparnew;
 
-        gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, bflux_in, bflux_out,
+        gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
 
         if (st.dt_actual < dt) {
@@ -257,6 +268,10 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
             gk_neut_species_bflux_set(app, &gkns->bflux, gkns->bflux.f, 2.0/3.0, gkns->bflux.fnew);
             gk_neut_species_bflux_calc_voltime_integrated_mom(app, gkns, &gkns->bflux, tcurr);
           }
+          // Step A_parallel.
+          gk_field_combine(app->field, app->field->apar1, 1.0/3.0, app->field->apar, 2.0/3.0, app->field->aparnew, 
+            &app->local_ext);
+          gk_field_copy_range(app->field, app->field->apar, app->field->apar1, &app->local_ext);
           app->stat.time_stepper_arithmetic_tm += gkyl_time_diff_now_sec(wst);
 
           // Apply positivity shift if requested.

From 08920437bcb5b82bcfe80e53223465196702ca6a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 13 Nov 2025 08:58:13 -0500
Subject: [PATCH 047/181] a 1/J factor was missing in the kernel, the e_3mag is
 now computed using sqrt(g33) and we make sure the metric coeff are deflated
 now.

---
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c | 32 +++----
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c | 96 +++++++++----------
 gyrokinetic/zero/gk_dg_geom.c                 |  3 +-
 gyrokinetic/zero/gk_geometry.c                |  2 +-
 4 files changed, 66 insertions(+), 67 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
index b6076faf53..70a81932f7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -72,8 +72,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -85,8 +85,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -110,8 +110,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -123,8 +123,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -148,8 +148,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -161,8 +161,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -186,8 +186,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -199,8 +199,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 9a79ad5431..bf11cf4394 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -78,9 +78,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -93,9 +93,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -120,9 +120,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -135,9 +135,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -162,9 +162,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -177,9 +177,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -204,9 +204,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -219,9 +219,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -246,9 +246,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -261,9 +261,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -288,9 +288,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -303,9 +303,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -330,9 +330,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -345,9 +345,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -372,9 +372,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -387,9 +387,9 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * Jc_quad/mag_e_3 * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/zero/gk_dg_geom.c b/gyrokinetic/zero/gk_dg_geom.c
index 16c43be256..be48188840 100644
--- a/gyrokinetic/zero/gk_dg_geom.c
+++ b/gyrokinetic/zero/gk_dg_geom.c
@@ -168,8 +168,7 @@ gkyl_gk_dg_geom_populate_vol(struct gkyl_dg_geom *dg_geom, struct gkyl_gk_dg_geo
       gkdgv[qvloc].g_33 = global_val[5]; // g_{33}
 
       // set magnitude of e_3
-      global_val = gkyl_array_cfetch(gk_geom->geo_int.dualmag_nodal, global_loc);
-      gkdgv[qvloc].mag_e_3 = global_val[2]; // |e^3|
+      gkdgv[qvloc].mag_e_3 = sqrt(gkdgv[qvloc].g_33); // |e_3|
     }
   }
 }
diff --git a/gyrokinetic/zero/gk_geometry.c b/gyrokinetic/zero/gk_geometry.c
index 55e5c0efb8..3a7ce6716b 100644
--- a/gyrokinetic/zero/gk_geometry.c
+++ b/gyrokinetic/zero/gk_geometry.c
@@ -373,7 +373,7 @@ gkyl_gk_geometry_deflate(const struct gk_geometry* up_3d, struct gkyl_gk_geometr
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.B3_nodal, up->geo_int.B3_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.bmag_nodal, up->geo_int.bmag_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.dualcurlbhat_nodal, up->geo_int.dualcurlbhat_nodal, 3);
-  gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.dualmag_nodal, up->geo_int.dualmag_nodal, 3);
+  gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.g_ij_nodal, up->geo_int.g_ij_nodal, 3);
   gkyl_deflate_geo_release(deflator);
 
   if (up->grid.ndim==1) {

From ef81b69e00405c02a034880015bfee958693a62b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 13 Nov 2025 13:31:41 -0500
Subject: [PATCH 048/181] introduce apar_curr which is the current RK stage
 version of apar and should be used in species->gyro_apar. Also fix array
 allocation errors when ES.

---
 gyrokinetic/apps/gk_field.c                   | 10 +++++-----
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  2 --
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c |  6 ++++--
 3 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index b3d65eaacf..c8a4463597 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -631,11 +631,10 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->step_apar = gk_field_step_apar_none;
   f->combine_func = gk_field_combine_static;
   f->copy_func = gk_field_copy_range_static;
-  f->apar_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar_curr = f->apar;
   if (f->is_em) {
-    f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar_curr = f->apar;
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
@@ -1011,6 +1010,7 @@ gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_a
   struct timespec wst = gkyl_wall_clock();
   field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
+  gkyl_array_clear(field->apardot, 0.0);
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -1149,11 +1149,11 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   gkyl_array_release(f->phi_smooth);
 
   // We need at least these two arrays even in ES case (kept 0).
-  gkyl_array_release(f->apar_smooth);
+  gkyl_array_release(f->apar);
   gkyl_array_release(f->apardot);
+  gkyl_array_release(f->apar_curr);
   if (f->is_em) {
     gkyl_array_release(f->apar);
-    gkyl_array_release(f->apar_curr);
     gkyl_array_release(f->apar1);
     gkyl_array_release(f->aparnew);
     gkyl_array_release(f->apar_fem);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index f80d0b9148..fe304c66b8 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1165,7 +1165,6 @@ struct gk_field {
       struct gkyl_array *apar, *apar1, *aparnew; // Array for A_parallel and RK stages.
       struct gkyl_array *apar_curr; // A_parallel at current RK stage.
       struct gkyl_array *apar_fem; // FEM A_parallel. 
-      struct gkyl_array *apar_smooth; // Smoothed A_parallel.
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
       struct gkyl_array *apardot_host; // Host copy for use IO.
@@ -3700,7 +3699,6 @@ void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field);
 
 /**
  * Step the parallel component of the magnetic vector potential, apar, forward in time.
- * Also update apar_smooth used in the GK characteristics.
  * 
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index 8698f624ef..f1df287b23 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -36,7 +36,6 @@ gyrokinetic_forward_euler(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_bflux_accumulate(app, &gkns->bflux, bflux_out_neut[i], 1.0, bflux_in_neut[i]);
   }
   gk_field_step_apar(app, app->field, aparout, dta, aparin);
-  app->field->apar_curr = aparout; // Update current A_parallel.
 
   app->stat.fwd_euler_step_f_tm += gkyl_time_diff_now_sec(wst);
   app->stat.fwd_euler_tm += gkyl_time_diff_now_sec(wst_fe);
@@ -80,6 +79,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar;
         aparout = app->field->apar1;
+        app->field->apar_curr = app->field->apar; // This is the A_parallel used in the species gyro_apar.
         for (int i=0; i<app->num_neut_species; ++i) {
           struct gk_neut_species *gkns = &app->neut_species[i];
           fin_neut[i] = gkns->f;
@@ -148,6 +148,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
+        app->field->apar_curr = app->field->apar1; // This is the A_parallel used in the species gyro_apar.
 
         gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -186,6 +187,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
             gk_neut_species_combine(gkns, gkns->f1, 3.0/4.0, gkns->f, 1.0/4.0, gkns->fnew, &gkns->local_ext);
             gk_neut_species_bflux_set(app, &gkns->bflux, gkns->bflux.f1, 1.0/4.0, gkns->bflux.fnew);
           }
+          gk_field_combine(app->field, app->field->apar1, 3.0/4.0, app->field->apar, 1.0/4.0, app->field->aparnew, &app->local_ext);
           app->stat.time_stepper_arithmetic_tm += gkyl_time_diff_now_sec(wst);
 
           // Compute the fields and apply BCs.
@@ -222,6 +224,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
+        app->field->apar_curr = app->field->apar1; // This is the A_parallel used in the species gyro_apar.
 
         gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -259,7 +262,6 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
             gk_species_bflux_set(app, &gks->bflux, gks->bflux.f, 2.0/3.0, gks->bflux.fnew);
             gk_species_bflux_calc_voltime_integrated_mom(app, gks, &gks->bflux, tcurr);
           }
-
           for (int i=0; i<app->num_neut_species; ++i) {
             struct gk_neut_species *gkns = &app->neut_species[i];
             gk_neut_species_combine(gkns, gkns->f1, 1.0/3.0, gkns->f, 2.0/3.0, gkns->fnew, &gkns->local_ext);

From 846f63fe13066ea6aa39b32fb521f9f73237a912 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 13 Nov 2025 13:31:54 -0500
Subject: [PATCH 049/181] typo in the new signature of the euler stepping
 method

---
 gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
index 2aa91e5e86..904c2ea035 100644
--- a/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_multib_update_ssp_rk3.c
@@ -114,8 +114,8 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
           }
         }
 
-        gyrokinetic_multib_forward_euler(app, tcurr, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
+        gyrokinetic_multib_forward_euler(app, tcurr, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
+          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
         dt = st.dt_actual;
 
         // Subtract boundary flux f from f1 so that we only step boundary
@@ -179,8 +179,8 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
           }
         }
 
-        gyrokinetic_multib_forward_euler(app, tcurr+dt, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
+        gyrokinetic_multib_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, 
+          bflux_in, bflux_out, fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
 
         if (st.dt_actual < dt) {
 
@@ -268,8 +268,8 @@ gyrokinetic_multib_update_ssp_rk3(struct gkyl_gyrokinetic_multib_app* app, doubl
           }
         }
 
-        gyrokinetic_multib_forward_euler(app, tcurr+dt/2, dt, fin, fout, bflux_in, bflux_out,
-          fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, aparin, aparout, &st);
+        gyrokinetic_multib_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout,
+          bflux_in, bflux_out, fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
 
         if (st.dt_actual < dt) {
           // Recalculate the field.

From 5293f642a1466850f4ee13ec3da6c027a8bf1fd1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 13 Nov 2025 13:35:09 -0500
Subject: [PATCH 050/181] remove a debugging clear line

---
 gyrokinetic/apps/gk_field.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index c8a4463597..eeaca95cb2 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -1010,7 +1010,6 @@ gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_a
   struct timespec wst = gkyl_wall_clock();
   field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
-  gkyl_array_clear(field->apardot, 0.0);
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 

From b49ebf86b4947e2d16b561efe1cbc5f65d13e464 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 14 Nov 2025 08:57:42 -0500
Subject: [PATCH 051/181] The kinetic alfven wave test is almost working but
 the frequency of the wave is not scaling as expected (too fast) and i see a
 weird sawtooth pattern that pollutes the moments, and this even in the main
 branch. Here are the changes: - The 1x Ohm's law is done with a weak division
 now (allow discontinuity which is necessary to have the cancellation 
 -dphidz-apardot=0) - The gk_species_collisionless_add_apardot_rhs now errase
 the fluxes before adding only the apardot contribution. This must be done in
 order to avoid double counting the surface term in the hyper_dg updater. -
 The boundary fluxes are computed before adding the apardot term, which is
 fine since Apardot leads a force, so no contribution to configuration space
 advection.

---
 gyrokinetic/apps/gk_field.c                 | 35 +++++++--------------
 gyrokinetic/apps/gk_species_collisionless.c |  6 ++--
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h    |  4 +--
 gyrokinetic/apps/gyrokinetic.c              | 14 ++++-----
 4 files changed, 23 insertions(+), 36 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index eeaca95cb2..826965c64e 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -184,7 +184,7 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
  * 
  * (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) dApar/dt = sum_s q_s int dv vpar d/dt(F_s)
  * 
- * The first parenthesis is computed in dApartdtSlvr_lhs_factor_global. The right hand side is in currentDensdot_global.
+ * The first parenthesis is computed in dApartdtSlvr_lhs_factor_global. The right hand side is in currentDensdot.
  */
 static void 
 gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
@@ -193,19 +193,11 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   // Compute the new dApartdtSlvr_kSq (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
   gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
   gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
-  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->dApartdtSlvr_lhs_factor, field->dApartdtSlvr_lhs_factor_global);
-  
-  gkyl_fem_parproj_release(field->fem_apardot_parproj);
-  field->fem_apardot_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
-    field->fem_parproj_ampere_bc, field->dApartdtSlvr_lhs_factor_global, 0, app->use_gpu);
-
-  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDensdot, field->currentDensdot_global);
-
-  gkyl_fem_parproj_set_rhs(field->fem_apardot_parproj, field->currentDensdot_global, field->currentDensdot_global);
-  gkyl_fem_parproj_solve(field->fem_apardot_parproj, field->phi_fem);
-
-  gkyl_array_copy_range_to_range(field->apardot, field->phi_fem, &app->local, &field->global_sub_range);
 
+  // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apardot, 0, field->currentDensdot, 
+    0, field->dApartdtSlvr_lhs_factor, &app->local);
+  
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -248,11 +240,11 @@ gk_field_step_apar_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, struct
 {
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
 
-  // Update the smooth version of Apar (out).
+  // Smooth apar
   // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
   // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
   // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
-  // gkyl_array_copy_range_to_range(field->apar_smooth, field->apar_fem, &app->local, &field->global_sub_range);
+  // gkyl_array_copy_range_to_range(out, field->apar_fem, &app->local, &field->global_sub_range);
 }
 
 static void
@@ -634,6 +626,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apar_curr = f->apar;
+  f->div_mem = NULL;
   if (f->is_em) {
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
@@ -653,9 +646,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
     if (app->cdim == 1) {
       f->currentDens_global = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
-      f->currentDensdot_global = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
       f->dApartdtSlvr_lhs_factor = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-      f->dApartdtSlvr_lhs_factor_global = mkarr(app->use_gpu, f->dApartdtSlvr_lhs_factor->ncomp, app->global_ext.volume);
+      f->div_mem = app->use_gpu? gkyl_dg_bin_op_mem_cu_dev_new(app->local.volume, app->basis.num_basis)
+        : gkyl_dg_bin_op_mem_new(app->local.volume, app->basis.num_basis);
       
       // Need to set weight to kperpsq*polarizationWeight for use in potential smoothing.
       gkyl_array_copy(f->lapWeightAmpere, app->gk_geom->geo_int.jacobgeo);
@@ -668,10 +661,6 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
         f->fem_parproj_ampere_bc, f->lapWeightAmpere, 0, app->use_gpu);
 
-      // Declare a dummy solver for d(Apar)/dt (will be updated at each time step).
-      f->fem_apardot_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
-        f->fem_parproj_ampere_bc, f->dApartdtSlvr_kSq, 0, app->use_gpu);
-
       f->ohm_solve = gk_field_ohm_solve_1x;
       f->ampere_solve = gk_field_ampere_solve_1x;
     } else if (app->cdim > 1) {
@@ -1164,13 +1153,11 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     if (app->cdim > 1) {
       gkyl_fem_poisson_perp_release(f->fem_apar_solver);
       gkyl_fem_poisson_perp_release(f->fem_apardot_solver);  
+      gkyl_dg_bin_op_mem_release(f->div_mem);
     }
     else {
       gkyl_array_release(f->currentDens_global);
-      gkyl_array_release(f->currentDensdot_global);
       gkyl_array_release(f->dApartdtSlvr_lhs_factor);
-      gkyl_array_release(f->dApartdtSlvr_lhs_factor_global);
-      gkyl_fem_parproj_release(f->fem_apardot_parproj);  
     }
     gkyl_fem_parproj_release(f->fem_apar_parproj);
     if (app->use_gpu) {
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index f583348e80..c487516be7 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -49,12 +49,14 @@ static void gk_species_collisionless_add_apardot_rhs_enabled(gkyl_gyrokinetic_ap
 {
   struct timespec wst = gkyl_wall_clock();
 
-  // Add Apardot surface flux contribution to RHS
+  // First remove the current ES+Apar contribution from the flux_surf array.
+  // Otherwise it will be counted twice in the gkyl_dg update.
+  gkyl_array_clear(gkcls->flux_surf, 0.0);
   gkyl_gk_collisionless_flux_surf(gkcls->add_apardot_surf_flux_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
     species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
 
-  // Advance the rhs adding only the Apardot volume contribution
+  // Advance the rhs adding only the Apardot volume contribution.
   gkyl_dg_updater_gyrokinetic_advance(gkcls->add_apardot_slvr, &species->local,
     fin, species->cflrate, rhs);
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index fe304c66b8..3b9cc6119d 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1171,14 +1171,12 @@ struct gk_field {
       struct gkyl_array *currentDens; // Current density.
       struct gkyl_array *currentDens_global; // Current density.
       struct gkyl_array *currentDensdot; // Time derivative of current density.
-      struct gkyl_array *currentDensdot_global; // Time derivative of current density (accross all MPI ranks).
       struct gkyl_array *dApartdtSlvr_kSq; // Contains sum_s q_s^2/m_s n_s.
       struct gkyl_array *dApartdtSlvr_lhs_factor; // Contains kperp^2/mu_0 + sum_s q_s^2/m_s n_s for 1D Ohm solve.
-      struct gkyl_array *dApartdtSlvr_lhs_factor_global; // Contains kperp^2/mu_0 + sum_s q_s^2/m_s n_s for 1D Ohm solve.
       struct gkyl_array *dApartdtSlvr_rhs; // Contains sum_s q_s int dv vpar d/dt(F_s)*.
+      gkyl_dg_bin_op_mem *div_mem; // Memory for div operation in 1x Ohm's law. 
       struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0).
       struct gkyl_fem_parproj *fem_apar_parproj; // FEM smoother for projecting Apar onto continuous FEM basis
-      struct gkyl_fem_parproj *fem_apardot_parproj; // FEM smoother for projecting d(Apar)/dt onto continuous FEM basis
       struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar.
       struct gkyl_fem_poisson_perp *fem_apardot_solver; // Solver for d(Apar)/dt.
       struct gkyl_poisson_bc ampere_bcs; // BCs for Apar and d(Apar)/dt.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 8dd96a4118..e26a5b6b0a 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1153,7 +1153,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     }
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
-  if (!(app->field->info.gkfield_id == GKYL_GK_FIELD_ES || app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
+  if (app->field->is_em) {
     const char *fmt1 = "%s-apar_%d.gkyl";
     int sz = gkyl_calc_strlen(fmt1, app->name, frame);
     char fileNm1[sz+1]; // ensures no buffer overflow
@@ -1212,7 +1212,7 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
-    bool write_em = !(app->field->info.gkfield_id == GKYL_GK_FIELD_ES || app->field->info.gkfield_id == GKYL_GK_FIELD_ES_IWL);
+    bool write_em = app->field->is_em;
     if (rank == 0) {
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).
@@ -1767,7 +1767,8 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
     gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
-  }
+    gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
+}
   for (int i=0; i<app->num_neut_species; ++i) {
     struct gk_neut_species *gk_ns = &app->neut_species[i];
     double dt1 = gk_neut_species_rhs(app, gk_ns, fin_neut[i], fout_neut[i], bflux_out_neut[i]);
@@ -1791,10 +1792,9 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
 
   // Add Apardot contributions to the collisionless update of charged species.
   for (int i=0; i<app->num_species; ++i) {
-    struct gk_species *s = &app->species[i];
-    gk_species_add_apardot_rhs(app, s, fin[i], fout[i], bflux_out[i]);
-    gk_species_update_bflux(app, s, fin[i], fout[i], bflux_out[i]);
-    double dt1 = gk_species_get_cfl(app, s, fin[i], fout[i], bflux_out[i]);
+    struct gk_species *gk_s = &app->species[i];
+    gk_species_add_apardot_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    double dt1 = gk_species_get_cfl(app, gk_s, fin[i], fout[i], bflux_out[i]);
     dtmin = fmin(dtmin, dt1);
   }
 

From 38ffe420c48ca3d8419c31836c4f4232418bb658 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 14 Nov 2025 11:29:01 -0800
Subject: [PATCH 052/181] the alfven test is still producing the wrong physics
 but it can do it on GPU now \o/

---
 gyrokinetic/zero/dg_gyrokinetic.c             |  2 +-
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         | 25 +++++--
 gyrokinetic/zero/gk_collisionless_flux.c      |  4 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  | 73 +++++++++++--------
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  9 ++-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  4 +-
 6 files changed, 71 insertions(+), 46 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 9eaa0b9903..4bd6a18884 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -54,7 +54,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
-      charge, mass, skip_cell_threshold, no_by, gk_geom, vel_map);
+      charge, mass, skip_cell_threshold, collless_type, only_apardot, gk_geom, vel_map);
 #endif
 
   struct dg_gyrokinetic *gyrokinetic = gkyl_malloc(sizeof(struct dg_gyrokinetic));
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 2aa30eac05..809ef4d175 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -37,7 +37,8 @@ gkyl_gyrokinetic_set_auxfields_cu(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_basis_type b_type,
-  int cv_index, int cdim, int vdim, int poly_order, const bool no_by)
+  int cv_index, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type collless_type, 
+  bool only_apardot)
 {
   gyrokinetic->auxfields.flux_surf = 0; 
   gyrokinetic->auxfields.phi = 0; 
@@ -49,6 +50,8 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->eqn.boundary_diag_term = boundary_diag;
 
   const gkyl_dg_gyrokinetic_vol_kern_list *vol_kernels, *vol_no_by_kernels;
+  const gkyl_dg_gyrokinetic_vol_add_apar_kern_list *vol_add_apar_kernels;
+  const gkyl_dg_gyrokinetic_vol_kern_list *vol_add_apardot_kernels;
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_x_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_y_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_z_kernels; 
@@ -61,6 +64,8 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   switch (b_type) {
     case GKYL_BASIS_MODAL_SERENDIPITY:
       vol_kernels = ser_vol_kernels;
+      vol_add_apar_kernels = ser_add_apar_vol_kernels;
+      vol_add_apardot_kernels = ser_add_apardot_vol_kernels;
       surf_x_kernels = ser_surf_x_kernels;
       surf_y_kernels = ser_surf_y_kernels;
       surf_z_kernels = ser_surf_z_kernels;
@@ -79,13 +84,19 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       break;    
   }  
 
-  if (no_by) {
+  if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
     gyrokinetic->eqn.vol_term = vol_no_by_kernels[cv_index].kernels[poly_order];
   }
   else {
-    gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
+    if (only_apardot)
+      gyrokinetic->eqn.vol_term = vol_add_apardot_kernels[cv_index].kernels[poly_order];
+    else
+      gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
   }
 
+  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM || GKYL_GK_COLLISIONLESS_EM_BPERP ? 
+    vol_add_apar_kernels[cv_index].kernels[poly_order] : dg_gyrokinetic_vol_return_zero;
+
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
   if (cdim>1)
     gyrokinetic->surf[1] = surf_y_kernels[cv_index].kernels[poly_order];
@@ -105,8 +116,8 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
 struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_cell_threshold, const bool no_by,
-  const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
+  const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
+  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
 {
   struct dg_gyrokinetic *gyrokinetic = (struct dg_gyrokinetic*) gkyl_malloc(sizeof(*gyrokinetic));
 
@@ -144,7 +155,7 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gkyl_cu_memcpy(gyrokinetic_cu, gyrokinetic, sizeof(struct dg_gyrokinetic), GKYL_CU_MEMCPY_H2D);
 
   dg_gyrokinetic_set_cu_dev_ptrs<<<1,1>>>(gyrokinetic_cu, cbasis->b_type, cv_index[cdim].vdim[vdim],
-    cdim, vdim, poly_order, no_by);
+    cdim, vdim, poly_order, collless_type, only_apardot);
 
   // set parent on_dev pointer
   gyrokinetic->eqn.on_dev = &gyrokinetic_cu->eqn;
@@ -154,4 +165,4 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gyrokinetic->vel_map = vel_map_ho; 
 
   return &gyrokinetic->eqn;
-}
+}
\ No newline at end of file
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 120323e373..bf54af5c24 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -25,7 +25,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis, 
-      charge, mass, no_by, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, type, only_apardot, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
@@ -96,7 +96,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
 #ifdef GKYL_HAVE_CUDA
   if (gkyl_array_is_cu_dev(flux_surf)) {
     return gkyl_gk_collisionless_flux_surf_cu(up, conf_range, phase_range,
-      conf_ext_range, phase_ext_range, phi, fin, flux_surf, cflrate);
+      conf_ext_range, phase_ext_range, phi, apar, fin, flux_surf, cflrate);
   }
 #endif
   int pdim = up->pdim;
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 21a88add72..12267a1d4d 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -18,7 +18,7 @@ __global__ void
 gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux *up, 
   struct gkyl_range conf_range, struct gkyl_range phase_range,
   struct gkyl_range conf_ext_range, struct gkyl_range phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
+  const struct gkyl_array *apar, const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 { 
   int pdim = up->pdim;
   int cdim = up->cdim;
@@ -47,6 +47,7 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
 
     const double *bmag_d = (const double*) gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = (const double*) gkyl_array_cfetch(phi, loc_conf);
+    const double *apar_d = (const double*) gkyl_array_cfetch(apar, loc_conf);
     const double *vmap_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -70,11 +71,11 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
       if (idx[dir] == phase_range.lower[dir]) {
         // Lower domain/block boundary.
         cflrate_d[0] += up->flux_surf_edge_lo[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
       } else {
         // Interior, lower cell surface.
         cflrate_d[0] += up->flux_surf[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
       }
 
       // If the phase space index is at the local configuration space upper value, we
@@ -100,7 +101,7 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
         double* flux_surf_ext_d = (double*) gkyl_array_fetch(flux_surf, loc_phase_ext);
 
         cflrate_ext_d[0] = up->flux_surf_edge_up[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, fL, fR, flux_surf_ext_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_ext_d);
       }  
     }
   }
@@ -110,7 +111,7 @@ __global__ void
 gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_flux *up, 
   struct gkyl_range conf_range, struct gkyl_range phase_range,
   struct gkyl_range conf_ext_range, struct gkyl_range phase_ext_range, struct gkyl_range vpar_range,
-  const struct gkyl_array *phi, const struct gkyl_array *fin, 
+  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *fin, 
   struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 { 
   int pdim = up->pdim;
@@ -141,6 +142,7 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
 
     const double *bmag_d = (const double*) gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = (const double*) gkyl_array_cfetch(phi, loc_conf);
+    const double *apar_d = (const double*) gkyl_array_cfetch(apar, loc_conf);
     const double *vmap_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -166,7 +168,7 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
     cflrate_d[0] += up->flux_surfvpar[0](xc, up->phase_grid.dx, 
       vpL, vpR,
       vmap_d, vmapSq_d, up->charge, up->mass,
-      dgv, gkdgv, bmag_d, phi_d,  fL, fR, flux_surf_d);
+      dgv, gkdgv, bmag_d, phi_d, apar_d,  fL, fR, flux_surf_d);
   }
 }
 
@@ -174,10 +176,10 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
 void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate)
+  const struct gkyl_array *apar, const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate)
 {
   gkyl_gk_collisionless_flux_surf_conf_cu_kernel<<<phase_range->volume, GKYL_DEFAULT_NUM_THREADS>>>(up->on_dev, 
-    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, phi->on_dev, fin->on_dev,
+    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, phi->on_dev, apar->on_dev, fin->on_dev,
     flux_surf->on_dev, cflrate->on_dev);
 
   struct gkyl_range vpar_range;
@@ -190,7 +192,7 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
   sublower[up->cdim] += 1;
   gkyl_sub_range_init(&vpar_range, phase_ext_range, sublower, subupper);
   gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel<<<vpar_range.volume, GKYL_DEFAULT_NUM_THREADS>>>(up->on_dev, 
-    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, vpar_range, phi->on_dev, fin->on_dev,
+    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, vpar_range, phi->on_dev, apar->on_dev, fin->on_dev,
     flux_surf->on_dev, cflrate->on_dev);
 
 }
@@ -199,36 +201,46 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
-  int cdim, int vdim, int poly_order, const bool no_by,
+  bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, bool only_apardot,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
-  if (no_by) {
+  if (only_apardot){
+    // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
     for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-        }
-        up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+      up->flux_surf[d] = gk_collisionless_flux_surf_return_zero;
+      up->flux_surf_edge_lo[d] = gk_collisionless_flux_surf_return_zero;
+      up->flux_surf_edge_up[d] = gk_collisionless_flux_surf_return_zero;
+    }
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
-    for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
-        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+    if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
+    } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
+      for (int d=0; d<cdim; ++d) {
+        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
+          poly_order, bctype_conf[d]);
+        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
+          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
+      }
+      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
   }
 }
 
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, const bool no_by,
+  const double charge, const double mass, enum gkyl_gk_collisionless_type type, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
@@ -245,6 +257,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
+  int em = (type == GKYL_GK_COLLISIONLESS_EM || type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 1 : 0;
 
   // Acquire pointers to on_dev objects so memcpy below copies those too.
   struct gk_geometry *geom_ho = gkyl_gk_geometry_acquire(gk_geom);
@@ -266,7 +279,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   struct gkyl_gk_collisionless_flux *up_cu = (struct gkyl_gk_collisionless_flux*) gkyl_cu_malloc(sizeof(*up_cu));
   gkyl_cu_memcpy(up_cu, up, sizeof(gkyl_gk_collisionless_flux), GKYL_CU_MEMCPY_H2D);
 
-  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, cdim, vdim, poly_order, no_by, bctype_conf_dev);
+  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, only_apardot, bctype_conf_dev);
 
   gkyl_cu_free(bctype_conf_dev);
 
@@ -280,4 +293,4 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   up->vel_map = vel_map_ho; 
   
   return up;
-}
+}
\ No newline at end of file
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 0f6497ee7e..9a14eb15dd 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -429,8 +429,9 @@ static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_apardot_vol_kernels[] = {
 };
 
 // To turn off EM effects:
-#include <gkyl_dg_gyrokinetic_kernels.h> 
-GKYL_CU_DH double dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+GKYL_CU_DH 
+static double 
+dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
     const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
@@ -674,8 +675,8 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
  */
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_if_smaller_than, const bool no_by,
-  const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
+  const double charge, const double mass, double skip_if_smaller_than, enum gkyl_gk_collisionless_type collless_type,
+  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**
  * CUDA device function to set the auxiliary fields (e.g. geometry & EM fields)
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index a8717a6062..c1d2a78ef1 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -767,7 +767,7 @@ choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  double charge, double mass, const bool no_by,
+  double charge, double mass, enum gkyl_gk_collisionless_type type, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf);
@@ -778,5 +778,5 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
 void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array* fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate);
+  const struct gkyl_array *apar, const struct gkyl_array* fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate);
 #endif

From 5b8708dd1332df4d9d69d247f5b35230267ea4a0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 14 Nov 2025 17:23:45 -0500
Subject: [PATCH 053/181] =?UTF-8?q?It=20is=20always=20one=20typo=20away=20?=
 =?UTF-8?q?=F0=9F=A4=AA=20alfven=20rt=20test=20now=20retrieves=20the=20cor?=
 =?UTF-8?q?rect=20frequency=20for=20betahat=3D1.0=20and=200.1,=20with=20ky?=
 =?UTF-8?q?=3D0.05=20and=200.01.=20However,=20I=20find=20spurious=20result?=
 =?UTF-8?q?s=20for=20betahat=3D10.0.=20Maybe=20the=20MHD=20limit=20deserve?=
 =?UTF-8?q?s=20careful=20resolution=20setting=20idk.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 826965c64e..2ad92f914a 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -652,7 +652,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
       
       // Need to set weight to kperpsq*polarizationWeight for use in potential smoothing.
       gkyl_array_copy(f->lapWeightAmpere, app->gk_geom->geo_int.jacobgeo);
-      gkyl_array_scale(f->lapWeightAmpere, f->info.kperpSq);
+      gkyl_array_scale(f->lapWeightAmpere, f->info.kperpSq/f->info.mu0);
 
       f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
       for (int d=0; d<app->num_periodic_dir; ++d)

From 7b2bae309a41ba3992da1b65a064acf53893b7c2 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 1 Dec 2025 16:27:06 -0500
Subject: [PATCH 054/181] The weak division memory was not released properly
 for Ohm's law in 1x

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 2ad92f914a..89d0bfec2e 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -1153,11 +1153,11 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
     if (app->cdim > 1) {
       gkyl_fem_poisson_perp_release(f->fem_apar_solver);
       gkyl_fem_poisson_perp_release(f->fem_apardot_solver);  
-      gkyl_dg_bin_op_mem_release(f->div_mem);
     }
     else {
       gkyl_array_release(f->currentDens_global);
       gkyl_array_release(f->dApartdtSlvr_lhs_factor);
+      gkyl_dg_bin_op_mem_release(f->div_mem);
     }
     gkyl_fem_parproj_release(f->fem_apar_parproj);
     if (app->use_gpu) {

From be8cb11bb61bddbf352e6c9bd58ce976615786b0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 2 Dec 2025 13:55:47 -0500
Subject: [PATCH 055/181] put the correct q profile (it was the PT discharge
 not the NT one before...)

---
 gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c | 2 +-
 gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index 46a66d7af1..9c758baa8f 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -52,7 +52,7 @@ double r_x(double x, double a_mid, double x_inner)
 // cubic polynomial fit to TCV NT q profile (discharge #65130)
 double qprofile(double R) {
   double qfit[4] = {
-    497.3420166252413, -1408.736172826569, 1331.4134861681464, -419.00692601227627
+    484.0615913225881, -1378.25993228584, 1309.3099150729233, -414.13270311478726
   };
   return qfit[0]*pow(R,3) + qfit[1]*pow(R,2) + qfit[2]*R + qfit[3];
 }
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 6e912d8602..a5474165e8 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -53,7 +53,7 @@ double r_x(double x, double a_mid, double x_inner)
 // cubic polynomial fit to TCV NT q profile (discharge #65130)
 double qprofile(double R) {
   double qfit[4] = {
-    497.3420166252413, -1408.736172826569, 1331.4134861681464, -419.00692601227627
+    484.0615913225881, -1378.25993228584, 1309.3099150729233, -414.13270311478726
   };
   return qfit[0]*pow(R,3) + qfit[1]*pow(R,2) + qfit[2]*R + qfit[3];
 }

From 4490d73a9feb98221b61a780f6ef1e4bcbf72cbc Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 2 Dec 2025 16:02:02 -0500
Subject: [PATCH 056/181] a 1/2 factor is missing in the computation of the
 electrostatic energy for the 1D case

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 89d0bfec2e..945d9d65cc 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -540,7 +540,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     if (f->gkfield_id == GKYL_GK_FIELD_BOLTZMANN)
       f->es_energy_fac_1d = polarization_weight;
     else
-      f->es_energy_fac_1d = polarization_weight*f->info.kperpSq + es_energy_fac_1d_adiabatic;
+      f->es_energy_fac_1d = 0.5*polarization_weight*f->info.kperpSq + es_energy_fac_1d_adiabatic;
 
     f->calc_em_energy = gkyl_array_integrate_new(&app->grid, &app->basis, 
       1, GKYL_ARRAY_INTEGRATE_OP_SQ, app->use_gpu);

From 3f3a56bc7b190fe7195c382e7df5888572b6eb78 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 2 Dec 2025 16:03:29 -0500
Subject: [PATCH 057/181] add diagnostics for energy stored in Aparallel and
 its time derivative, we may want to merge this into the field diagnostics
 later

---
 gyrokinetic/apps/gk_field.c                   | 87 +++++++++++++++++++
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      | 18 +++-
 gyrokinetic/apps/gyrokinetic.c                | 41 ++++++++-
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c |  2 +
 4 files changed, 143 insertions(+), 5 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 945d9d65cc..9dfd837eef 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -38,6 +38,15 @@ gk_field_calc_energy_dt_active(gkyl_gyrokinetic_app *app, const struct gk_field
   app->stat.phidot_tm += gkyl_time_diff_now_sec(wst);
 }
 
+static void
+gk_field_calc_apar_energy_dt_active(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_integrate_advance(field->calc_em_energy, field->apar, 
+    1.0/dt, field->apar_energy_fac, &app->local, &app->local, energy_reduced);
+  app->stat.phidot_tm += gkyl_time_diff_now_sec(wst);
+}
+
 static void
 gk_field_calc_energy_dt_none(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
 {
@@ -49,6 +58,12 @@ gk_field_calc_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field,
   field->calc_energy_dt_func(app, field, dt, energy_reduced);
 }
 
+void
+gk_field_calc_apar_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
+{
+  field->calc_apar_energy_dt_func(app, field, dt, energy_reduced);
+}
+
 static void
 gk_field_add_TSBC_and_SSFG_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -554,6 +569,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
 
   f->calc_energy_dt_func = gk_field_calc_energy_dt_none;
+  f->calc_apar_energy_dt_func = gk_field_calc_energy_dt_none;
   if (f->info.time_rate_diagnostics) {
     f->calc_energy_dt_func = gk_field_calc_energy_dt_active;
     if (app->use_gpu) {
@@ -569,6 +585,22 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     }
     f->integ_energy_dot = gkyl_dynvec_new(GKYL_DOUBLE, 1);
     f->is_first_energy_dot_write_call = true;
+    if (f->is_em){
+      f->calc_apar_energy_dt_func = gk_field_calc_apar_energy_dt_active;
+      if (app->use_gpu) {
+        f->apar_energy_red_new = gkyl_cu_malloc(sizeof(double[1]));
+        f->apar_energy_red_old = gkyl_cu_malloc(sizeof(double[1]));
+        gkyl_cu_memset(f->apar_energy_red_new, 0, sizeof(double[1]));
+        gkyl_cu_memset(f->apar_energy_red_old, 0, sizeof(double[1]));
+      } else {
+        f->apar_energy_red_new = gkyl_malloc(sizeof(double[1]));
+        f->apar_energy_red_old = gkyl_malloc(sizeof(double[1]));
+        memset(f->apar_energy_red_new, 0, sizeof(double[1]));
+        memset(f->apar_energy_red_old, 0, sizeof(double[1]));
+      }
+      f->integ_apar_energy_dot = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+    }
+    f->is_first_apar_energy_dot_write_call = true;
   }
 
   // setup biased lower wall (same size as electrostatic potential), by default is 0.0
@@ -721,6 +753,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     }
     // Diagnostic for integrated Aparallel energy.
     f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+    f->integ_apardot_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
   }
 
   // Create operator needed for FLR effects.
@@ -1106,6 +1139,7 @@ gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_field
   }
 
   if (field->is_em) {
+    // Calculate Aparallel energy.
     gkyl_array_integrate_advance(field->calc_em_energy, field->apar, 
       1.0, field->apar_energy_fac, &app->local, &app->local, field->em_energy_red);
 
@@ -1121,6 +1155,48 @@ gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_field
       energy_global[0] *= field->apar_energy_fac_1d; 
 
     gkyl_dynvec_append(field->integ_apar_energy, tm, energy_global);
+    
+    // Calculate d(Aparallel)/dt energy.
+    gkyl_array_integrate_advance(field->calc_em_energy, field->apardot, 
+      1.0, field->apar_energy_fac, &app->local, &app->local, field->em_energy_red);
+
+    gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->em_energy_red, field->em_energy_red_global);
+
+    double energy_dot_global[1] = { 0.0 };
+    if (app->use_gpu)
+      gkyl_cu_memcpy(energy_dot_global, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+    else
+      energy_dot_global[0] = field->em_energy_red_global[0];
+    
+    // if (app->cdim == 1)
+    //   energy_dot_global[0] *= field->apar_energy_fac_1d;
+
+    gkyl_dynvec_append(field->integ_apardot_energy, tm, energy_dot_global);
+
+    if (field->info.time_rate_diagnostics) {
+      gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->apar_energy_red_old, field->em_energy_red_global);
+      double energy_dot_global_old[1] = { 0.0 };
+      if (app->use_gpu)
+        gkyl_cu_memcpy(energy_dot_global_old, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+      else
+        energy_dot_global_old[0] = field->em_energy_red_global[0];
+      if (app->cdim == 1)
+        energy_dot_global_old[0] *= field->apar_energy_fac_1d; 
+      
+      gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->apar_energy_red_new, field->em_energy_red_global);
+      double energy_dot_global_new[1] = { 0.0 };
+      if (app->use_gpu)
+        gkyl_cu_memcpy(energy_dot_global_new, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+      else
+        energy_dot_global_new[0] = field->em_energy_red_global[0];
+      if (app->cdim == 1)
+        energy_dot_global_new[0] *= field->apar_energy_fac_1d; 
+
+      double energy_dot_global[1] = { 0.0 };
+      energy_dot_global[0] = energy_dot_global_new[0] - energy_dot_global_old[0];
+
+      gkyl_dynvec_append(field->integ_apar_energy_dot, tm, energy_dot_global);
+    }
   }
 
   app->stat.field_diag_calc_tm += gkyl_time_diff_now_sec(wst);
@@ -1165,6 +1241,7 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
       gkyl_array_release(f->apardot_host);
     }
     gkyl_dynvec_release(f->integ_apar_energy);
+    gkyl_dynvec_release(f->integ_apardot_energy);
   }
 
   if (f->init_phi_pol) {
@@ -1224,6 +1301,16 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
       gkyl_free(f->em_energy_red_new);
       gkyl_free(f->em_energy_red_old);
     }
+    if (f->is_em) {
+      gkyl_dynvec_release(f->integ_apar_energy_dot);
+      if (app->use_gpu) {
+        gkyl_cu_free(f->apar_energy_red_new);
+        gkyl_cu_free(f->apar_energy_red_old);
+      } else {
+        gkyl_free(f->apar_energy_red_new);
+        gkyl_free(f->apar_energy_red_old);
+      }
+    }
   }
 
   gkyl_array_release(f->phi_wall_lo);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 3b9cc6119d..6f09f1e40c 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1213,11 +1213,15 @@ struct gk_field {
   double *em_energy_red, *em_energy_red_global; // memory for use in GPU reduction of EM energy
   gkyl_dynvec integ_energy; // integrated energy components
   gkyl_dynvec integ_apar_energy; // integrated EM energy components (separate from electrostatic energy for debugging purposes)
+  gkyl_dynvec integ_apardot_energy; // time derivative of integrated EM energy components
   bool is_first_energy_write_call; // flag for energy dynvec written first time
 
   double *em_energy_red_old, *em_energy_red_new; // memory for use in GPU reduction of old EM energy.
   gkyl_dynvec integ_energy_dot; // d/dt of integrated energy components.
   bool is_first_energy_dot_write_call; // flag for d(energy)/dt dynvec written first time
+  double *apar_energy_red_old, *apar_energy_red_new; // memory for use in GPU reduction of old Apar energy.
+  gkyl_dynvec integ_apar_energy_dot; // d/dt of integrated EM energy components (separate from electrostatic energy for debugging purposes)
+  bool is_first_apar_energy_dot_write_call; // flag for d(energy)/dt dynvec written first time
 
   bool has_phi_wall_lo; // flag to indicate there is biased wall potential on lower wall
   bool phi_wall_lo_evolve; // flag to indicate biased wall potential on lower wall is time dependent
@@ -1233,7 +1237,8 @@ struct gk_field {
 
   // Pointer to function that computes the time rate of change of the energy.
   void (*calc_energy_dt_func)(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced);
-
+  void (*calc_apar_energy_dt_func)(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced);
+  
   // Objects used in IWL simulations and TS BCs.
   struct gkyl_bc_twistshift *bc_T_LU_lo; // TS BC updater.
   // Objects used by the skin surface to ghost (SSFG) operator.
@@ -3788,6 +3793,17 @@ void gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_
  */
 void gk_field_calc_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced);
 
+/**
+ * Compute Apar energy divided by dt for energy balance diagnostics.
+ *
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
+ * @param dt Time step.
+ * @param energy_reduced Integrated field energy (single element double array).
+ */
+void gk_field_calc_apar_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced);
+
+
 /**
  * Release resources allocated by field.
  *
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index e26a5b6b0a..86efae21ed 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1209,6 +1209,11 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     char fileNm0_apar[sz0_apar+1]; // ensures no buffer overflow
     snprintf(fileNm0_apar, sizeof fileNm0_apar, fmt0_apar, app->name);
 
+    const char *fmt0_apardot = "%s-apardot_energy.gkyl";
+    int sz0_apardot = gkyl_calc_strlen(fmt0_apardot, app->name);
+    char fileNm0_apardot[sz0_apardot+1]; // ensures no buffer overflow
+    snprintf(fileNm0_apardot, sizeof fileNm0_apardot, fmt0_apardot, app->name);
+
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
@@ -1218,22 +1223,27 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
         // Write to a new file (this ensure previous output is removed).
         gkyl_dynvec_write(app->field->integ_energy, fileNm0);
 
-        if (write_em)
+        if (write_em) {
           gkyl_dynvec_write(app->field->integ_apar_energy, fileNm0_apar);
-
+          gkyl_dynvec_write(app->field->integ_apardot_energy, fileNm0_apardot);
+        }
         app->field->is_first_energy_write_call = false;
       }
       else {
         // Append to existing file.
         gkyl_dynvec_awrite(app->field->integ_energy, fileNm0);
-        if (write_em)
+        if (write_em) {
           gkyl_dynvec_awrite(app->field->integ_apar_energy, fileNm0_apar);
+          gkyl_dynvec_awrite(app->field->integ_apardot_energy, fileNm0_apardot);
+        }
       }
       app->stat.n_field_diag_io += 1;
     }
     gkyl_dynvec_clear(app->field->integ_energy);
-    if (write_em)
+    if (write_em) {
       gkyl_dynvec_clear(app->field->integ_apar_energy);
+      gkyl_dynvec_clear(app->field->integ_apardot_energy);
+    }
 
     if (app->field->info.time_rate_diagnostics) {
       // Write out the time rate of change of the field energy.
@@ -1255,6 +1265,27 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
         app->stat.n_field_diag_io += 1;
       }
       gkyl_dynvec_clear(app->field->integ_energy_dot);
+      if (write_em) {
+        // Write out the time rate of change of the field energy.
+        const char *fmt2 = "%s-apar_energy_dot.gkyl";
+        int sz2 = gkyl_calc_strlen(fmt2, app->name);
+        char fileNm2[sz2+1]; // ensures no buffer overflow
+        snprintf(fileNm2, sizeof fileNm2, fmt2, app->name);
+
+        if (rank == 0) {
+          if (app->field->is_first_apar_energy_dot_write_call) {
+            // Write to a new file (this ensure previous output is removed).
+            gkyl_dynvec_write(app->field->integ_apar_energy_dot, fileNm2);
+            app->field->is_first_apar_energy_dot_write_call = false;
+          }
+          else {
+            // Append to existing file.
+            gkyl_dynvec_awrite(app->field->integ_apar_energy_dot, fileNm2);
+          }
+          app->stat.n_field_diag_io += 1;
+        }
+        gkyl_dynvec_clear(app->field->integ_apar_energy_dot);
+      }
     }
 
     app->stat.field_diag_io_tm += gkyl_time_diff_now_sec(wtm);
@@ -2716,6 +2747,7 @@ gkyl_gyrokinetic_app_from_frame_field(gkyl_gyrokinetic_app *app, int frame)
   struct gkyl_app_restart_status rstat = gkyl_gyrokinetic_app_from_file_field(app, fileNm.str);
   app->field->is_first_energy_write_call = false; // Append to existing diagnostic.
   app->field->is_first_energy_dot_write_call = false; // Append to existing diagnostic.
+  app->field->is_first_apar_energy_dot_write_call = false; // Append to existing diagnostic.
   cstr_drop(&fileNm);
   
   return rstat;
@@ -2858,6 +2890,7 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
   }
   app->field->is_first_energy_write_call = false; // Append to existing diagnostic.
   app->field->is_first_energy_dot_write_call = false; // Append to existing diagnostic.
+  app->field->is_first_apar_energy_dot_write_call = false; // Append to existing diagnostic.
   return rstat;
 }
 
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index f1df287b23..5fbbc575db 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -122,6 +122,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
 
         // Compute field energy divided by dt for energy balance diagnostics.
         gk_field_calc_energy_dt(app, app->field, dt, app->field->em_energy_red_old);
+        gk_field_calc_apar_energy_dt(app, app->field, dt, app->field->apar_energy_red_old);
 
         // Compute the fields and apply BCs.
         gyrokinetic_calc_field_and_apply_bc(app, tcurr, fout, bflux_out, fout_neut);
@@ -315,6 +316,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
 
           // Compute field energy divided by dt for energy balance diagnostics.
           gk_field_calc_energy_dt(app, app->field, dt, app->field->em_energy_red_new);
+          gk_field_calc_apar_energy_dt(app, app->field, dt, app->field->apar_energy_red_new);
 
           state = RK_COMPLETE;
         }

From 5f1f9dab4020bc16b804eb0e711b0d79e12a11ef Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 12:01:56 -0500
Subject: [PATCH 058/181] We accumulate the helmholtz constant for the Ohm
 solve just before solving Ohm. Before it was computed at the same time as the
 charge density (more optimized but not sure about program flow).

---
 gyrokinetic/apps/gk_field.c              | 76 ++++++++++++++++++------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  7 ++-
 gyrokinetic/apps/gyrokinetic.c           |  2 +-
 3 files changed, 65 insertions(+), 20 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 9dfd837eef..c34640e789 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -155,6 +155,30 @@ gk_field_accumulate_current_dens_dot_none(gkyl_gyrokinetic_app *app, struct gk_f
 {
 }
 
+static void
+gk_field_accumulate_ohms_kSq_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    gk_species_moment_calc(&s->m0, s->local, app->local, fin[i]);
+    // Gyroaverage the density if needed.
+    s->gyroaverage(app, s, s->m0.marr, s->m0_gyroavg);
+    // Use m0 to update also update the kSq matrix for the Ohm's law solver.
+    double fac = s->info.charge*s->info.charge/s->info.mass;
+    gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
+  }
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void
+gk_field_accumulate_ohms_kSq_none(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+}
+
 static void
 gk_field_accumulate_current_dens_dot_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, 
   struct gkyl_array *rhs_in[])
@@ -205,8 +229,10 @@ static void
 gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
 
-  // Compute the new dApartdtSlvr_kSq (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
-  gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
+  // Compute the LHS factor (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
+  // gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
+  gkyl_array_clear(field->dApartdtSlvr_lhs_factor, 0.0);
+  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq, &app->local);
   gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
 
   // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )
@@ -214,6 +240,13 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
     0, field->dApartdtSlvr_lhs_factor, &app->local);
   
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+
+  // // Smooth apardot
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->apardot, field->rho_c_global_dg);
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
+  // gkyl_array_copy_range_to_range(field->apardot, field->apar_fem, &app->local, &field->global_sub_range);
+  
 }
 
 static void 
@@ -233,12 +266,17 @@ static void
 gk_field_ampere_solve_1x(gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
 
-  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDens, field->currentDens_global);
 
-  gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->currentDens_global, field->currentDens_global);
-  gkyl_fem_parproj_solve(field->fem_apar_parproj, field->phi_fem);
+  // Weak division method Apar = sum_s q_s int dv vpar F_s / (k_perp^2/mu_0)
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apar, 0, field->currentDens, 
+    0, field->lapWeightAmpere, &app->local);
+  
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDens, field->currentDens_global);
+
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->currentDens_global, field->currentDens_global);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->phi_fem);
 
-  gkyl_array_copy_range_to_range(field->apar, field->phi_fem, &app->local, &field->global_sub_range);
+  // gkyl_array_copy_range_to_range(field->apar, field->phi_fem, &app->local, &field->global_sub_range);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -260,6 +298,7 @@ gk_field_step_apar_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, struct
   // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
   // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
   // gkyl_array_copy_range_to_range(out, field->apar_fem, &app->local, &field->global_sub_range);
+  
 }
 
 static void
@@ -652,12 +691,13 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->ampere_solve = gk_field_ampere_solve_none;
   f->accumulate_current = gk_field_accumulate_current_dens_none;
   f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_none;
+  f->accumulate_ohms_kSq = gk_field_accumulate_ohms_kSq_none;
   f->step_apar = gk_field_step_apar_none;
   f->combine_func = gk_field_combine_static;
   f->copy_func = gk_field_copy_range_static;
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  f->apar_curr = f->apar;
+  f->apar_curr = gkyl_array_acquire(f->apar);
   f->div_mem = NULL;
   if (f->is_em) {
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
@@ -691,7 +731,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
         if (app->periodic_dirs[d] == app->cdim-1) f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_PERIODIC;
 
       f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
-        f->fem_parproj_ampere_bc, f->lapWeightAmpere, 0, app->use_gpu);
+        f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
 
       f->ohm_solve = gk_field_ohm_solve_1x;
       f->ampere_solve = gk_field_ampere_solve_1x;
@@ -736,6 +776,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     }
     f->accumulate_current = gk_field_accumulate_current_dens_dyn;
     f->accumulate_current_dot = gk_field_accumulate_current_dens_dot_dyn;
+    f->accumulate_ohms_kSq = gk_field_accumulate_ohms_kSq_dyn;
     f->step_apar = gk_field_step_apar_dyn;
     f->combine_func = gk_field_combine_dynamic;
     f->copy_func = gk_field_copy_range_dynamic;
@@ -838,8 +879,8 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
   const struct gkyl_array *fin[], struct gkyl_array **bflux[])
 {
   struct timespec wst = gkyl_wall_clock();
-  if (field->is_em)
-    gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
+  // if (field->is_em)
+  //   gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
   gkyl_array_clear(field->rho_c, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
@@ -871,11 +912,11 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
         double dg_norm = pow(sqrt(2),app->basis.ndim);
         gkyl_array_shiftc_range(field->rho_c, q_s*n_s0*dg_norm, 0, &app->local);
       }
-      if (field->is_em) {
-        // Use m0 to update also update the kSq matrix for the Ohm's law solver.
-        double fac = s->info.charge*s->info.charge/s->info.mass;
-        gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
-      }
+      // if (field->is_em) {
+      //   // Use m0 to update also update the kSq matrix for the Ohm's law solver.
+      //   double fac = s->info.charge*s->info.charge/s->info.mass;
+      //   gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
+      // }
     }
   } 
   app->stat.field_phi_rhs_tm += gkyl_time_diff_now_sec(wst);
@@ -1027,9 +1068,10 @@ gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
 }
 
 void
-gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[])
+gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
 {
   struct timespec wst = gkyl_wall_clock();
+  field->accumulate_ohms_kSq(app, field, f_in);
   field->accumulate_current_dot(app, field, rhs_in);
   field->ohm_solve(app, field);
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
@@ -1215,8 +1257,8 @@ gk_field_release(const gkyl_gyrokinetic_app* app, struct gk_field *f)
   // We need at least these two arrays even in ES case (kept 0).
   gkyl_array_release(f->apar);
   gkyl_array_release(f->apardot);
-  gkyl_array_release(f->apar_curr);
   if (f->is_em) {
+    gkyl_array_release(f->apar_curr);
     gkyl_array_release(f->apar);
     gkyl_array_release(f->apar1);
     gkyl_array_release(f->aparnew);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 6f09f1e40c..16a857e486 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1175,7 +1175,7 @@ struct gk_field {
       struct gkyl_array *dApartdtSlvr_lhs_factor; // Contains kperp^2/mu_0 + sum_s q_s^2/m_s n_s for 1D Ohm solve.
       struct gkyl_array *dApartdtSlvr_rhs; // Contains sum_s q_s int dv vpar d/dt(F_s)*.
       gkyl_dg_bin_op_mem *div_mem; // Memory for div operation in 1x Ohm's law. 
-      struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0).
+      struct gkyl_array *lapWeightAmpere; // Factor in front of the laplacian operator (1/mu0 or kperp^2/mu0 for 1D).
       struct gkyl_fem_parproj *fem_apar_parproj; // FEM smoother for projecting Apar onto continuous FEM basis
       struct gkyl_fem_poisson_perp *fem_apar_solver; // Solver for IC Apar.
       struct gkyl_fem_poisson_perp *fem_apardot_solver; // Solver for d(Apar)/dt.
@@ -1250,6 +1250,8 @@ struct gk_field {
   // Pointer to function for electromagnetic field solve.
   void (*accumulate_current) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
     const struct gkyl_array *fin[]);
+  void (*accumulate_ohms_kSq) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
+    const struct gkyl_array *fin[]);
   void (*accumulate_current_dot) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
     struct gkyl_array *rhs_in[]);
   void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
@@ -3755,9 +3757,10 @@ void gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field);
  *
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
+ * @param fin[] Input distribution function (num_species size).
  * @param rhs_in[] right-hand side of the ES GK equation for each species.
  */
-void gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *rhs_in[]);
+void gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[], struct gkyl_array *rhs_in[]);
 
 /**
  * Read the field from a file.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 86efae21ed..8ff19c0bee 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1817,7 +1817,7 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   }
 
   // Compute Apardot (solves Ohm's law using the previously built RHS).
-  gk_field_em_rhs(app, app->field, fout);
+  gk_field_em_rhs(app, app->field, fin, fout);
   // Update aparout.
   gk_field_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
 

From ea235781a75a3a7c5c2798b638ec08c5fe6a40c9 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 10:18:23 -0800
Subject: [PATCH 059/181] apar_curr is now allocated as a normal gkyl array and
 we copy the current apar in the RK stages. I think this is not optimal, but
 it is safer than changing the pointer address for now.

---
 gyrokinetic/apps/gk_field.c                   | 2 +-
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index c34640e789..c669390637 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -697,7 +697,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->copy_func = gk_field_copy_range_static;
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  f->apar_curr = gkyl_array_acquire(f->apar);
+  f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->div_mem = NULL;
   if (f->is_em) {
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index 5fbbc575db..f6dd5b911e 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -79,7 +79,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar;
         aparout = app->field->apar1;
-        app->field->apar_curr = app->field->apar; // This is the A_parallel used in the species gyro_apar.
+        gkyl_array_copy_range(app->field->apar_curr, app->field->apar, &app->local); // Update apar_curr to latest A_parallel.
         for (int i=0; i<app->num_neut_species; ++i) {
           struct gk_neut_species *gkns = &app->neut_species[i];
           fin_neut[i] = gkns->f;
@@ -149,7 +149,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        app->field->apar_curr = app->field->apar1; // This is the A_parallel used in the species gyro_apar.
+        gkyl_array_copy_range(app->field->apar_curr, app->field->apar1, &app->local); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -225,7 +225,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        app->field->apar_curr = app->field->apar1; // This is the A_parallel used in the species gyro_apar.
+        gkyl_array_copy_range(app->field->apar_curr, app->field->apar1, &app->local); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);

From 3346a44300150f9308698a92d18868acfd9b8c23 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 14:58:08 -0500
Subject: [PATCH 060/181] clean unused code. This code can retrieve the
 frequencies measured in Mandell's thesis with three important caveats: -the
 frequencies at small ky are incorrect if we use static ions - I had to reduce
 vparmax and Nz to delay the recurrence effects for beta=10.0in order to
 measure at least two peaks. - The damping rates are not retrieve very
 accurately for kyrho_s<0.1, I guess we have to play with resolution to get it
 right.

---
 gyrokinetic/apps/gk_field.c | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index c669390637..bdcfbc907e 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -879,8 +879,6 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
   const struct gkyl_array *fin[], struct gkyl_array **bflux[])
 {
   struct timespec wst = gkyl_wall_clock();
-  // if (field->is_em)
-  //   gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
   gkyl_array_clear(field->rho_c, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
@@ -912,11 +910,6 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
         double dg_norm = pow(sqrt(2),app->basis.ndim);
         gkyl_array_shiftc_range(field->rho_c, q_s*n_s0*dg_norm, 0, &app->local);
       }
-      // if (field->is_em) {
-      //   // Use m0 to update also update the kSq matrix for the Ohm's law solver.
-      //   double fac = s->info.charge*s->info.charge/s->info.mass;
-      //   gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
-      // }
     }
   } 
   app->stat.field_phi_rhs_tm += gkyl_time_diff_now_sec(wst);

From 04b132a336ee283f3236ef0840d8ff77d9eb0e9a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 12:12:26 -0800
Subject: [PATCH 061/181] update alfven wave reg test. This commit is multi GPU
 compute-sanitize clean for this version of the alfven regression test.

---
 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c | 149 ++++++++++++++++++---
 1 file changed, 127 insertions(+), 22 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
index 2856df023f..48cd1f09e3 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
@@ -25,6 +25,7 @@ struct gk_app_ctx {
   double z_min;  double z_max;
 
   double kperp;  // Perpendicular wavenumber.
+  double beta_hat; // Plasma beta parameter.
 
   // Plasma parameters.
   double me;  double qe;
@@ -82,6 +83,30 @@ void temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT f
   fout[0] = app->Te0;
 }
 
+// Electron source profiles.
+void density_src(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 1e-40;
+}
+void upar_elc_src(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_elc_src(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+
+// Ion source profiles.
+void upar_ion_src(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_ion_src(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+
 // Slab magnetic equilibrium.
 static inline void
 mapc2p(double t, const double* xc, double* GKYL_RESTRICT xp, void* ctx)
@@ -98,6 +123,54 @@ void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *c
   fout[2] = app->B;
 }
 
+void
+write_ctx_to_json(const struct gk_app_ctx *ctx)
+{
+  FILE *fp = fopen("ctx.json", "w");
+  if (!fp) {
+    perror("Error opening file for writing context");
+    return;
+  }
+
+  fprintf(fp, "{\n");
+  fprintf(fp, "  \"cdim\": %d,\n", ctx->cdim);
+  fprintf(fp, "  \"vdim\": %d,\n", ctx->vdim);
+  fprintf(fp, "  \"mu0\": %e,\n", ctx->mu0);
+  fprintf(fp, "  \"R\": %e,\n", ctx->R);
+  fprintf(fp, "  \"a\": %e,\n", ctx->a);
+  fprintf(fp, "  \"r\": %e,\n", ctx->r);
+  fprintf(fp, "  \"B\": %e,\n", ctx->B);
+  fprintf(fp, "  \"z_min\": %e,\n", ctx->z_min);
+  fprintf(fp, "  \"z_max\": %e,\n", ctx->z_max);
+  fprintf(fp, "  \"kperp\": %e,\n", ctx->kperp);
+  fprintf(fp, "  \"beta_hat\": %e,\n", ctx->beta_hat);
+  fprintf(fp, "  \"me\": %e,\n", ctx->me);
+  fprintf(fp, "  \"qe\": %e,\n", ctx->qe);
+  fprintf(fp, "  \"mi\": %e,\n", ctx->mi);
+  fprintf(fp, "  \"qi\": %e,\n", ctx->qi);
+  fprintf(fp, "  \"n0\": %e,\n", ctx->n0);
+  fprintf(fp, "  \"Te0\": %e,\n", ctx->Te0);
+  fprintf(fp, "  \"Ti0\": %e,\n", ctx->Ti0);
+  fprintf(fp, "  \"kz_min\": %e,\n", ctx->kz_min);
+  fprintf(fp, "  \"Nz\": %d,\n", ctx->Nz);
+  fprintf(fp, "  \"Nvpar\": %d,\n", ctx->Nvpar);
+  fprintf(fp, "  \"Nmu\": %d,\n", ctx->Nmu);
+  fprintf(fp, "  \"poly_order\": %d,\n", ctx->poly_order);
+  fprintf(fp, "  \"vpar_max_elc\": %e,\n", ctx->vpar_max_elc);
+  fprintf(fp, "  \"mu_max_elc\": %e,\n", ctx->mu_max_elc);
+  fprintf(fp, "  \"vpar_max_ion\": %e,\n", ctx->vpar_max_ion);
+  fprintf(fp, "  \"mu_max_ion\": %e,\n", ctx->mu_max_ion);
+  fprintf(fp, "  \"t_end\": %e,\n", ctx->t_end);
+  fprintf(fp, "  \"num_frames\": %d,\n", ctx->num_frames);
+  fprintf(fp, "  \"write_phase_freq\": %e,\n", ctx->write_phase_freq);
+  fprintf(fp, "  \"int_diag_calc_num\": %d,\n", ctx->int_diag_calc_num);
+  fprintf(fp, "  \"dt_failure_tol\": %e,\n", ctx->dt_failure_tol);
+  fprintf(fp, "  \"num_failures_max\": %d\n", ctx->num_failures_max);
+  fprintf(fp, "}\n");
+
+  fclose(fp);
+}
+
 struct gk_app_ctx
 create_ctx(void)
 {
@@ -107,7 +180,7 @@ create_ctx(void)
   double qi = eV; // ion charge
   double qe = -eV; // electron charge
   double me = GKYL_ELECTRON_MASS;
-  double mp = GKYL_PROTON_MASS;
+  double mi = 2*GKYL_PROTON_MASS;
   double mu0 = GKYL_MU0;
   // Geometry, magnetic field and gradients.
   double R0 = 1.313; // Major radius of the simulation box [m].
@@ -115,12 +188,13 @@ create_ctx(void)
   double B0 = 1.91; // Magnetic field magnitude in the simulation box [T].
   double Ti0 = 2072*eV;
   double eps_n = 0.2;
-  // double eta_e = 2.0; // Comes from rt-alfven-p1.lua but unused.
-  // double eta_i = 2.5; // Comes from rt-alfven-p1.lua but unused.
-  double ky_rhos = 0.01;
   double kz_Ln = 1.0;
-  double beta_hat = 10.0; // beta_e/2*m_p/m_e.
-  double beta_e = beta_hat*2.0*me/mp;
+
+  double beta_hat = 0.1; // gkylscan can parameter.
+  double ky_rhos = 0.5; // gkylscan can parameter.
+  double nperiod = 5.0;
+
+  double beta_e = beta_hat*2.0*me/mi;
   double tau = 1.0; // Ti/Te.
   // Derived paramters.
   double r0 = 0.5*a; // Minor radius of the simulation box [m].
@@ -129,16 +203,19 @@ create_ctx(void)
   double Te0 = Ti0/tau; // Electron temperature [J].
   double n0 = beta_e*B*B/(2*mu0*Te0); // Density [m^-3].
   double vte = sqrt(Te0/me); // Electron thermal speed [m/s].
-  double vti = sqrt(Ti0/mp); // Ion thermal speed [m/s].
-  double c_s = sqrt(Te0/mp); // Sound speed [m/s].
-  double omega_ci = fabs(qi*B/mp); // Ion cyclotron frequency [rad/s].
+  double vti = sqrt(Ti0/mi); // Ion thermal speed [m/s].
+  double c_s = sqrt(Te0/mi); // Sound speed [m/s].
+  double omega_ci = fabs(qi*B/mi); // Ion cyclotron frequency [rad/s].
   double rho_s = c_s/omega_ci; // Ion sound gyroradius [m
   double ky_min = ky_rhos/rho_s; // Minimum perpendicular wavenumber [1/m].
   double L_n = R*eps_n; // Density gradient scale length [m].
   double kz_min = kz_Ln/L_n; // Minimum parallel wavenumber [1/m].
-  double L_parallel = 2*M_PI/kz_min; // Domain size in z [m].
   // Expected frequency from dispersion relation:
-  double omega = kz_min*c_s*sqrt(2/beta_e/(1+beta_hat*pow(ky_rhos,2)));
+  // double omega = kz_min*c_s*sqrt(2/beta_e/(1+beta_hat*pow(ky_rhos,2)));
+  double va = vte/sqrt(beta_hat); // Alfvén speed [m/s].
+  // double omega = kz_min*va; // Shear Alfvén wave frequency [rad/s].
+  double omega = sqrt(pow(kz_min*va,2)/(1+beta_hat*pow(ky_rhos,2))); // KAW frequency [rad/s].
+  // double omega = sqrt(pow(kz_min,2)*2/beta_e*pow(c_s,2)/(1+beta_hat*pow(ky_rhos,2)));
 
   // Velocity grid parameters.
   double vpar_max_elc = 6.0*vte; // Max electron parallel velocity [m/s].
@@ -146,18 +223,18 @@ create_ctx(void)
   double vpar_max_ion = 6.0*vti; // Max ion parallel velocity [m/s].
   double vpar_min_ion = -vpar_max_ion; // Min ion parallel
   double mu_max_elc = me*pow(4*vte,2)/(2*B); // Max electron mu [J/T].
-  double mu_max_ion = mp*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
+  double mu_max_ion = mi*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
 
   // Grid parameters
-  int Nz = 8;
-  int Nvpar = 8;
-  int Nmu = 6;
+  int Nz = 8; // Reduce this to delay recurrence effect.
+  int Nvpar = 32; // Increase this to delay recurrence effect.
+  int Nmu = 1; // useless
   int poly_order = 1;
 
-  double t_end = 2*M_PI/omega; // End time [s].
-  int num_frames = 1;
-  double write_phase_freq = 0.1; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
-  int int_diag_calc_num = num_frames*100;
+  double t_end = nperiod*2*M_PI/omega; // End time [s].
+  int num_frames = 100;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*1000;
   double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
   int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
 
@@ -167,13 +244,14 @@ create_ctx(void)
     .mu0 = mu0,
     .R = R,
     .B = B,
+    .beta_hat = beta_hat,
     .z_min = -M_PI/kz_min,  .z_max = M_PI/kz_min,
   
     .kperp = ky_min,
     .kz_min = kz_min,
   
     .me = me,  .qe = qe,
-    .mi = mp,  .qi = qi,
+    .mi = mi,  .qi = qi,
     .n0 = n0,  .Te0 = Te0,  .Ti0 = Ti0,
     
     .Nz = Nz,
@@ -193,7 +271,6 @@ create_ctx(void)
   return ctx;
 }
 
-
 int main(int argc, char **argv)
 {
   struct gkyl_app_args app_args = parse_app_args(argc, argv);
@@ -250,11 +327,18 @@ int main(int argc, char **argv)
     .num_integrated_diag_moments = 1,
     .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
     .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
   };
 
   // Ions.
   struct gkyl_gyrokinetic_species ion = {
     .name = "ion",
+    .is_static = false,
     .charge = ctx.qi, .mass = ctx.mi,
     .vdim = ctx.vdim,
     .lower = { -ctx.vpar_max_ion, 0.0},
@@ -273,7 +357,9 @@ int main(int argc, char **argv)
       .temp = temp_ion,      
     },
 
-    .is_static = true,
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
     
     .num_diag_moments = 9,
     .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
@@ -282,17 +368,34 @@ int main(int argc, char **argv)
     .num_integrated_diag_moments = 1,
     .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
     .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
   };
 
   // field
   struct gkyl_gyrokinetic_field field = {
     .kperpSq = ctx.kperp * ctx.kperp,
     .mu0 = ctx.mu0,
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_PERIODIC, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_PERIODIC, },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_PERIODIC, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_PERIODIC, },
+    },
+    .time_rate_diagnostics = true,
   };
 
   // GK app
   struct gkyl_gk app_inp = {
     .name = "gk_em_alfven_1x2v_p1",
+    .cfl_frac = 1.0,
+    .cfl_frac_omegaH = 1.0,
 
     .cdim = ctx.cdim,
     .lower = { ctx.z_min },
@@ -339,6 +442,8 @@ int main(int argc, char **argv)
     },
   };
 
+  write_ctx_to_json(&ctx);
+
   gkyl_gyrokinetic_run_simulation(&run_inp);
 
   gkyl_gyrokinetic_comms_release(comm);

From 331ec9f6287a8e0f728a3b7761c1f82363b35e9f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 16:31:45 -0500
Subject: [PATCH 062/181] reduction of the rt alfven 1x2v frame number to 1

---
 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
index 48cd1f09e3..74e5e59bbe 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
@@ -232,9 +232,9 @@ create_ctx(void)
   int poly_order = 1;
 
   double t_end = nperiod*2*M_PI/omega; // End time [s].
-  int num_frames = 100;
+  int num_frames = 1;
   double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
-  int int_diag_calc_num = num_frames*1000;
+  int int_diag_calc_num = num_frames*100;
   double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
   int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
 

From 1d15fd89a68c26ad16b2279694535838c9089ffd Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 8 Dec 2025 16:51:24 -0500
Subject: [PATCH 063/181] Reorganize the allocation for cdim>1 and use
 gk_field_copy_range to update apar_curr (so that it works in electrostatic
 limit)

---
 gyrokinetic/apps/gk_field.c                   | 2 +-
 gyrokinetic/apps/gk_species.c                 | 5 ++++-
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c | 6 +++---
 3 files changed, 8 insertions(+), 5 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index bdcfbc907e..987c9c9243 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -697,9 +697,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->copy_func = gk_field_copy_range_static;
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-  f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->div_mem = NULL;
   if (f->is_em) {
+    f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 91822b6b5f..66d3020803 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1586,7 +1586,10 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   }
 
   // We do not have FLR effects for EM yet.
-  gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_ES)
+    gks->gyro_apar = gkyl_array_acquire(app->field->apar);
+  else
+    gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);
   gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
 
   // Initialize the collisionless solver.
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index f6dd5b911e..2b6520e7bc 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -79,7 +79,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar;
         aparout = app->field->apar1;
-        gkyl_array_copy_range(app->field->apar_curr, app->field->apar, &app->local); // Update apar_curr to latest A_parallel.
+        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar, &app->local_ext); // Update apar_curr to latest A_parallel.
         for (int i=0; i<app->num_neut_species; ++i) {
           struct gk_neut_species *gkns = &app->neut_species[i];
           fin_neut[i] = gkns->f;
@@ -149,7 +149,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        gkyl_array_copy_range(app->field->apar_curr, app->field->apar1, &app->local); // Update apar_curr to latest A_parallel.
+        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -225,7 +225,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        gkyl_array_copy_range(app->field->apar_curr, app->field->apar1, &app->local); // Update apar_curr to latest A_parallel.
+        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);

From 4d65045aa804b6d41b8441637e5357b520bade0a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 9 Dec 2025 11:25:58 -0800
Subject: [PATCH 064/181] Bug fix: the new metric variables used in 2x2v EM
 kernels were not set properly, thanks @akashukla !

---
 gyrokinetic/zero/calc_metric.c | 2 ++
 gyrokinetic/zero/gk_geometry.c | 2 +-
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/gyrokinetic/zero/calc_metric.c b/gyrokinetic/zero/calc_metric.c
index cc588bfcaa..a1c3a05577 100644
--- a/gyrokinetic/zero/calc_metric.c
+++ b/gyrokinetic/zero/calc_metric.c
@@ -1277,6 +1277,8 @@ void gkyl_calc_metric_advance_interior(gkyl_calc_metric *up, struct gk_geometry
 
          double Jsq = gFld_n[0]*(gFld_n[3]*gFld_n[5] - gFld_n[4]*gFld_n[4] ) - gFld_n[1]*(gFld_n[1]*gFld_n[5] - gFld_n[4]*gFld_n[2] ) + gFld_n[2]*(gFld_n[1]*gFld_n[4] - gFld_n[3]*gFld_n[2] );
          double J = sqrt(Jsq);
+         double *jFld_n= gkyl_array_fetch(gk_geom->geo_int.jacobgeo_nodal, gkyl_range_idx(&gk_geom->nrange_int, cidx));
+         jFld_n[0] = J;
          double e_1[3], e_2[3], e_3[3];
          e_1[0] = dxdz[0][0]; e_1[1] = dxdz[1][0]; e_1[2] = dxdz[2][0];
          e_2[0] = dxdz[0][1]; e_2[1] = dxdz[1][1]; e_2[2] = dxdz[2][1];
diff --git a/gyrokinetic/zero/gk_geometry.c b/gyrokinetic/zero/gk_geometry.c
index 3a7ce6716b..850cc9efb9 100644
--- a/gyrokinetic/zero/gk_geometry.c
+++ b/gyrokinetic/zero/gk_geometry.c
@@ -373,7 +373,7 @@ gkyl_gk_geometry_deflate(const struct gk_geometry* up_3d, struct gkyl_gk_geometr
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.B3_nodal, up->geo_int.B3_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.bmag_nodal, up->geo_int.bmag_nodal, 1);
   gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.dualcurlbhat_nodal, up->geo_int.dualcurlbhat_nodal, 3);
-  gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.g_ij_nodal, up->geo_int.g_ij_nodal, 3);
+  gkyl_deflate_geo_advance_nodal(deflator, &up_3d->nrange_int, &up->nrange_int, up_3d->geo_int.g_ij_nodal, up->geo_int.g_ij_nodal, 6);
   gkyl_deflate_geo_release(deflator);
 
   if (up->grid.ndim==1) {

From 0e511ca5ba2643531c5a61d805e4324ad1e4028c Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 9 Dec 2025 15:33:31 -0500
Subject: [PATCH 065/181] indent correctly some lines for readability (I know
 this is already refactored in main...)

---
 gyrokinetic/apps/gk_field.c | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 987c9c9243..4cd9e8bfac 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -489,11 +489,10 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
             for (int i=0; i<3; i++)
               poisson_bcs.up_value[d].v[i] = bc_up->value[i];
           }
-        }
-	else {
+        } else {
           poisson_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
           poisson_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
-	}
+	      }
       }
       // Detect if this process contains an edge in the z dimension.
       // for applying bias at the extremal z planes only.

From 12f34ff42e0a4514c70ad17ef2bc0dc9556e8ba3 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 9 Dec 2025 15:57:16 -0500
Subject: [PATCH 066/181] ampere bc are now overwritten by periodicity as for
 the es field.

---
 gyrokinetic/apps/gk_field.c | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 4cd9e8bfac..4b201f06f5 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -215,6 +215,9 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
 
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
   gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
+
+  // gkyl_array_clear_range(field->apardot, 0.0, &app->local_ext);
+
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -293,6 +296,8 @@ gk_field_step_apar_dyn(gkyl_gyrokinetic_app *app, struct gk_field *field, struct
 {
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
 
+  // gkyl_array_clear_range(out, 0.0, &app->local_ext);
+
   // Smooth apar
   // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
   // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
@@ -744,18 +749,23 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
       // Translate input file BCs into Ampere BCs.
       for (int d=0; d<app->cdim-1; d++) {
-        struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
-        if (bc_lo != 0) {
-          f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
-          for (int i=0; i<3; i++)
-            f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
-        }
+        if (bc_is_np[d]) {
+          struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
+          if (bc_lo != 0) {
+            f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
+            for (int i=0; i<3; i++)
+              f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+          }
 
-        struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
-        if (bc_up != 0) {
-          f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
-          for (int i=0; i<3; i++)
-            f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+          struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
+          if (bc_up != 0) {
+            f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
+            for (int i=0; i<3; i++)
+              f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+          }
+        } else {
+          f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
+          f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
         }
       }
 

From 52ee2a06225f88d1331d03174b749a3a39fb8beb Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 10 Dec 2025 13:25:51 -0500
Subject: [PATCH 067/181] the definition of the lapWeightAmpere was not
 compatible with higher dimensionalities

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 4b201f06f5..3c17a406b9 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -717,7 +717,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
     f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->lapWeightAmpere = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->lapWeightAmpere = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
     f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
     if (app->cdim == 1) {

From 31218d92ee4762753f29a310f94a5ee236b7bc64 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 10 Dec 2025 17:24:55 -0500
Subject: [PATCH 068/181] add regression test for alfven wave 2x2v

---
 gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c | 450 +++++++++++++++++++++
 1 file changed, 450 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
new file mode 100644
index 0000000000..8f186a7c16
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
@@ -0,0 +1,450 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  double mu0;
+
+  // Geometry and magnetic field.
+  double R; // Major radius of the simulation box [m].
+  double a; // Minor radius at outboard midplane [m].
+  double r; // Minor radius of the simulation box [m].
+  double B; // Magnetic field magnitude in the simulation box [T].
+  double z_min;  double z_max;
+
+  double kperp;  // Perpendicular wavenumber.
+  double beta_hat; // Plasma beta parameter.
+
+  // Plasma parameters.
+  double me;  double qe;
+  double mi;  double qi;
+  double n0;  double Te0;  double Ti0; 
+
+  // Grid parameters.
+  double kz_min;
+  double x_min, x_max; // Min and max x-coordinates.
+  int Nx, Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc;  double mu_max_elc;
+  double vpar_max_ion;  double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Ion initial conditions.
+void density_init_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->n0;
+}
+void upar_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Ti0;
+}
+
+// Electron initial conditions.
+void density_init_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double z = xn[1];
+  fout[0] = app->n0 * (1 + 1e-6*cos(app->kz_min*z));
+}
+void upar_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Te0;
+}
+
+// Slab magnetic equilibrium.
+static inline void
+mapc2p(double t, const double* xc, double* GKYL_RESTRICT xp, void* ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xc[0], y = xc[1], z = xc[2];
+  xp[0] = x; xp[1] = y; xp[2] = z;
+}
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = 0.0;
+  fout[1] = 0.0;
+  fout[2] = app->B;
+}
+
+void
+write_ctx_to_json(const struct gk_app_ctx *ctx)
+{
+  FILE *fp = fopen("ctx.json", "w");
+  if (!fp) {
+    perror("Error opening file for writing context");
+    return;
+  }
+
+  fprintf(fp, "{\n");
+  fprintf(fp, "  \"cdim\": %d,\n", ctx->cdim);
+  fprintf(fp, "  \"vdim\": %d,\n", ctx->vdim);
+  fprintf(fp, "  \"mu0\": %e,\n", ctx->mu0);
+  fprintf(fp, "  \"R\": %e,\n", ctx->R);
+  fprintf(fp, "  \"a\": %e,\n", ctx->a);
+  fprintf(fp, "  \"r\": %e,\n", ctx->r);
+  fprintf(fp, "  \"B\": %e,\n", ctx->B);
+  fprintf(fp, "  \"z_min\": %e,\n", ctx->z_min);
+  fprintf(fp, "  \"z_max\": %e,\n", ctx->z_max);
+  fprintf(fp, "  \"kperp\": %e,\n", ctx->kperp);
+  fprintf(fp, "  \"beta_hat\": %e,\n", ctx->beta_hat);
+  fprintf(fp, "  \"me\": %e,\n", ctx->me);
+  fprintf(fp, "  \"qe\": %e,\n", ctx->qe);
+  fprintf(fp, "  \"mi\": %e,\n", ctx->mi);
+  fprintf(fp, "  \"qi\": %e,\n", ctx->qi);
+  fprintf(fp, "  \"n0\": %e,\n", ctx->n0);
+  fprintf(fp, "  \"Te0\": %e,\n", ctx->Te0);
+  fprintf(fp, "  \"Ti0\": %e,\n", ctx->Ti0);
+  fprintf(fp, "  \"kz_min\": %e,\n", ctx->kz_min);
+  fprintf(fp, "  \"Nz\": %d,\n", ctx->Nz);
+  fprintf(fp, "  \"Nvpar\": %d,\n", ctx->Nvpar);
+  fprintf(fp, "  \"Nmu\": %d,\n", ctx->Nmu);
+  fprintf(fp, "  \"poly_order\": %d,\n", ctx->poly_order);
+  fprintf(fp, "  \"vpar_max_elc\": %e,\n", ctx->vpar_max_elc);
+  fprintf(fp, "  \"mu_max_elc\": %e,\n", ctx->mu_max_elc);
+  fprintf(fp, "  \"vpar_max_ion\": %e,\n", ctx->vpar_max_ion);
+  fprintf(fp, "  \"mu_max_ion\": %e,\n", ctx->mu_max_ion);
+  fprintf(fp, "  \"t_end\": %e,\n", ctx->t_end);
+  fprintf(fp, "  \"num_frames\": %d,\n", ctx->num_frames);
+  fprintf(fp, "  \"write_phase_freq\": %e,\n", ctx->write_phase_freq);
+  fprintf(fp, "  \"int_diag_calc_num\": %d,\n", ctx->int_diag_calc_num);
+  fprintf(fp, "  \"dt_failure_tol\": %e,\n", ctx->dt_failure_tol);
+  fprintf(fp, "  \"num_failures_max\": %d\n", ctx->num_failures_max);
+  fprintf(fp, "}\n");
+
+  fclose(fp);
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 2, vdim = 2; // Dimensionality.
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+  double me = GKYL_ELECTRON_MASS;
+  double mi = 2*GKYL_PROTON_MASS;
+  double mu0 = GKYL_MU0;
+  // Geometry, magnetic field and gradients.
+  double R0 = 1.313; // Major radius of the simulation box [m].
+  double a = 0.4701; // Minor radius at outboard midplane [m].
+  double B0 = 1.91; // Magnetic field magnitude in the simulation box [T].
+  double Ti0 = 2072*eV;
+  double eps_n = 0.2;
+  double kz_Ln = 1.0;
+
+  double beta_hat = 0.1; // gkylscan can parameter.
+  double kperp_rhos = 0.5; // gkylscan can parameter.
+  double nperiod = 3.0;
+
+  double beta_e = beta_hat*2.0*me/mi;
+  double tau = 1.0; // Ti/Te.
+  // Derived paramters.
+  double r0 = 0.5*a; // Minor radius of the simulation box [m].
+  double R = R0 + r0; // Major radius at center of simulation box [m].
+  double B = B0 * R0/R; // Magnetic field at center of simulation box [T].
+  double Te0 = Ti0/tau; // Electron temperature [J].
+  double n0 = beta_e*B*B/(2*mu0*Te0); // Density [m^-3].
+  double vte = sqrt(Te0/me); // Electron thermal speed [m/s].
+  double vti = sqrt(Ti0/mi); // Ion thermal speed [m/s].
+  double c_s = sqrt(Te0/mi); // Sound speed [m/s].
+  double omega_ci = fabs(qi*B/mi); // Ion cyclotron frequency [rad/s].
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius [m]
+  double L_n = R*eps_n; // Density gradient scale length [m].
+  double kz_min = kz_Ln/L_n; // Minimum parallel wavenumber [1/m].
+  // Expected frequency from dispersion relation:
+  // double omega = kz_min*c_s*sqrt(2/beta_e/(1+beta_hat*pow(ky_rhos,2)));
+  double va = vte/sqrt(beta_hat); // Alfvén speed [m/s].
+  // double omega = kz_min*va; // Shear Alfvén wave frequency [rad/s].
+  double omega = sqrt(pow(kz_min*va,2)/(1+beta_hat*pow(kperp_rhos,2))); // KAW frequency [rad/s].
+  // double omega = sqrt(pow(kz_min,2)*2/beta_e*pow(c_s,2)/(1+beta_hat*pow(ky_rhos,2)));
+  
+  double kperp = kperp_rhos/rho_s; // Minimum perpendicular wavenumber [1/m].
+  double Lx = M_PI/kperp; // Domain length in x-direction [m].
+
+  // Grid parameters
+  int Nz = 12; // Reduce this to delay recurrence effect.
+  double z_min = -M_PI/kz_min;  // Min z-coordinate [m].
+  double z_max = M_PI/kz_min;   // Max z-coordinate [m].
+  int Nvpar = 16; // Increase this to delay recurrence effect.
+  double vpar_max_elc = 5.0*vte; // Max electron parallel velocity [m/s].
+  double vpar_min_elc = -vpar_max_elc; // Min electron parallel velocity [m/s].
+  double vpar_max_ion = 5.0*vti; // Max ion parallel velocity [m/s].
+  double vpar_min_ion = -vpar_max_ion; // Min ion parallel
+  // The x and mu directions are not playing a role in the dynamics.
+  int Nx = 16; // Number of cells in x-direction.
+  double x_min = -Lx/2;
+  double x_max = Lx/2;
+  int Nmu = 2;
+  double mu_max_elc = me*pow(4*vte,2)/(2*B); // Max electron mu [J/T].
+  double mu_max_ion = mi*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
+  int poly_order = 1;
+
+  double t_end = nperiod*2*M_PI/omega; // End time [s].
+  int num_frames = 1;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*1000;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .mu0 = mu0,
+    .R = R,
+    .B = B,
+    .beta_hat = beta_hat,
+    .me = me,  .qe = qe,
+    .mi = mi,  .qi = qi,
+    .n0 = n0,  .Te0 = Te0,  .Ti0 = Ti0,
+
+    .Nx = Nx,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .x_min = x_min,
+    .x_max = x_max,
+    .z_min = z_min,
+    .z_max = z_max,
+    .kperp = kperp,
+    .kz_min = kz_min,
+    .vpar_max_elc = vpar_max_elc,  .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion,  .mu_max_ion = mu_max_ion,
+    .cells = {Nx, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+
+    .t_end = t_end,  .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+int main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // Electrons.
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_elc, 0.0},
+    .upper = {  ctx.vpar_max_elc, ctx.mu_max_elc}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_elc,
+      .ctx_upar = &ctx,
+      .upar= upar_elc,
+      .ctx_temp = &ctx,
+      .temp = temp_elc,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+    },
+
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Ions.
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .is_static = false,
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = {  ctx.vpar_max_ion, ctx.mu_max_ion}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_ion,
+      .ctx_upar = &ctx,
+      .upar= upar_ion,
+      .ctx_temp = &ctx,
+      .temp = temp_ion,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+    },
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Field.
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .mu0 = ctx.mu0,
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .name = "gk_em_alfven_2x2v_p1",
+    .cfl_frac = 1.0,
+    .cfl_frac_omegaH = 1.0,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx
+    },
+
+    .num_periodic_dir = 1,
+    .periodic_dirs = {1},
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .cuts = { app_args.cuts[0], app_args.cuts[1] },
+      .comm = comm,
+    },
+  };
+
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  write_ctx_to_json(&ctx);
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+  return 0;
+}

From 1bb5ceebf1ef66c5f81113561145e982f71392be Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 22 Dec 2025 11:42:39 -0500
Subject: [PATCH 069/181] The EM terms are now implemented with the latest gk
 field refactor. 1x2v and 2x2v em testcases are leak clean on CPU. will test
 GPU and MPI more thoroughly on Perlmutter.

---
 gyrokinetic/apps/gk_field.c                 | 281 +++++++++++++++++++-
 gyrokinetic/apps/gk_field_1x.c              | 139 +++++++++-
 gyrokinetic/apps/gk_field_2x3x.c            | 141 +++++++++-
 gyrokinetic/apps/gk_species.c               | 133 ++++++---
 gyrokinetic/apps/gk_species_collisionless.c |  67 ++++-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h    |  24 ++
 gyrokinetic/apps/gyrokinetic.c              |  66 ++++-
 7 files changed, 786 insertions(+), 65 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 81064610d9..06eb6e8fdb 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -68,9 +68,19 @@ gk_field_calc_energy_dt_active(gkyl_gyrokinetic_app *app, const struct gk_field
   app->stat.phidot_tm += gkyl_time_diff_now_sec(wst);
 }
 
+static void
+gk_field_calc_apar_energy_dt_active(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_integrate_advance(field->calc_em_energy, field->apar, 
+    1.0/dt, field->apar_energy_fac, &app->local, &app->local, energy_reduced);
+  app->stat.phidot_tm += gkyl_time_diff_now_sec(wst);
+}
+
 static void
 gk_field_calc_energy_dt_none(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
 {
+  // Do nothing.
 }
 
 static void
@@ -122,6 +132,67 @@ gk_field_calc_energy_enabled(struct gkyl_gyrokinetic_app *app, const struct gk_f
 
     gkyl_dynvec_append(field->integ_energy_dot, tm, energy_dot_global);
   }
+
+  if (field->is_em) {
+    // Calculate Aparallel energy.
+    gkyl_array_integrate_advance(field->calc_em_energy, field->apar, 
+      1.0, field->apar_energy_fac, &app->local, &app->local, field->em_energy_red);
+
+    gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->em_energy_red, field->em_energy_red_global);
+
+    double energy_global[1] = { 0.0 };
+    if (app->use_gpu)
+      gkyl_cu_memcpy(energy_global, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+    else
+      energy_global[0] = field->em_energy_red_global[0];
+
+    if (app->cdim == 1)
+      energy_global[0] *= field->apar_energy_fac_1d; 
+
+    gkyl_dynvec_append(field->integ_apar_energy, tm, energy_global);
+    
+    // Calculate d(Aparallel)/dt energy.
+    gkyl_array_integrate_advance(field->calc_em_energy, field->apardot, 
+      1.0, field->apar_energy_fac, &app->local, &app->local, field->em_energy_red);
+
+    gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->em_energy_red, field->em_energy_red_global);
+
+    double energy_dot_global[1] = { 0.0 };
+    if (app->use_gpu)
+      gkyl_cu_memcpy(energy_dot_global, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+    else
+      energy_dot_global[0] = field->em_energy_red_global[0];
+    
+    // if (app->cdim == 1)
+    //   energy_dot_global[0] *= field->apar_energy_fac_1d;
+
+    gkyl_dynvec_append(field->integ_apardot_energy, tm, energy_dot_global);
+
+    if (field->info.time_rate_diagnostics) {
+      gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->apar_energy_red_old, field->em_energy_red_global);
+      double energy_dot_global_old[1] = { 0.0 };
+      if (app->use_gpu)
+        gkyl_cu_memcpy(energy_dot_global_old, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+      else
+        energy_dot_global_old[0] = field->em_energy_red_global[0];
+      if (app->cdim == 1)
+        energy_dot_global_old[0] *= field->apar_energy_fac_1d; 
+      
+      gkyl_comm_allreduce(app->comm, GKYL_DOUBLE, GKYL_SUM, 1, field->apar_energy_red_new, field->em_energy_red_global);
+      double energy_dot_global_new[1] = { 0.0 };
+      if (app->use_gpu)
+        gkyl_cu_memcpy(energy_dot_global_new, field->em_energy_red_global, sizeof(double[1]), GKYL_CU_MEMCPY_D2H);
+      else
+        energy_dot_global_new[0] = field->em_energy_red_global[0];
+      if (app->cdim == 1)
+        energy_dot_global_new[0] *= field->apar_energy_fac_1d; 
+
+      double energy_dot_global[1] = { 0.0 };
+      energy_dot_global[0] = energy_dot_global_new[0] - energy_dot_global_old[0];
+
+      gkyl_dynvec_append(field->integ_apar_energy_dot, tm, energy_dot_global);
+    }
+  }
 }
 
 static void
@@ -130,6 +201,60 @@ gk_field_calc_energy_disabled(struct gkyl_gyrokinetic_app *app, const struct gk_
   // Do nothing.
 }
 
+static void
+gk_field_combine_enabled(struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  gkyl_array_accumulate_range(gkyl_array_set_range(out, c1, arr1, rng),
+    c2, arr2, rng);
+}
+
+static void
+gk_field_combine_disabled(struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  // Do nothing.
+}
+
+static void
+gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
+  const struct gkyl_array* inp)
+{
+  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
+
+  // gkyl_array_clear_range(out, 0.0, &app->local_ext);
+
+  // Smooth apar
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
+  // gkyl_array_copy_range_to_range(out, field->apar_fem, &app->local, &field->global_sub_range);
+  
+}
+
+static void
+gk_field_step_apar_disabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
+  const struct gkyl_array* inp)
+{
+  // Do nothing.
+}
+
+static void
+gk_field_copy_range_enabled(struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  gkyl_array_copy_range(out, inp, range);
+}
+
+static void 
+gk_field_copy_range_disabled(struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  // Do nothing.
+}
+
 static void
 gk_field_time_rate_diags_new(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -147,6 +272,22 @@ gk_field_time_rate_diags_new(struct gkyl_gyrokinetic_app *app, struct gk_field *
   }
   f->integ_energy_dot = gkyl_dynvec_new(GKYL_DOUBLE, 1);
   f->is_first_energy_dot_write_call = true;
+  if (f->is_em){
+    f->calc_apar_energy_dt_func = gk_field_calc_apar_energy_dt_active;
+    if (app->use_gpu) {
+      f->apar_energy_red_new = gkyl_cu_malloc(sizeof(double[1]));
+      f->apar_energy_red_old = gkyl_cu_malloc(sizeof(double[1]));
+      gkyl_cu_memset(f->apar_energy_red_new, 0, sizeof(double[1]));
+      gkyl_cu_memset(f->apar_energy_red_old, 0, sizeof(double[1]));
+    } else {
+      f->apar_energy_red_new = gkyl_malloc(sizeof(double[1]));
+      f->apar_energy_red_old = gkyl_malloc(sizeof(double[1]));
+      memset(f->apar_energy_red_new, 0, sizeof(double[1]));
+      memset(f->apar_energy_red_old, 0, sizeof(double[1]));
+    }
+    f->integ_apar_energy_dot = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+  }
+  f->is_first_apar_energy_dot_write_call = true;
 }
 
 static void
@@ -165,15 +306,22 @@ gk_field_energy_new(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->is_first_energy_write_call = true;
 
   f->calc_energy_func = gk_field_calc_energy_enabled;
+
   f->calc_energy_dt_func = gk_field_calc_energy_dt_none;
-  
-  if (f->info.time_rate_diagnostics) {
+  f->calc_apar_energy_dt_func = gk_field_calc_energy_dt_none;
+  if (f->info.time_rate_diagnostics)
     gk_field_time_rate_diags_new(app, f);
-  }
 
   // Factors for ES energy.
   f->es_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
   f->es_energy_fac_1d = 0.0;
+
+  if (f->is_em) {
+    f->integ_apar_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+    f->integ_apardot_energy = gkyl_dynvec_new(GKYL_DOUBLE, 1);
+    f->apar_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
+    f->apar_energy_fac_1d = 0;
+  }
 }
 
 static void
@@ -188,6 +336,16 @@ gk_field_time_rate_diags_release(const struct gkyl_gyrokinetic_app *app, struct
     gkyl_free(f->em_energy_red_old);
   }
   gkyl_dynvec_release(f->integ_energy_dot);
+  if (f->is_em) {
+    if (app->use_gpu) {
+      gkyl_cu_free(f->apar_energy_red_new);
+      gkyl_cu_free(f->apar_energy_red_old);
+    } else {
+      gkyl_free(f->apar_energy_red_new);
+      gkyl_free(f->apar_energy_red_old);
+    }
+    gkyl_dynvec_release(f->integ_apar_energy_dot);
+  }
 }
 
 static void
@@ -208,6 +366,12 @@ gk_field_energy_release(const struct gkyl_gyrokinetic_app *app, struct gk_field
   }
 
   gkyl_array_release(f->es_energy_fac);
+
+  if (f->is_em) {
+    gkyl_dynvec_release(f->integ_apar_energy);
+    gkyl_dynvec_release(f->integ_apardot_energy);
+    gkyl_array_release(f->apar_energy_fac);
+  }
 }
 
 // Related to enforcing parallel Vlasov boundary conditions
@@ -226,6 +390,25 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   f->info = gk->field;
 
   f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD_ES;
+  
+  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM || f->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
+  // Ensure that if any species is electromagnetic, the field is electromagnetic.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    f->is_em = f->is_em || s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || 
+                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP ||
+                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPAR;
+  }
+  if (f->is_em) {
+    assert(f->info.mu0 > 0.0);
+    f->step_apar = gk_field_step_apar_enabled;
+    f->combine_func = gk_field_combine_enabled;
+    f->copy_func = gk_field_copy_range_enabled;
+  } else {
+    f->step_apar = gk_field_step_apar_disabled;
+    f->combine_func = gk_field_combine_disabled;
+    f->copy_func = gk_field_copy_range_disabled;
+  }
 
   f->calc_init_field = !f->info.zero_init_field;
   f->update_field = !f->info.is_static;
@@ -269,6 +452,44 @@ gk_field_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field)
   app->stat.field_phi_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
+void
+gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
+{
+  // Compute Apardot through Ohm's law.
+  struct timespec wst = gkyl_wall_clock();
+  field->em_rhs_func(app, field, f_in, rhs_in);
+  app->stat.field_tm += gkyl_time_diff_now_sec(wst);
+}
+
+void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field)
+{
+  struct timespec wst = gkyl_wall_clock();
+  field->ampere_solve(app, field);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp)
+{
+  struct timespec wst = gkyl_wall_clock();
+  field->step_apar(app, field, out, a, inp);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+void
+gk_field_combine(struct gk_field *field, struct gkyl_array *out, double c1,
+  const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
+  const struct gkyl_range *rng)
+{
+  field->combine_func(out, c1, arr1, c2, arr2, rng);
+}
+
+void
+gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
+  const struct gkyl_array *inp, const struct gkyl_range *range)
+{
+  field->copy_func(out, inp, range);
+}
+
 void
 gk_field_calc_energy(gkyl_gyrokinetic_app *app, double tm, const struct gk_field *field)
 {
@@ -283,6 +504,12 @@ gk_field_calc_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field,
   field->calc_energy_dt_func(app, field, dt, energy_reduced);
 }
 
+void
+gk_field_calc_apar_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced)
+{
+  field->calc_apar_energy_dt_func(app, field, dt, energy_reduced);
+}
+
 void gk_field_accumulate_rho_c_adiabatic(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gk_species *s, struct gkyl_array **bflux)
 {
   // Gyroaverage the density if needed.
@@ -316,6 +543,54 @@ gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field,
   app->stat.field_phi_rhs_tm += gkyl_time_diff_now_sec(wst);
 }
 
+void
+gk_field_accumulate_current_dens(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->currentDens, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
+    gkyl_array_accumulate_range(field->currentDens, s->info.charge, s->m1.marr, &app->local);
+  } 
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
+void
+gk_field_accumulate_current_dens_dot(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  struct gkyl_array *rhs_in[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->currentDensdot, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+
+    gk_species_moment_calc(&s->m1, s->local, app->local, rhs_in[i]);
+
+    gkyl_array_accumulate_range(field->currentDensdot, s->info.charge, s->m1.marr, &app->local);
+  } 
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
+void
+gk_field_accumulate_ohms_kSq(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[])
+{
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_array_clear(field->dApartdtSlvr_kSq, 0.0);
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *s = &app->species[i];
+    gk_species_moment_calc(&s->m0, s->local, app->local, fin[i]);
+    // Gyroaverage the density if needed.
+    s->gyroaverage(app, s, s->m0.marr, s->m0_gyroavg);
+    // Use m0 to update also update the kSq matrix for the Ohm's law solver.
+    double fac = s->info.charge*s->info.charge/s->info.mass;
+    gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
+  }
+  app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
+}
+
 void
 gk_field_fem_projection_par(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *arr_dg, struct gkyl_array *arr_fem)
 {
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index a26b84ab45..28d3568fcf 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -19,6 +19,68 @@ gk_field_rhs_phi_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field)
   gk_field_fem_projection_par(app, field, field->rho_c, field->phi_smooth);
 }
 
+static void 
+gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+
+  // Compute the LHS factor (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
+  // gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
+  gkyl_array_clear(field->dApartdtSlvr_lhs_factor, 0.0);
+  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq, &app->local);
+  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
+
+  // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apardot, 0, field->currentDensdot, 
+    0, field->dApartdtSlvr_lhs_factor, &app->local);
+  
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+
+  // // Smooth apardot
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->apardot, field->rho_c_global_dg);
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
+  // gkyl_array_copy_range_to_range(field->apardot, field->apar_fem, &app->local, &field->global_sub_range);
+  
+}
+
+static void 
+gk_field_ampere_solve_1x_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+
+
+  // Weak division method Apar = sum_s q_s int dv vpar F_s / (k_perp^2/mu_0)
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apar, 0, field->currentDens, 
+    0, field->lapWeightAmpere, &app->local);
+  
+  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDens, field->currentDens_global);
+
+  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->currentDens_global, field->currentDens_global);
+  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->phi_fem);
+
+  // gkyl_array_copy_range_to_range(field->apar, field->phi_fem, &app->local, &field->global_sub_range);
+
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void 
+gk_field_ampere_solve_1x_none(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  // Do nothing.
+}
+
+static void
+gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
+{
+  gk_field_accumulate_current_dens_dot(app, field, rhs_in);
+  gk_field_accumulate_ohms_kSq(app, field, f_in);
+  gk_field_ohm_solve_1x(app, field);
+}
+
+static void
+gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
+{
+  // Do nothing.
+}
+
 static void
 gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -26,10 +88,26 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->rho_c_global_dg);
   gkyl_array_release(f->phi_smooth);
   gkyl_array_release(f->phi_fem);
+  gkyl_array_release(f->apar);
+  gkyl_array_release(f->apardot);
 
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
+  if (f->is_em) {
+    gkyl_array_release(f->apar_curr);
+    gkyl_array_release(f->apar1);
+    gkyl_array_release(f->aparnew);
     gkyl_array_release(f->apar_fem);
-    gkyl_array_release(f->apardot_fem);
+    gkyl_array_release(f->currentDens);
+    gkyl_array_release(f->currentDensdot);
+    gkyl_array_release(f->currentDens_global);
+    gkyl_array_release(f->dApartdtSlvr_lhs_factor);
+    gkyl_array_release(f->lapWeightAmpere);
+    gkyl_array_release(f->dApartdtSlvr_kSq);
+    gkyl_dg_bin_op_mem_release(f->div_mem);
+    gkyl_fem_parproj_release(f->fem_apar_parproj);
+    if (app->use_gpu) {
+      gkyl_array_release(f->apar_host);
+      gkyl_array_release(f->apardot_host);
+    }
   }
 
   if (app->use_gpu) {
@@ -61,11 +139,50 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Allocate arrays for electrostatic potential.
   f->phi_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
   f->phi_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+
+  // Allocate additional arrays for EM case.
+  if (f->is_em) {
+    f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+    
+    f->apar_host = f->apar;
+    f->apardot_host = f->apardot;
+    if (app->use_gpu) {
+      f->apar_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+      f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+    }
 
-  // Allocate electromagnetic arrays if needed.
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->lapWeightAmpere = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
+    f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    
+    f->currentDens_global = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+    f->dApartdtSlvr_lhs_factor = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->div_mem = app->use_gpu? gkyl_dg_bin_op_mem_cu_dev_new(app->local.volume, app->basis.num_basis)
+      : gkyl_dg_bin_op_mem_new(app->local.volume, app->basis.num_basis);
+    
+    // Need to set weight to kperpsq*polarizationWeight for use in potential smoothing.
+    gkyl_array_copy(f->lapWeightAmpere, app->gk_geom->geo_int.jacobgeo);
+    gkyl_array_scale(f->lapWeightAmpere, f->info.kperpSq/f->info.mu0);
+
+    f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
+    for (int d=0; d<app->num_periodic_dir; ++d)
+      if (app->periodic_dirs[d] == app->cdim-1) f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_PERIODIC;
+
+    f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+      f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
+
+    f->ampere_solve = gk_field_ampere_solve_1x_enabled;
+    f->em_rhs_func = gk_field_em_rhs_enabled;
+
+    assert(f->info.mu0 > 0.0);
+    f->apar_energy_fac_1d = 0.5/f->info.mu0 * f->info.kperpSq;
+    f->apar_energy_fac_1d *= -1.0; // the -1 is to be consistent with ES energy.
   }
   
   // Allocate phi_host for I/O.
@@ -74,7 +191,15 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->phi_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
   }
 
+  // Set function pointers.
   f->rhs_phi_func = gk_field_rhs_phi_1x;
+  if (f->is_em) {
+    f->em_rhs_func = gk_field_em_rhs_none;
+    f->ampere_solve = gk_field_ampere_solve_1x_none;
+  } else {
+    f->em_rhs_func = gk_field_em_rhs_none;
+    f->ampere_solve = gk_field_ampere_solve_1x_none;
+  }
 
   // Allocate array for the polarization weight times geometric coefficients.
   f->epsilon = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
@@ -135,7 +260,7 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       fem_parproj_bc, epsilon_global, 0, app->use_gpu);
   }
 
-  f->es_energy_fac_1d = polarization_weight*f->info.kperpSq + es_energy_fac_1d_adiabatic;
+  f->es_energy_fac_1d = 0.5*polarization_weight*f->info.kperpSq + es_energy_fac_1d_adiabatic;
 
   f->calc_em_energy = gkyl_array_integrate_new(&app->grid, &app->basis, 
     1, GKYL_ARRAY_INTEGRATE_OP_SQ, app->use_gpu);
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 403e2ff32c..2e256381ec 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -121,6 +121,53 @@ gk_field_rhs_deflate_poisson_es_iwl(struct gkyl_gyrokinetic_app *app, struct gk_
   field->enforce_parallel_bc_func(app, field, field->phi_smooth);
 }
 
+static void 
+gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+  
+  // The update of kSq is causing issues with leaks and valgrind.
+  // gkyl_fem_poisson_perp_update_kSq(field->fem_apardot_solver, field->dApartdtSlvr_kSq);
+
+  // Temporary solution to avoid superLU leak when updating kSq: we release and re-create the solver
+  gkyl_fem_poisson_perp_release(field->fem_apardot_solver);
+  field->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+    &field->ampere_bcs, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
+
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
+  gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
+
+  // gkyl_array_clear_range(field->apardot, 0.0, &app->local_ext);
+
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void 
+gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  struct timespec wst = gkyl_wall_clock();
+  gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
+  gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
+  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
+}
+
+static void 
+gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field){
+  // Do nothing.
+}
+
+static void
+gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
+{
+  gk_field_accumulate_current_dens_dot(app, field, rhs_in);
+  gk_field_accumulate_ohms_kSq(app, field, f_in);
+  gk_field_ohm_solve(app, field);
+}
+
+static void
+gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
+{
+  // Do nothing.
+}
+
 static void
 gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -129,10 +176,26 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->rho_c_global_smooth);
   gkyl_array_release(f->phi_fem);
   gkyl_array_release(f->phi_smooth);
+  gkyl_array_release(f->apar);
+  gkyl_array_release(f->apardot);
 
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
+  if (f->is_em) {
+    gkyl_array_release(f->apar_curr);
+    gkyl_array_release(f->apar1);
+    gkyl_array_release(f->aparnew);
     gkyl_array_release(f->apar_fem);
-    gkyl_array_release(f->apardot_fem);
+    gkyl_array_release(f->currentDens);
+    gkyl_array_release(f->currentDensdot);
+    gkyl_array_release(f->lapWeightAmpere);
+    gkyl_array_release(f->dApartdtSlvr_kSq);
+    gkyl_array_release(f->currentDens_global);
+    gkyl_fem_parproj_release(f->fem_apar_parproj);
+    gkyl_fem_poisson_perp_release(f->fem_apar_solver);
+    gkyl_fem_poisson_perp_release(f->fem_apardot_solver);
+    if (app->use_gpu) {
+      gkyl_array_release(f->apar_host);
+      gkyl_array_release(f->apardot_host);
+    }
   }
 
   if (app->use_gpu) {
@@ -183,11 +246,28 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Allocate arrays for electrostatic potential.
   f->phi_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
   f->phi_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+
+  f->em_rhs_func = gk_field_em_rhs_none;
+  // Setup electromagnetic variables if needed.
+  if (f->is_em) {
+    f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
+    
+    f->apar_host = f->apar;
+    f->apardot_host = f->apardot;
+    if (app->use_gpu) {
+      f->apar_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+      f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+    }
 
-  // Allocate electromagnetic arrays if needed.
-  if (f->gkfield_id == GKYL_GK_FIELD_EM) {
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apardot_fem = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    f->lapWeightAmpere = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
+    f->dApartdtSlvr_kSq = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   }
 
   // Allocate phi_host for I/O.
@@ -202,6 +282,9 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->accumulate_rhoc_func = gk_field_accumulate_rho_c_poisson;
   }
 
+  f->ampere_solve = gk_field_ampere_solve_none;
+  f->em_rhs_func = gk_field_em_rhs_none;
+
   double polarization_weight = 0.0;
   double polarization_bmag = f->info.polarization_bmag ? f->info.polarization_bmag : app->bmag_ref;
   // Linearized polarization density
@@ -218,6 +301,14 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_set_offset(f->epsilon, polarization_weight, Jgij[i], i*app->basis.num_basis);
   }
 
+  if (f->is_em) {
+    // Compute the weights in front of the laplacian operator (metric x 1/mu0)
+    for (int i=0; i<app->cdim-2/app->cdim; i++) {
+      gkyl_array_set_offset(f->lapWeightAmpere, 1.0/f->info.mu0, Jgij[i], i*app->basis.num_basis);
+    }
+    gkyl_array_set(f->apar_energy_fac, -0.5, f->lapWeightAmpere);
+  }
+
   // Translate input file BCs into Poisson BCs.
   struct gkyl_poisson_bc poisson_bcs = { };
 
@@ -327,6 +418,44 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       fem_parproj_bc, 0, 0, app->use_gpu);
   }
 
+  // Setup EM solvers.
+  if (f->is_em) {
+    // Translate input file BCs into Ampere BCs.
+    for (int d=0; d<app->cdim-1; d++) {
+      if (bc_is_np[d]) {
+        struct gkyl_gyrokinetic_bc *bc_lo = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_LOWER_EDGE);
+        if (bc_lo != 0) {
+          f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_lo->type);
+          for (int i=0; i<3; i++)
+            f->ampere_bcs.lo_value[d].v[i] = bc_lo->value[i];
+        }
+
+        struct gkyl_gyrokinetic_bc *bc_up = gk_fetch_bc_with_dir_edge(f->info.ampere_bcs, 2*app->cdim, d, GKYL_UPPER_EDGE);
+        if (bc_up != 0) {
+          f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(bc_up->type);
+          for (int i=0; i<3; i++)
+            f->ampere_bcs.up_value[d].v[i] = bc_up->value[i];
+        }
+      } else {
+        f->ampere_bcs.lo_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
+        f->ampere_bcs.up_type[d] = gkyl_gyrokinetic_translate_poisson_bc_type(GKYL_BC_GK_FIELD_PERIODIC);
+      }
+    }
+    // FEM solver for Ampere equation (solved at IC only).
+    f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+        &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+    // FEM solver for Ohm's law (evolves d(Apart)/dt).
+    f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
+      &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+    // FEM smoother for Aparallel.
+    f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
+    f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
+      f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
+
+    f->ampere_solve = gk_field_ampere_solve_enabled;
+    f->em_rhs_func = gk_field_em_rhs_enabled;
+  }
+
   gkyl_array_set(f->es_energy_fac, 0.5, f->epsilon);
 
   f->calc_em_energy = gkyl_array_integrate_new(&app->grid, &app->basis, 
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 4074d267d0..63235031fd 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -73,7 +73,52 @@ gk_species_omegaH_dt(gkyl_gyrokinetic_app *app, struct gk_species *gks, const st
   }
 }
 
+static void
+gk_species_update_bflux_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  // Compute and store (in the ghost cell of rhs) the boundary fluxes.
+  gk_species_bflux_rhs(app, &species->bflux, fin, rhs);
+
+  // Compute diagnostic moments of the boundary fluxes.
+  gk_species_bflux_calc_moms(app, &species->bflux, rhs, bflux_moms);
+}
+
 static double
+gk_species_get_cfl_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  // Reduce the CFL frequency anc compute stable dt needed by this species.
+  app->stat.n_species_omega_cfl +=1;
+  struct timespec tm = gkyl_wall_clock();
+  gkyl_array_reduce_range(species->omega_cfl, species->cflrate, GKYL_MAX, &species->local);
+
+  double omega_cfl_ho[1];
+  if (app->use_gpu) {
+    gkyl_cu_memcpy(omega_cfl_ho, species->omega_cfl, sizeof(double), GKYL_CU_MEMCPY_D2H);
+  }
+  else {
+    omega_cfl_ho[0] = species->omega_cfl[0];
+  }
+  double dt_out = app->cfl/omega_cfl_ho[0];
+  
+  // Enforce the omega_H constraint on dt.
+  double dt_omegaH = gk_species_omegaH_dt(app, species, fin);
+  dt_out = fmin(dt_out, dt_omegaH);
+
+  app->stat.species_omega_cfl_tm += gkyl_time_diff_now_sec(tm);
+  return dt_out;
+}
+
+static double
+gk_species_get_cfl_static(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  double omega_cfl = 1/DBL_MAX;
+  return app->cfl/omega_cfl;
+}
+
+static void
 gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
@@ -110,36 +155,17 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 
   // Heating source.
   gk_species_heating_rhs(app, species, &species->heat_src, fin, rhs);
+}
 
-  // Compute and store (in the ghost cell of rhs and in an array in bflux) the boundary fluxes.
-  gk_species_bflux_rhs(app, &species->bflux, fin, rhs);
-
-  // Compute moments of the boundary fluxes.
-  gk_species_bflux_calc_moms(app, &species->bflux, rhs, bflux_moms);
-
-  // Multiply CFL rate by the df/dt multiplier.
-  gk_species_fdot_multiplier_advance_times_cfl(app, species, &species->fdot_mult, app->field->phi_smooth, species->cflrate);
-  
-  // Reduce the CFL frequency anD compute stable dt needed by this species.
-  app->stat.n_species_omega_cfl +=1;
-  struct timespec tm = gkyl_wall_clock();
-  gkyl_array_reduce_range(species->omega_cfl, species->cflrate, GKYL_MAX, &species->local);
+static void
+gk_species_add_apardot_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  struct timespec wst = gkyl_wall_clock();
 
-  double omega_cfl_ho[1];
-  if (app->use_gpu) {
-    gkyl_cu_memcpy(omega_cfl_ho, species->omega_cfl, sizeof(double), GKYL_CU_MEMCPY_D2H);
-  }
-  else {
-    omega_cfl_ho[0] = species->omega_cfl[0];
-  }
-  double dt_out = app->cfl/omega_cfl_ho[0];
-  
-  // Enforce the omega_H constraint on dt.
-  double dt_omegaH = gk_species_omegaH_dt(app, species, fin);
-  dt_out = fmin(dt_out, dt_omegaH);
+  gk_species_collisionless_add_apardot_rhs(app, species, &species->collisionless, fin, rhs);
 
-  app->stat.species_omega_cfl_tm += gkyl_time_diff_now_sec(tm);
-  return dt_out;
+  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
 static double
@@ -172,12 +198,11 @@ gk_species_rhs_implicit_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *sp
   return app->cfl/omega_cfl;
 }
 
-static double
+static void
 gk_species_rhs_static(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  double omega_cfl = 1/DBL_MAX;
-  return app->cfl/omega_cfl;
+  // Do nothing.
 }
 
 static double
@@ -952,6 +977,12 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)
+    gks->add_apardot_rhs_func = gk_species_add_apardot_dynamic;
+  else
+    gks->add_apardot_rhs_func = gk_species_rhs_static;
+  gks->bflux_update = gk_species_update_bflux_dynamic;
+  gks->get_cfl = gk_species_get_cfl_dynamic;
   gks->bc_func = gk_species_apply_bc_dynamic;
   gks->release_func = gk_species_release_dynamic;
   gks->step_f_func = gk_species_step_f_dynamic;
@@ -986,6 +1017,9 @@ gk_species_init_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
+  gks->add_apardot_rhs_func = gk_species_rhs_static;
+  gks->bflux_update = gk_species_rhs_static;
+  gks->get_cfl = gk_species_get_cfl_static;  
   gks->bc_func = gk_species_apply_bc_static;
   gks->release_func = gk_species_release_static;
   gks->step_f_func = gk_species_step_f_static;
@@ -1479,6 +1513,16 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gks->gyro_phi = gkyl_array_acquire(app->field->phi_smooth);
   }
 
+  // We do not have FLR effects for EM yet.
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_ES)
+    gks->gyro_apar = gkyl_array_acquire(app->field->apar);
+  else
+    gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);
+  gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
+
+  // To compute current density for Ampere's law and current dot for Ohm's law.
+  gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
+
   // Initialize the collisionless solver.
   gks->collisionless = (struct gk_collisionless) { };
   gk_species_collisionless_init(app, gks, &gks->collisionless);
@@ -1762,11 +1806,32 @@ gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *gks_self
   }
 }
 
-double
+void
 gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  return species->rhs_func(app, species, fin, rhs, bflux_moms);
+  species->rhs_func(app, species, fin, rhs, bflux_moms);
+}
+
+void
+gk_species_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  species->add_apardot_rhs_func(app, species, fin, rhs, bflux_moms);
+}
+
+void 
+gk_species_update_bflux(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  species->bflux_update(app, species, fin, rhs, bflux_moms);
+}
+
+double 
+gk_species_get_cfl(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
+{
+  return species->get_cfl(app, species, fin, rhs, bflux_moms);
 }
 
 double
@@ -1921,5 +1986,9 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
     gkyl_deflated_fem_poisson_release(s->flr_op);
   }
 
+  gkyl_array_release(s->gyro_apar);
+  gkyl_array_release(s->gyro_apardot);
+  gk_species_moment_release(app, &s->m1);
+
   s->release_func(app, s);
 }
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index a3f41128c0..c610b72336 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -20,7 +20,7 @@ gk_species_collisionless_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_speci
   // where they are not defined.
   gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, fin, gkcls->flux_surf, species->cflrate);
+    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
 }
 
 static void
@@ -45,6 +45,25 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
+static void gk_species_collisionless_add_apardot_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
+{
+  struct timespec wst = gkyl_wall_clock();
+
+  // First remove the current ES+Apar contribution from the flux_surf array.
+  // Otherwise it will be counted twice in the gkyl_dg update.
+  gkyl_array_clear(gkcls->flux_surf, 0.0);
+  gkyl_gk_collisionless_flux_surf(gkcls->add_apardot_surf_flux_op, 
+    &app->local, &species->local, &app->local_ext, &species->local_ext, 
+    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
+
+  // Advance the rhs adding only the Apardot volume contribution.
+  gkyl_dg_updater_gyrokinetic_advance(gkcls->add_apardot_slvr, &species->local,
+    fin, species->cflrate, rhs);
+
+  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
+}
+
 static void
 gk_species_collisionless_fdot_scaling_disabled(gkyl_gyrokinetic_app *app, struct gk_species *gks,
   struct gk_collisionless *gkcls, struct gkyl_array *rhs, struct gkyl_array *cflrate, struct gkyl_range *rng)
@@ -81,11 +100,13 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   struct gk_collisionless *gkcls)
 {
   gkcls->collisionless_id = gks->info.collisionless.type;
+  gkcls->no_by = gks->info.collisionless.no_by;
   gkcls->write_diagnostics = gks->info.collisionless.write_diagnostics;
 
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
+  gkcls->add_apardot_rhs_func = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -123,32 +144,23 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Allocate arrays to store surface phase space flux.
     gkcls->flux_surf = mkarr(app->use_gpu, flux_surf_sz, gks->local_ext.volume);
 
-    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
-      // Parallel component of magnetic vector potential.
-      gkcls->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-      gkcls->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);    
-    }
-    else {
-      gkcls->apar    = gkyl_array_acquire(app->field->phi_smooth); // Not used.
-      gkcls->apardot = gkyl_array_acquire(app->field->phi_smooth); // Not used.
-    }
-
     enum gkyl_gyrokinetic_bc_type bctype_conf[2*GKYL_MAX_CDIM];
     for (int d=0; d<app->cdim; d++) {
       bctype_conf[d] = gks->lower_bc[d].type;
       bctype_conf[GKYL_MAX_CDIM+d] = gks->upper_bc[d].type;
     }
 
+    bool only_apardot = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->collisionless_id, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
-      .phi = gks->gyro_phi, .apar = gkcls->apar, .apardot = gkcls->apardot };
+      .phi = gks->gyro_phi, .apar = gks->gyro_apar, .apardot = gks->gyro_apardot };
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->collisionless_id, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     gkcls->scale_fac = -1.0; // Not used if scale_factor in input file is not given.
@@ -164,6 +176,21 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     if (gkcls->write_diagnostics) {
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
     }
+    // Electromagnetic set up.
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+      only_apardot = true;
+      // Create a special flux operator that only adds the AparDot contribution.
+      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+        gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
+        app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
+      // Create solver that only adds AparDot terms.
+      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+        &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
+        gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
+        &aux_inp, app->use_gpu);
+      // Methods chosen at runtime.
+      gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
+    }
   }
 }
 
@@ -181,6 +208,13 @@ gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *speci
   gkcls->rhs_func(app, species, gkcls, fin, rhs);
 }
 
+void 
+gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
+{
+  gkcls->add_apardot_rhs_func(app, species, gkcls, fin, rhs);
+}
+
 void
 gk_species_collisionless_write_diags(gkyl_gyrokinetic_app* app, struct gk_species *gks,
   struct gk_collisionless *gkcls, double tm, int frame)
@@ -200,6 +234,11 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+      gkyl_gk_collisionless_flux_release(gkcls->add_apardot_surf_flux_op);
+      gkyl_dg_updater_gyrokinetic_release(gkcls->add_apardot_slvr);
+    }
+
     if (gkcls->write_diagnostics) {
     }
   }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index f6e81425b7..84c71c5675 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1351,6 +1351,8 @@ struct gk_field {
   // Pointer to function to calculate the potential.
   void (*rhs_phi_func) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
 
+  void (*em_rhs_func) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[]);
+
   void (*calc_energy_func) (gkyl_gyrokinetic_app *app, const struct gk_field *field, double tm);
   
   void (*accumulate_rhoc_func) (gkyl_gyrokinetic_app *app, struct gk_field *field, struct gk_species *s, struct gkyl_array **bflux);
@@ -4020,6 +4022,28 @@ void gk_field_accumulate_rho_c(gkyl_gyrokinetic_app *app, struct gk_field *field
 void gk_field_accumulate_current_dens(gkyl_gyrokinetic_app *app, struct gk_field *field, 
   const struct gkyl_array *fin[]);
 
+/**
+ * Accumulate time derivative of current density for Ohm solve.
+ *
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
+ * @param rhs_in[] right-hand side of the ES GK equation for each species.
+ */
+void
+gk_field_accumulate_current_dens_dot(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  struct gkyl_array *rhs_in[]);
+
+/**
+ * Accumulate kSq term for Ohm solve.
+ *
+ * @param app gyrokinetic app object.
+ * @param field Pointer to field.
+ * @param fin[] Input distribution function (num_species size).
+ */
+void
+gk_field_accumulate_ohms_kSq(gkyl_gyrokinetic_app *app, struct gk_field *field, 
+  const struct gkyl_array *fin[]);
+
 /**
  * Compute initial magnetic vector parallel component
  * 
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 8065d8c90e..3263e4eddd 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1248,6 +1248,7 @@ gkyl_gyrokinetic_app_calc_field_energy(gkyl_gyrokinetic_app* app, double tm)
   }
 }
 
+
 void
 gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
 {
@@ -1259,22 +1260,46 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
     char fileNm0[sz0+1]; // ensures no buffer overflow
     snprintf(fileNm0, sizeof fileNm0, fmt0, app->name);
 
+    const char *fmt0_apar = "%s-apar_energy.gkyl";
+    int sz0_apar = gkyl_calc_strlen(fmt0_apar, app->name);
+    char fileNm0_apar[sz0_apar+1]; // ensures no buffer overflow
+    snprintf(fileNm0_apar, sizeof fileNm0_apar, fmt0_apar, app->name);
+
+    const char *fmt0_apardot = "%s-apardot_energy.gkyl";
+    int sz0_apardot = gkyl_calc_strlen(fmt0_apardot, app->name);
+    char fileNm0_apardot[sz0_apardot+1]; // ensures no buffer overflow
+    snprintf(fileNm0_apardot, sizeof fileNm0_apardot, fmt0_apardot, app->name);
+
     int rank;
     gkyl_comm_get_rank(app->comm, &rank);
 
+    bool write_em = app->field->is_em;
     if (rank == 0) {
       if (app->field->is_first_energy_write_call) {
         // Write to a new file (this ensure previous output is removed).
         gkyl_dynvec_write(app->field->integ_energy, fileNm0);
+
+        if (write_em) {
+          gkyl_dynvec_write(app->field->integ_apar_energy, fileNm0_apar);
+          gkyl_dynvec_write(app->field->integ_apardot_energy, fileNm0_apardot);
+        }
         app->field->is_first_energy_write_call = false;
       }
       else {
         // Append to existing file.
         gkyl_dynvec_awrite(app->field->integ_energy, fileNm0);
+        if (write_em) {
+          gkyl_dynvec_awrite(app->field->integ_apar_energy, fileNm0_apar);
+          gkyl_dynvec_awrite(app->field->integ_apardot_energy, fileNm0_apardot);
+        }
       }
       app->stat.n_field_diag_io += 1;
     }
     gkyl_dynvec_clear(app->field->integ_energy);
+    if (write_em) {
+      gkyl_dynvec_clear(app->field->integ_apar_energy);
+      gkyl_dynvec_clear(app->field->integ_apardot_energy);
+    }
 
     if (app->field->info.time_rate_diagnostics) {
       // Write out the time rate of change of the field energy.
@@ -1296,6 +1321,27 @@ gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
         app->stat.n_field_diag_io += 1;
       }
       gkyl_dynvec_clear(app->field->integ_energy_dot);
+      if (write_em) {
+        // Write out the time rate of change of the field energy.
+        const char *fmt2 = "%s-apar_energy_dot.gkyl";
+        int sz2 = gkyl_calc_strlen(fmt2, app->name);
+        char fileNm2[sz2+1]; // ensures no buffer overflow
+        snprintf(fileNm2, sizeof fileNm2, fmt2, app->name);
+
+        if (rank == 0) {
+          if (app->field->is_first_apar_energy_dot_write_call) {
+            // Write to a new file (this ensure previous output is removed).
+            gkyl_dynvec_write(app->field->integ_apar_energy_dot, fileNm2);
+            app->field->is_first_apar_energy_dot_write_call = false;
+          }
+          else {
+            // Append to existing file.
+            gkyl_dynvec_awrite(app->field->integ_apar_energy_dot, fileNm2);
+          }
+          app->stat.n_field_diag_io += 1;
+        }
+        gkyl_dynvec_clear(app->field->integ_apar_energy_dot);
+      }
     }
 
     app->stat.field_diag_io_tm += gkyl_time_diff_now_sec(wtm);
@@ -1841,7 +1887,8 @@ gkyl_gyrokinetic_app_write(gkyl_gyrokinetic_app* app, double tm, int frame)
 void
 gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   const struct gkyl_array *fin[], struct gkyl_array *fout[], struct gkyl_array **bflux_out[], 
-  const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], struct gkyl_array **bflux_out_neut[], 
+  const struct gkyl_array *fin_neut[], struct gkyl_array *fout_neut[], struct gkyl_array **bflux_out_neut[],
+  const struct gkyl_array *aparin, struct gkyl_array *aparout,
   struct gkyl_update_status *st)
 {
   double dtmin = DBL_MAX;
@@ -1885,8 +1932,8 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   // Compute df/dt (not including sources).
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
-    double dt1 = gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
-    dtmin = fmin(dtmin, dt1);
+    gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
   }
   for (int i=0; i<app->num_neut_species; ++i) {
     struct gk_neut_species *gk_ns = &app->neut_species[i];
@@ -1904,6 +1951,19 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
+  // Compute Apardot (solves Ohm's law using the previously built RHS).
+  gk_field_em_rhs(app, app->field, fin, fout);
+  // Update aparout.
+  gk_field_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
+
+  // Add Apardot contributions to the collisionless update of charged species.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *gk_s = &app->species[i];
+    gk_species_add_apardot_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    double dt1 = gk_species_get_cfl(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    dtmin = fmin(dtmin, dt1);
+  }
+
   // Multiply dfdt by a factor.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gks = &app->species[i];

From 3d1ecbd4cdb84b307c0090df15fe9cdef676e67b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 22 Dec 2025 13:35:32 -0500
Subject: [PATCH 070/181] EM function pointers were not activated correctly in
 gk_field_1x after the refactor. (KAW test is still correct.)

---
 gyrokinetic/apps/gk_field_1x.c   | 7 ++-----
 gyrokinetic/apps/gk_field_2x3x.c | 6 ++----
 2 files changed, 4 insertions(+), 9 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 28d3568fcf..5214ec630a 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -177,9 +177,6 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
       f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
 
-    f->ampere_solve = gk_field_ampere_solve_1x_enabled;
-    f->em_rhs_func = gk_field_em_rhs_enabled;
-
     assert(f->info.mu0 > 0.0);
     f->apar_energy_fac_1d = 0.5/f->info.mu0 * f->info.kperpSq;
     f->apar_energy_fac_1d *= -1.0; // the -1 is to be consistent with ES energy.
@@ -194,8 +191,8 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Set function pointers.
   f->rhs_phi_func = gk_field_rhs_phi_1x;
   if (f->is_em) {
-    f->em_rhs_func = gk_field_em_rhs_none;
-    f->ampere_solve = gk_field_ampere_solve_1x_none;
+    f->em_rhs_func = gk_field_em_rhs_enabled;
+    f->ampere_solve = gk_field_ampere_solve_1x_enabled;
   } else {
     f->em_rhs_func = gk_field_em_rhs_none;
     f->ampere_solve = gk_field_ampere_solve_1x_none;
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 2e256381ec..82eb06432a 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -249,7 +249,6 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
-  f->em_rhs_func = gk_field_em_rhs_none;
   // Setup electromagnetic variables if needed.
   if (f->is_em) {
     f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
@@ -282,9 +281,6 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->accumulate_rhoc_func = gk_field_accumulate_rho_c_poisson;
   }
 
-  f->ampere_solve = gk_field_ampere_solve_none;
-  f->em_rhs_func = gk_field_em_rhs_none;
-
   double polarization_weight = 0.0;
   double polarization_bmag = f->info.polarization_bmag ? f->info.polarization_bmag : app->bmag_ref;
   // Linearized polarization density
@@ -418,6 +414,8 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       fem_parproj_bc, 0, 0, app->use_gpu);
   }
 
+  f->ampere_solve = gk_field_ampere_solve_none;
+  f->em_rhs_func = gk_field_em_rhs_none;
   // Setup EM solvers.
   if (f->is_em) {
     // Translate input file BCs into Ampere BCs.

From 0189c183d4f687b6133e0b2e48b3f6511a3ce71f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 22 Dec 2025 15:11:11 -0500
Subject: [PATCH 071/181] =?UTF-8?q?caught=20a=20sign=20error=20in=20the=20?=
 =?UTF-8?q?setting=20of=20Ohm's=20law=20for=202x2v=20My=20collection=20is?=
 =?UTF-8?q?=20increasing:=20=F0=9F=90=9B=F0=9F=AA=B2=F0=9F=AA=B3?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/apps/gk_field.c    | 2 +-
 gyrokinetic/apps/gk_field_1x.c | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 06eb6e8fdb..f759a5e2b3 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -585,7 +585,7 @@ gk_field_accumulate_ohms_kSq(gkyl_gyrokinetic_app *app, struct gk_field *field,
     // Gyroaverage the density if needed.
     s->gyroaverage(app, s, s->m0.marr, s->m0_gyroavg);
     // Use m0 to update also update the kSq matrix for the Ohm's law solver.
-    double fac = s->info.charge*s->info.charge/s->info.mass;
+    double fac = -s->info.charge*s->info.charge/s->info.mass;
     gkyl_array_accumulate_range(field->dApartdtSlvr_kSq, fac, s->m0_gyroavg, &app->local);
   }
   app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 5214ec630a..06c20df08a 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -26,7 +26,7 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   // Compute the LHS factor (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
   // gkyl_array_set(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq);
   gkyl_array_clear(field->dApartdtSlvr_lhs_factor, 0.0);
-  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->dApartdtSlvr_kSq, &app->local);
+  gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor,-1.0, field->dApartdtSlvr_kSq, &app->local);
   gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
 
   // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )

From abe304bf6c09d7fdbb1147b09961aeb6883e5b4c Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 22 Dec 2025 15:29:00 -0500
Subject: [PATCH 072/181] update alfven 2x2v regression test

---
 gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
index 8f186a7c16..6eeeefe4cb 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
@@ -200,13 +200,13 @@ create_ctx(void)
   int Nz = 12; // Reduce this to delay recurrence effect.
   double z_min = -M_PI/kz_min;  // Min z-coordinate [m].
   double z_max = M_PI/kz_min;   // Max z-coordinate [m].
-  int Nvpar = 16; // Increase this to delay recurrence effect.
-  double vpar_max_elc = 5.0*vte; // Max electron parallel velocity [m/s].
+  int Nvpar = 24; // Increase this to delay recurrence effect.
+  double vpar_max_elc = 6.0*vte; // Max electron parallel velocity [m/s].
   double vpar_min_elc = -vpar_max_elc; // Min electron parallel velocity [m/s].
-  double vpar_max_ion = 5.0*vti; // Max ion parallel velocity [m/s].
+  double vpar_max_ion = 6.0*vti; // Max ion parallel velocity [m/s].
   double vpar_min_ion = -vpar_max_ion; // Min ion parallel
   // The x and mu directions are not playing a role in the dynamics.
-  int Nx = 16; // Number of cells in x-direction.
+  int Nx = 2; // Number of cells in x-direction.
   double x_min = -Lx/2;
   double x_max = Lx/2;
   int Nmu = 2;

From b9111933390d00c9e586bcc8558002f6eec97a39 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 22 Dec 2025 14:08:21 -0800
Subject: [PATCH 073/181] EM frames wirting disapeared during the merge with
 main

---
 gyrokinetic/apps/gyrokinetic.c | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 3263e4eddd..1f7625c8a1 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1228,6 +1228,27 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
 
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
+    if (app->field->is_em) {
+      // Copy data from device to host before writing it out.
+      if (app->use_gpu) {
+        gkyl_array_copy(app->field->apar_host, app->field->apar);
+        gkyl_array_copy(app->field->apardot_host, app->field->apardot);
+      }
+      const char *fmt_apar = "%s-apar_%d.gkyl";
+      int sz_apar = gkyl_calc_strlen(fmt_apar, app->name, frame);
+      char fileNm_apar[sz_apar+1]; // ensures no buffer overflow
+      snprintf(fileNm_apar, sizeof fileNm_apar, fmt_apar, app->name, frame);
+
+      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm_apar);
+
+      const char *fmt_apardot = "%s-apardot_%d.gkyl";
+      int sz_apardot = gkyl_calc_strlen(fmt_apardot, app->name, frame);
+      char fileNm_apardot[sz_apardot+1]; // ensures no buffer overflow
+      snprintf(fileNm_apardot, sizeof fileNm_apardot, fmt_apardot, app->name, frame);
+
+      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm_apardot);
+    }
+
     gk_array_meta_release(mt);
 
     app->stat.field_io_tm += gkyl_time_diff_now_sec(wtm);

From b3dccac9c6814ba671261b3369515174d5d045b0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 23 Dec 2025 10:58:52 -0500
Subject: [PATCH 074/181] remove unused global current density array release in
 gk_field_fem_release_2x3x

---
 gyrokinetic/apps/gk_field_2x3x.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 82eb06432a..0feefa08ff 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -188,7 +188,6 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
     gkyl_array_release(f->dApartdtSlvr_kSq);
-    gkyl_array_release(f->currentDens_global);
     gkyl_fem_parproj_release(f->fem_apar_parproj);
     gkyl_fem_poisson_perp_release(f->fem_apar_solver);
     gkyl_fem_poisson_perp_release(f->fem_apardot_solver);

From 4bde80a9c4034bbf84df859b061c124a4825ecef Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 24 Dec 2025 10:38:35 -0500
Subject: [PATCH 075/181] =?UTF-8?q?=F0=9F=90=9B=F0=9F=AA=A4=20found=20a=20?=
 =?UTF-8?q?bug=20where=20apar=20was=20passed=20instead=20of=20apardot=20in?=
 =?UTF-8?q?=20the=20collisionless=20flux=20surf=20computation=20?=
 =?UTF-8?q?=F0=9F=A4=AA?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/apps/gk_species_collisionless.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index c610b72336..e714112ddb 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -55,7 +55,7 @@ static void gk_species_collisionless_add_apardot_rhs_enabled(gkyl_gyrokinetic_ap
   gkyl_array_clear(gkcls->flux_surf, 0.0);
   gkyl_gk_collisionless_flux_surf(gkcls->add_apardot_surf_flux_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
+    species->gyro_phi, species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
 
   // Advance the rhs adding only the Apardot volume contribution.
   gkyl_dg_updater_gyrokinetic_advance(gkcls->add_apardot_slvr, &species->local,

From f18632cc33368163759402f54767567da56181db Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 24 Dec 2025 12:09:08 -0500
Subject: [PATCH 076/181] update documentation for
 gkyl_gk_collisionless_flux_new to clarify that we should pass apardot instead
 of apar when adding appardot only

---
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index 43db9539a5..ecdb5c1c05 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -52,7 +52,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
  * @param conf_ext_range Extended configuration space range (so we obtain geo quantities at all the needed surfaces).
  * @param phase_ext_range Extended Phase space range (so we obtain alpha_surf at all the needed surfaces).
  * @param phi Electrostatic potential.
- * @param apar Parallel component of vector potential.
+ * @param apar Parallel component of vector potential OR should be Apardot if only_apardot is true.
  * @param fin Distribution function.
  * @param flux_surf Output surface expansion in a cell on the *lower* edge in each direction.
  * @param clfrate Output CFL rate.

From 545b397c102935796dcfa8e9ee9e45c018672c46 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 10:13:38 -0500
Subject: [PATCH 077/181] create function to pointer to enable or not the
 twist-and-shift application (allows to remove the last (?) if statement in
 the field rhs computation)

---
 gyrokinetic/apps/gk_field_2x3x.c         | 38 ++++++++++++++++++++++--
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  2 ++
 2 files changed, 37 insertions(+), 3 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 0feefa08ff..d65faf6f21 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -55,6 +55,16 @@ gk_field_2x3x_add_TSBC_and_SSFG_updaters(struct gkyl_gyrokinetic_app *app, struc
     app->basis, &app->lower_skin_par_core,  &app->lower_ghost_par_core, app->use_gpu);
 }
 
+static void 
+gk_field_twistshift_enabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
+  gkyl_bc_twistshift_advance(up, fdo, ftar);
+}
+
+static void
+gk_field_twistshift_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
+  // Do nothing
+}
+
 static void
 gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
 {
@@ -66,9 +76,7 @@ gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_
     num_periodic_dir, periodic_dirs, finout); 
   
   // Update the lower z ghosts with twist-and-shift if we are in 3x2v
-  if (app->cdim == 3) {
-    gkyl_bc_twistshift_advance(field->bc_T_LU_lo, finout, finout);
-  }
+   field->twistshift_func(field->bc_T_LU_lo, finout, finout);
 
   // Sync ghost cells between MPI processes.
   gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);
@@ -77,6 +85,23 @@ gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_
   gkyl_skin_surf_from_ghost_advance(field->ssfg_z_lo, finout);
 }
 
+static void
+gk_field_enforce_parallel_bc_em_enabled(const struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
+{
+  // Apply the periodicity along the field to fill ghost cells.
+  int num_periodic_dir = 1;
+  int par_dir = app->cdim - 1;
+  int periodic_dirs[] = {par_dir};
+  gkyl_comm_array_per_sync(app->comm, &app->local, &app->local_ext,
+    num_periodic_dir, periodic_dirs, finout); 
+  
+  // Update the lower z ghosts with twist-and-shift if we are in 3x2v
+  field->twistshift_func(field->bc_T_LU_lo, finout, finout);
+
+  // Sync ghost cells between MPI processes.
+  gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);
+}
+
 static void
 gk_field_rhs_poisson_perp_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *field)
 {
@@ -146,6 +171,7 @@ gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field)
   struct timespec wst = gkyl_wall_clock();
   gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
   gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
+  field->enforce_parallel_bc_em_func(app, field, field->apar);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -160,6 +186,7 @@ gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const
   gk_field_accumulate_current_dens_dot(app, field, rhs_in);
   gk_field_accumulate_ohms_kSq(app, field, f_in);
   gk_field_ohm_solve(app, field);
+  field->enforce_parallel_bc_em_func(app, field, field->apardot);
 }
 
 static void
@@ -473,9 +500,14 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
   f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_disabled;
+  f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_disabled;
+  f->twistshift_func = gk_field_twistshift_disabled;
   if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
     gk_field_2x3x_add_TSBC_and_SSFG_updaters(app,f);
     f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_enabled;
+    f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_em_enabled;
+    if (app->cdim == 3)
+      f->twistshift_func = gk_field_twistshift_enabled;
   }
 
   f->solver_release_func = gk_field_fem_release_2x3x;
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 84c71c5675..3a5fbe249e 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1334,6 +1334,8 @@ struct gk_field {
   
   // Pointer to functions for the twist-and-shift BCs.
   void (*enforce_parallel_bc_func) (const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout);
+  void (*enforce_parallel_bc_em_func) (const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout);
+  void (*twistshift_func) (struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
 
   // Pointer to function for electromagnetic field solve.
   void (*accumulate_current) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 

From a3beadea658f1f889bedd2a16d0c7190480137f5 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 10:31:49 -0500
Subject: [PATCH 078/181] put back the new multiplier for CFL rate in
 gk_species_get_cfl_dynamic function

---
 gyrokinetic/apps/gk_species.c | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 63235031fd..6666dfb195 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -88,6 +88,10 @@ static double
 gk_species_get_cfl_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
+
+  // Multiply CFL rate by the df/dt multiplier.
+  gk_species_fdot_multiplier_advance_times_cfl(app, species, &species->fdot_mult, app->field->phi_smooth, species->cflrate);
+  
   // Reduce the CFL frequency anc compute stable dt needed by this species.
   app->stat.n_species_omega_cfl +=1;
   struct timespec tm = gkyl_wall_clock();

From c4724b6f20d31824bd2486949993379a8d1b3349 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 10:40:33 -0500
Subject: [PATCH 079/181] remove unused gkcls->apar and apardot arrays.

---
 gyrokinetic/apps/gk_species_collisionless.c | 5 +----
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h    | 3 ---
 2 files changed, 1 insertion(+), 7 deletions(-)

diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index e714112ddb..df582cadf2 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -227,10 +227,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
 {
   if (gkcls->collisionless_id) {
 
-    gkyl_array_release(gkcls->flux_surf);
-    gkyl_array_release(gkcls->apar);
-    gkyl_array_release(gkcls->apardot);
-  
+    gkyl_array_release(gkcls->flux_surf);  
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 3a5fbe249e..71a9c0aa8b 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -295,9 +295,6 @@ struct gk_collisionless {
     // Charged (gyrokinetic) species ............................................ //
     struct {
       struct gkyl_array *flux_surf; // Array for surface phase space flux
-      struct gkyl_array *apar; // A_parallel.
-      struct gkyl_array *apardot; // d/dt A_parallel.
-
       struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
   struct gkyl_gk_collisionless_flux *add_apardot_surf_flux_op; // Updater to add Apardot terms to fluxes.
       gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.

From f96b303384f42d6187c3ca25b63862f96e0747e8 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 11:13:01 -0500
Subject: [PATCH 080/181] remove the "es" in the electrostatic kernel naming to
 ease comparison with main

---
 ...llisionless_flux_edge_surfx_1x1v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfx_1x2v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfx_2x2v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfx_3x2v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfy_2x2v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfy_3x2v_ser_p1.c} |   2 +-
 ...llisionless_flux_edge_surfz_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_1x1v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_1x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfx_1x1v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfx_1x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfx_2x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfx_3x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfy_2x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfy_3x2v_ser_p1.c} |   2 +-
 ..._flux_multib_boundary_surfz_3x2v_ser_p1.c} |   2 +-
 ...nless_flux_no_by_edge_surfx_2x2v_ser_p1.c} |   2 +-
 ...nless_flux_no_by_edge_surfx_3x2v_ser_p1.c} |   2 +-
 ...nless_flux_no_by_edge_surfy_2x2v_ser_p1.c} |   2 +-
 ...nless_flux_no_by_edge_surfy_3x2v_ser_p1.c} |   2 +-
 ...nless_flux_no_by_edge_surfz_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |   2 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |   2 +-
 ...no_by_multib_boundary_surfx_2x2v_ser_p1.c} |   2 +-
 ...no_by_multib_boundary_surfx_3x2v_ser_p1.c} |   2 +-
 ...no_by_multib_boundary_surfy_2x2v_ser_p1.c} |   2 +-
 ...no_by_multib_boundary_surfy_3x2v_ser_p1.c} |   2 +-
 ...no_by_multib_boundary_surfz_3x2v_ser_p1.c} |   2 +-
 ...ionless_flux_no_by_surfvpar_2x2v_ser_p1.c} |   2 +-
 ...ionless_flux_no_by_surfvpar_3x2v_ser_p1.c} |   2 +-
 ...lisionless_flux_no_by_surfx_2x2v_ser_p1.c} |   2 +-
 ...lisionless_flux_no_by_surfx_3x2v_ser_p1.c} |   2 +-
 ...lisionless_flux_no_by_surfy_2x2v_ser_p1.c} |   2 +-
 ...lisionless_flux_no_by_surfy_3x2v_ser_p1.c} |   2 +-
 ...lisionless_flux_no_by_surfz_3x2v_ser_p1.c} |   2 +-
 .../gk_collisionless_flux_surf_return_zero.h  |   0
 ...collisionless_flux_surfvpar_1x1v_ser_p1.c} |   2 +-
 ...collisionless_flux_surfvpar_1x2v_ser_p1.c} |   2 +-
 ...collisionless_flux_surfvpar_2x2v_ser_p1.c} |   2 +-
 ...collisionless_flux_surfvpar_3x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfx_1x1v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfx_1x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfx_2x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfx_3x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfy_2x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfy_3x2v_ser_p1.c} |   2 +-
 ...gk_collisionless_flux_surfz_3x2v_ser_p1.c} |   2 +-
 .../gkyl_gk_collisionless_flux_kernels.h      | 164 +++++++++---------
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 128 +++++++-------
 57 files changed, 200 insertions(+), 200 deletions(-)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c => gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c => gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c} (97%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c => gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c => gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c => gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c => gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c => gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c => gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c => gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c => gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c => gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c} (99%)
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c => gk_collisionless_flux_surfvpar_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c => gk_collisionless_flux_surfvpar_1x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c => gk_collisionless_flux_surfvpar_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c => gk_collisionless_flux_surfvpar_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfx_1x1v_ser_p1.c => gk_collisionless_flux_surfx_1x1v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfx_1x2v_ser_p1.c => gk_collisionless_flux_surfx_1x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfx_2x2v_ser_p1.c => gk_collisionless_flux_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfx_3x2v_ser_p1.c => gk_collisionless_flux_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfy_2x2v_ser_p1.c => gk_collisionless_flux_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfy_3x2v_ser_p1.c => gk_collisionless_flux_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_es_collisionless_flux_surfz_3x2v_ser_p1.c => gk_collisionless_flux_surfz_3x2v_ser_p1.c} (99%)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index d7f1f29371..d238da4c5a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index fa28b49982..8b28a452a8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 75e84d9c3b..92e198ca2b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 8dc4411306..88ca99e273 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index e215d93f53..9bd473b754 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index f652909b64..0b8ed9317d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index dbd8a403b4..498a277666 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
similarity index 97%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 5785598e11..9839938bde 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 06ca58eb62..59741c6716 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 0f2d981a99..4d2caaa586 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 1b9321b513..654ae35df3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 60bcacccbf..d6718fe837 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index b56c6ed521..5d062b6954 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index c3754a76cb..e0bf10f4f3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 7a83dfb7d7..3e0e9a58ee 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 8c87e41043..57462146c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 269ebb4f13..6cf635577b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index c22156e4a5..1abad940db 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index d904ffa7e2..f850648838 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index b154574b8c..13cc478df5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index b488afb742..988d136907 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 06e461b179..6184d536a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index 8b374aa03d..a2da499294 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index d7829367ba..4ca93d910c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index c7a64c66af..43d4ce97f4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 93fa848cf7..403e5afe85 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 6285424c1e..55a1af88c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 24221faffb..a71b45ec40 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 1c708dfcfc..a9079ef2ed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 78f9967ed0..6646198205 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 2a4e2a1571..6284a429d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 155776e47f..944529819a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 4ce5e84e81..b45acf2030 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 075d642123..1be9740d4c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 534e2bf9e2..b2df2b4cc8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 1354d3cf3b..9ccf675e30 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index ea348fddf8..46856edd2a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 3ec5aaba66..33349ec571 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index 46a7a88a7f..c6fa855f0b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index 4b9a8bb519..8e0df1984a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index ded8d71bd9..a602b33749 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index a41d62efb5..8907a70957 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index c53c21ad48..a7d42b1e38 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.h
deleted file mode 100644
index e69de29bb2..0000000000
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index b90e4c516e..54c9a9bc01 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 514289668e..3b76a0d173 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 30fcac6cbb..45c4f44187 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index c73cce228a..462e705775 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
     const double *w, const double *dxv, 
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 8852610f72..8351564ace 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index afd77e6998..afb03ca1e1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index 5603465778..46e83b07d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 35b0e14ae6..1e92b3a798 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index dc2ab8c70a..c176ec2db1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index f2d015a6b2..5c178c9917 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 6f2c48ea9f..9a58c63c81 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_es_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_es_collisionless_flux_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index e85e84282d..eb0719694f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -7,7 +7,7 @@
 
 EXTERN_C_BEG
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -15,7 +15,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -23,7 +23,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -31,7 +31,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -39,7 +39,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -47,7 +47,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p1(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -55,7 +55,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x1v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -63,7 +63,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x1v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -71,7 +71,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x1v_ser_p2(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -95,7 +95,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -111,7 +111,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -127,7 +127,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p1(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -135,7 +135,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_1x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -143,7 +143,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_1x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -151,7 +151,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -167,7 +167,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_1x2v_ser_p2(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -175,7 +175,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -191,7 +191,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -199,7 +199,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -207,7 +207,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -215,7 +215,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -223,7 +223,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -231,7 +231,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -239,7 +239,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p1(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -247,7 +247,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -255,7 +255,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -263,7 +263,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -271,7 +271,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -279,7 +279,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -287,7 +287,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -295,7 +295,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -303,7 +303,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -311,7 +311,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -319,7 +319,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -327,7 +327,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -335,7 +335,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfy_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -343,7 +343,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -351,7 +351,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -359,7 +359,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -367,7 +367,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -375,7 +375,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -383,7 +383,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_2x2v_ser_p2(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -391,7 +391,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -399,7 +399,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -407,7 +407,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -415,7 +415,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -423,7 +423,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -431,7 +431,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -439,7 +439,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -447,7 +447,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -455,7 +455,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -463,7 +463,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfx_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -471,7 +471,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -479,7 +479,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfy_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -487,7 +487,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfy_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -495,7 +495,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfz_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -503,7 +503,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -511,7 +511,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -519,7 +519,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -527,7 +527,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -535,7 +535,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -543,7 +543,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -551,7 +551,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -559,7 +559,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_surfvpar_3x2v_ser_p1(
                 const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
                 double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -567,7 +567,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -575,7 +575,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -583,7 +583,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -591,7 +591,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -599,7 +599,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -607,7 +607,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -615,7 +615,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -623,7 +623,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -631,7 +631,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -639,7 +639,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_, 
@@ -647,7 +647,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
                     const double *w, const double *dxv,
                     
                     const double *vmap, const double *vmapSq, const double q_, const double m_,
@@ -655,7 +655,7 @@ GKYL_CU_DH double gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v
                     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
                     const double *phi, const double *apar, const double *JfL, const double *JfR, 
                     double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
                 const double *w, const double *dxv,
                 const double *vmap_prime_l, const double *vmap_prime_r, 
                 const double *vmap, const double *vmapSq, const double q_, const double m_, 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index c1d2a78ef1..4fbc7c1f4d 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -71,10 +71,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -92,10 +92,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -115,8 +115,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -136,8 +136,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -158,7 +158,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -179,7 +179,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -197,10 +197,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_surfvpar_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -221,10 +221,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -242,10 +242,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[] = {
   {
     .kernels_list= {
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -265,8 +265,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -286,8 +286,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   .kernels_list = {
     { NULL, NULL, NULL }, // 0
     { NULL, NULL, NULL }, // 1
-    { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -308,7 +308,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -329,7 +329,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -351,10 +351,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -372,10 +372,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -395,8 +395,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -416,8 +416,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -438,7 +438,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -459,7 +459,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -477,10 +477,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_no_by_surfvpar_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -501,10 +501,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[] = {
   {
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -522,10 +522,10 @@ GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[] = {
   { 
     .kernels_list = {
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_es_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -545,8 +545,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -566,8 +566,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -588,7 +588,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -609,7 +609,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_es_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   },
   {

From 66b6702426f54a5a2c5f21d777a49f007d50011d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 11:41:13 -0500
Subject: [PATCH 081/181] finish the removal of GKYL_GK_COLLISIONLESS_ES_NO_BY
 and replace by a flag passed to the collisionless table. It's better like
 this because otherwise we would need a colliisonless type for ES and each EM
 scenarii.

---
 core/zero/gkyl_eqn_type.h                              |  1 -
 gyrokinetic/apps/gk_species_collisionless.c            |  8 ++++----
 .../creg/rt_gk_multib_step_nonuniform_2x2v_p1.c        |  6 ++++--
 gyrokinetic/zero/dg_gyrokinetic.c                      |  6 +++---
 gyrokinetic/zero/dg_gyrokinetic_cu.cu                  |  8 ++++----
 gyrokinetic/zero/dg_updater_gyrokinetic.c              |  4 ++--
 gyrokinetic/zero/gk_collisionless_flux.c               |  6 +++---
 gyrokinetic/zero/gk_collisionless_flux_cu.cu           | 10 ++++++----
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h                 |  3 ++-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h            |  2 +-
 gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h         |  5 +++--
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h          |  7 ++++---
 gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h     |  2 +-
 13 files changed, 37 insertions(+), 31 deletions(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 156814972a..0047add7aa 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -180,7 +180,6 @@ enum gkyl_gk_anomalous_diff_id {
 enum gkyl_gk_collisionless_type {
   GKYL_GK_COLLISIONLESS_NONE = 0, // Turns off collisionless terms.
   GKYL_GK_COLLISIONLESS_ES, // Electrostatic.
-  GKYL_GK_COLLISIONLESS_ES_NO_BY, // Electrostatic, w/o toroidal field (b_y=0).
   GKYL_GK_COLLISIONLESS_EM_BPERP, // Electromagnetic with B_perp fluctuations.
   GKYL_GK_COLLISIONLESS_EM_BPAR, // Electromagnetic with B_par fluctuations.
   GKYL_GK_COLLISIONLESS_EM, // Electromagnetic with B_perp and B_par fluctuations.
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index df582cadf2..ec938ff2f8 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -152,7 +152,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
 
     bool only_apardot = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->collisionless_id,  gkcls->no_by, only_apardot, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -160,7 +160,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     gkcls->scale_fac = -1.0; // Not used if scale_factor in input file is not given.
@@ -181,12 +181,12 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       only_apardot = true;
       // Create a special flux operator that only adds the AparDot contribution.
       gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-        gks->info.charge, gks->info.mass, gkcls->collisionless_id, only_apardot, app->gk_geom, 
+        gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, 
         app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
       // Create solver that only adds AparDot terms.
       gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
         &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gks->info.skip_cell_threshold, gkcls->collisionless_id, only_apardot, app->gk_geom, gks->vel_map, 
+        gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, gks->vel_map, 
         &aux_inp, app->use_gpu);
       // Methods chosen at runtime.
       gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
diff --git a/gyrokinetic/creg/rt_gk_multib_step_nonuniform_2x2v_p1.c b/gyrokinetic/creg/rt_gk_multib_step_nonuniform_2x2v_p1.c
index c28f335b1a..a2ac35472e 100644
--- a/gyrokinetic/creg/rt_gk_multib_step_nonuniform_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_multib_step_nonuniform_2x2v_p1.c
@@ -1355,7 +1355,8 @@ main(int argc, char **argv)
     .num_diag_moments = 7,
     .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
     .num_integrated_diag_moments = 1,
     .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
@@ -1727,7 +1728,8 @@ main(int argc, char **argv)
     .num_diag_moments = 7,
     .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO_BY,
+      .type = GKYL_GK_COLLISIONLESS_ES,
+      .no_by = true,
     },
     .num_integrated_diag_moments = 1,
     .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 4bd6a18884..b5c6f203d1 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -47,14 +47,14 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
-      charge, mass, skip_cell_threshold, collless_type, only_apardot, gk_geom, vel_map);
+      charge, mass, skip_cell_threshold, collless_type, no_by, only_apardot, gk_geom, vel_map);
 #endif
 
   struct dg_gyrokinetic *gyrokinetic = gkyl_malloc(sizeof(struct dg_gyrokinetic));
@@ -112,7 +112,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       break;
   }
 
-  if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+  if (no_by) {
     gyrokinetic->eqn.vol_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 809ef4d175..52f1e81284 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -38,7 +38,7 @@ gkyl_gyrokinetic_set_auxfields_cu(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_
 __global__ static void 
 dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_basis_type b_type,
   int cv_index, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type collless_type, 
-  bool only_apardot)
+  bool no_by, bool only_apardot)
 {
   gyrokinetic->auxfields.flux_surf = 0; 
   gyrokinetic->auxfields.phi = 0; 
@@ -84,7 +84,7 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       break;    
   }  
 
-  if (collless_type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+  if (no_by) {
     gyrokinetic->eqn.vol_term = vol_no_by_kernels[cv_index].kernels[poly_order];
   }
   else {
@@ -117,7 +117,7 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
-  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
+  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
 {
   struct dg_gyrokinetic *gyrokinetic = (struct dg_gyrokinetic*) gkyl_malloc(sizeof(*gyrokinetic));
 
@@ -155,7 +155,7 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gkyl_cu_memcpy(gyrokinetic_cu, gyrokinetic, sizeof(struct dg_gyrokinetic), GKYL_CU_MEMCPY_H2D);
 
   dg_gyrokinetic_set_cu_dev_ptrs<<<1,1>>>(gyrokinetic_cu, cbasis->b_type, cv_index[cdim].vdim[vdim],
-    cdim, vdim, poly_order, collless_type, only_apardot);
+    cdim, vdim, poly_order, collless_type, no_by, only_apardot);
 
   // set parent on_dev pointer
   gyrokinetic->eqn.on_dev = &gyrokinetic_cu->eqn;
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 322aa2558d..80e204c622 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -22,7 +22,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom, 
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -30,7 +30,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, collless_type, only_apardot, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, collless_type, no_by, only_apardot, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index bf54af5c24..422024d157 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -18,14 +18,14 @@ gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type type,
-  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
 {
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis, 
-      charge, mass, type, only_apardot, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, type, no_by, only_apardot, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
@@ -57,7 +57,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
     int em = (type == GKYL_GK_COLLISIONLESS_EM || type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 1 : 0;
-    if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+    if (no_by) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
         up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 12267a1d4d..fa2ef0a8aa 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -201,7 +201,8 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
-  bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, bool only_apardot,
+  bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, 
+  bool no_by, bool only_apardot,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
   if (only_apardot){
@@ -213,7 +214,7 @@ gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up,
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
-    if (type == GKYL_GK_COLLISIONLESS_ES_NO_BY) {
+    if (no_by) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
         up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
@@ -240,7 +241,8 @@ gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up,
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  const double charge, const double mass, enum gkyl_gk_collisionless_type type, const bool only_apardot,
+  const double charge, const double mass, enum gkyl_gk_collisionless_type type, 
+  const bool no_by, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
@@ -279,7 +281,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   struct gkyl_gk_collisionless_flux *up_cu = (struct gkyl_gk_collisionless_flux*) gkyl_cu_malloc(sizeof(*up_cu));
   gkyl_cu_memcpy(up_cu, up, sizeof(gkyl_gk_collisionless_flux), GKYL_CU_MEMCPY_H2D);
 
-  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, only_apardot, bctype_conf_dev);
+  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, no_by, only_apardot, bctype_conf_dev);
 
   gkyl_cu_free(bctype_conf_dev);
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index 43ec48ee34..fe5581fa6d 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -28,6 +28,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (set b_y=0).
  * @param only_apardot Whether we want to only add the apardot term.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
@@ -37,7 +38,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 9a14eb15dd..62687abb43 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -676,7 +676,7 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_if_smaller_than, enum gkyl_gk_collisionless_type collless_type,
-  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
+  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**
  * CUDA device function to set the auxiliary fields (e.g. geometry & EM fields)
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 3512e87fe7..619bfed7d5 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -30,6 +30,7 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param mass Species mass
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (set b_y=0).
  * @param only_apardot Whether we want to only add the apardot term.
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
@@ -41,8 +42,8 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  enum gkyl_gk_collisionless_type collless_type, const bool only_apardot, const struct gk_geometry *gk_geom,
-  const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, 
+  const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
  * Acquire gyrokinetic equation object.
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index ecdb5c1c05..efe8da3aaa 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -23,6 +23,7 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * @param charge Species charge
  * @param mass Species mass
  * @param collless_type Type of collisionless terms.
+ * @param no_by Whether to neglect the toroidal field (set b_y=0).
  * @param only_apardot Whether to only add Apardot terms to the flux.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
@@ -35,9 +36,9 @@ struct gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
-  const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
-  const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
-  const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
+  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, 
+  const struct gkyl_dg_geom *dg_geom, const struct gkyl_gk_dg_geom *gk_dg_geom, 
+  const struct gkyl_velocity_map *vel_map, const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
 
 /**
  * Compute surface expansion of phase space flux alpha
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 4fbc7c1f4d..9300629745 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -767,7 +767,7 @@ choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  double charge, double mass, enum gkyl_gk_collisionless_type type, const bool only_apardot,
+  double charge, double mass, enum gkyl_gk_collisionless_type type, const bool no_by, const bool only_apardot,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf);

From 2f312d67f0cd61ffd0c39d6abd9e49b999d23187 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 11:55:15 -0500
Subject: [PATCH 082/181] remove one indentation to reduce the number of
 changed lines and ease PR review

---
 .../gkyl_gk_collisionless_flux_kernels.h      | 2256 ++++++++---------
 1 file changed, 1128 insertions(+), 1128 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index eb0719694f..f0cb7189da 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -8,1316 +8,1316 @@
 EXTERN_C_BEG
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                    const double *w, const double *dxv,
-                    
-                    const double *vmap, const double *vmapSq, const double q_, const double m_,
-                    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                    const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                    double* GKYL_RESTRICT flux_surf); 
+                  const double *w, const double *dxv,
+                  
+                  const double *vmap, const double *vmapSq, const double q_, const double m_,
+                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
+                  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-                const double *w, const double *dxv,
-                const double *vmap_prime_l, const double *vmap_prime_r, 
-                const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-                const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                double* GKYL_RESTRICT flux_surf); 
+              const double *w, const double *dxv,
+              const double *vmap_prime_l, const double *vmap_prime_r, 
+              const double *vmap, const double *vmapSq, const double q_, const double m_, 
+              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
+              double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
             const double *w, const double *dxv,

From 4b30097f41bf292bf6e139938b52b9014edc286f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 12:12:55 -0500
Subject: [PATCH 083/181] Add em extension to the naming of the copy and
 combine field method to reflect that they are disabled if we are in the
 electrostatic case.

---
 gyrokinetic/apps/gk_field.c                   | 16 ++++++++--------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      | 12 ++++++------
 gyrokinetic/apps/gyrokinetic.c                |  2 +-
 gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c | 12 ++++++------
 4 files changed, 21 insertions(+), 21 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index f759a5e2b3..148b070b74 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -402,12 +402,12 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
     f->step_apar = gk_field_step_apar_enabled;
-    f->combine_func = gk_field_combine_enabled;
-    f->copy_func = gk_field_copy_range_enabled;
+    f->em_combine_func = gk_field_combine_enabled;
+    f->em_copy_func = gk_field_copy_range_enabled;
   } else {
     f->step_apar = gk_field_step_apar_disabled;
-    f->combine_func = gk_field_combine_disabled;
-    f->copy_func = gk_field_copy_range_disabled;
+    f->em_combine_func = gk_field_combine_disabled;
+    f->em_copy_func = gk_field_copy_range_disabled;
   }
 
   f->calc_init_field = !f->info.zero_init_field;
@@ -476,18 +476,18 @@ void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struc
 }
 
 void
-gk_field_combine(struct gk_field *field, struct gkyl_array *out, double c1,
+gk_field_em_combine(struct gk_field *field, struct gkyl_array *out, double c1,
   const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
   const struct gkyl_range *rng)
 {
-  field->combine_func(out, c1, arr1, c2, arr2, rng);
+  field->em_combine_func(out, c1, arr1, c2, arr2, rng);
 }
 
 void
-gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
+gk_field_em_copy_range(struct gk_field *field, struct gkyl_array *out,
   const struct gkyl_array *inp, const struct gkyl_range *range)
 {
-  field->copy_func(out, inp, range);
+  field->em_copy_func(out, inp, range);
 }
 
 void
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 71a9c0aa8b..4114169b30 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1344,8 +1344,8 @@ struct gk_field {
   void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
   void (*step_apar) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
-  void (*combine_func) (struct gkyl_array *out, double c1, const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,const struct gkyl_range *rng);
-  void (*copy_func) (struct gkyl_array *out, const struct gkyl_array *inp, const struct gkyl_range *range);
+  void (*em_combine_func) (struct gkyl_array *out, double c1, const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,const struct gkyl_range *rng);
+  void (*em_copy_func) (struct gkyl_array *out, const struct gkyl_array *inp, const struct gkyl_range *range);
 
   // Pointer to function to calculate the potential.
   void (*rhs_phi_func) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
@@ -4065,7 +4065,7 @@ void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struc
   const struct gkyl_array* inp);
 
 /**
- * Combine for rk3 method.
+ * Combine method for Apar stepping, disabled if electrostatic.
  *
  * @param field Pointer to field.
  * @param out Output array.
@@ -4075,19 +4075,19 @@ void gk_field_step_apar(gkyl_gyrokinetic_app *app, struct gk_field *field, struc
  * @param arr2 Input array.
  * @param rng Range.
  */
-void gk_field_combine(struct gk_field *field, struct gkyl_array *out, double c1,
+void gk_field_em_combine(struct gk_field *field, struct gkyl_array *out, double c1,
   const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,
   const struct gkyl_range *rng);
 
 /**
- * Copy for rk3 method.
+ * Copy method for Apar stepping, disabled if electrostatic.
  *
  * @param field Pointer to field.
  * @param out Output array.
  * @param inp Input array.
  * @param range Range.
  */
-void gk_field_copy_range(struct gk_field *field, struct gkyl_array *out,
+void gk_field_em_copy_range(struct gk_field *field, struct gkyl_array *out,
   const struct gkyl_array *inp, const struct gkyl_range *range);
 
 
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 1f7625c8a1..7f58334f02 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1975,7 +1975,7 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   // Compute Apardot (solves Ohm's law using the previously built RHS).
   gk_field_em_rhs(app, app->field, fin, fout);
   // Update aparout.
-  gk_field_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
+  gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
 
   // Add Apardot contributions to the collisionless update of charged species.
   for (int i=0; i<app->num_species; ++i) {
diff --git a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
index 9a2cdb0478..6198691816 100644
--- a/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
+++ b/gyrokinetic/apps/gyrokinetic_update_ssp_rk3.c
@@ -79,7 +79,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar;
         aparout = app->field->apar1;
-        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar, &app->local_ext); // Update apar_curr to latest A_parallel.
+        gk_field_em_copy_range(app->field, app->field->apar_curr, app->field->apar, &app->local_ext); // Update apar_curr to latest A_parallel.
         for (int i=0; i<app->num_neut_species; ++i) {
           struct gk_neut_species *gkns = &app->neut_species[i];
           fin_neut[i] = gkns->f;
@@ -149,7 +149,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
+        gk_field_em_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -188,7 +188,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
             gk_neut_species_combine(gkns, gkns->f1, 3.0/4.0, gkns->f, 1.0/4.0, gkns->fnew, &gkns->local_ext);
             gk_neut_species_bflux_set(app, &gkns->bflux, gkns->bflux.f1, 1.0/4.0, gkns->bflux.fnew);
           }
-          gk_field_combine(app->field, app->field->apar1, 3.0/4.0, app->field->apar, 1.0/4.0, app->field->aparnew, &app->local_ext);
+          gk_field_em_combine(app->field, app->field->apar1, 3.0/4.0, app->field->apar, 1.0/4.0, app->field->aparnew, &app->local_ext);
           app->stat.time_stepper_arithmetic_tm += gkyl_time_diff_now_sec(wst);
 
           // Compute the fields and apply BCs.
@@ -225,7 +225,7 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
         }
         aparin = app->field->apar1;
         aparout = app->field->aparnew;
-        gk_field_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
+        gk_field_em_copy_range(app->field, app->field->apar_curr, app->field->apar1, &app->local_ext); // Update apar_curr to latest A_parallel.
 
         gyrokinetic_forward_euler(app, tcurr+dt/2, dt, fin, fout, aparin, aparout, bflux_in, bflux_out,
           fin_neut, fout_neut, bflux_in_neut, bflux_out_neut, &st);
@@ -272,9 +272,9 @@ gyrokinetic_update_ssp_rk3(gkyl_gyrokinetic_app* app, double dt0)
             gk_neut_species_bflux_calc_voltime_integrated_mom(app, gkns, &gkns->bflux, tcurr);
           }
           // Step A_parallel.
-          gk_field_combine(app->field, app->field->apar1, 1.0/3.0, app->field->apar, 2.0/3.0, app->field->aparnew, 
+          gk_field_em_combine(app->field, app->field->apar1, 1.0/3.0, app->field->apar, 2.0/3.0, app->field->aparnew, 
             &app->local_ext);
-          gk_field_copy_range(app->field, app->field->apar, app->field->apar1, &app->local_ext);
+          gk_field_em_copy_range(app->field, app->field->apar, app->field->apar1, &app->local_ext);
           app->stat.time_stepper_arithmetic_tm += gkyl_time_diff_now_sec(wst);
 
           // Apply positivity shift if requested.

From 90d71502f25de672cdc6707c8143fc3971922d69 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 13:47:53 -0500
Subject: [PATCH 084/181] Remove unused apar_fem array

---
 gyrokinetic/apps/gk_field.c              | 11 +----------
 gyrokinetic/apps/gk_field_1x.c           |  8 --------
 gyrokinetic/apps/gk_field_2x3x.c         |  2 --
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  1 -
 4 files changed, 1 insertion(+), 21 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 148b070b74..cc4084c76c 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -222,16 +222,7 @@ static void
 gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
-  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
-
-  // gkyl_array_clear_range(out, 0.0, &app->local_ext);
-
-  // Smooth apar
-  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, out, field->rho_c_global_dg);
-  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
-  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
-  // gkyl_array_copy_range_to_range(out, field->apar_fem, &app->local, &field->global_sub_range);
-  
+  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);  
 }
 
 static void
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 06c20df08a..e6bb35444f 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -34,12 +34,6 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
     0, field->dApartdtSlvr_lhs_factor, &app->local);
   
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
-
-  // // Smooth apardot
-  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->apardot, field->rho_c_global_dg);
-  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->rho_c_global_dg, field->rho_c_global_dg);
-  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->apar_fem);
-  // gkyl_array_copy_range_to_range(field->apardot, field->apar_fem, &app->local, &field->global_sub_range);
   
 }
 
@@ -95,7 +89,6 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_release(f->apar_curr);
     gkyl_array_release(f->apar1);
     gkyl_array_release(f->aparnew);
-    gkyl_array_release(f->apar_fem);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->currentDens_global);
@@ -147,7 +140,6 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index d65faf6f21..ace2c75b46 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -210,7 +210,6 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_release(f->apar_curr);
     gkyl_array_release(f->apar1);
     gkyl_array_release(f->aparnew);
-    gkyl_array_release(f->apar_fem);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
@@ -280,7 +279,6 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 4114169b30..ab1ba821fb 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1249,7 +1249,6 @@ struct gk_field {
     struct {
       struct gkyl_array *apar, *apar1, *aparnew; // Array for A_parallel and RK stages.
       struct gkyl_array *apar_curr; // A_parallel at current RK stage.
-      struct gkyl_array *apar_fem; // FEM A_parallel. 
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
       struct gkyl_array *apardot_host; // Host copy for use IO.

From 0a1fbadc85133ffb86b5510fd1dd45d00606fcb0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 14:33:34 -0500
Subject: [PATCH 085/181] correct logic for IWL EM

---
 gyrokinetic/apps/gk_field_2x3x.c | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index ace2c75b46..a111fb1276 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -500,12 +500,13 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_disabled;
   f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_disabled;
   f->twistshift_func = gk_field_twistshift_disabled;
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     gk_field_2x3x_add_TSBC_and_SSFG_updaters(app,f);
-    f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_enabled;
-    f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_em_enabled;
     if (app->cdim == 3)
       f->twistshift_func = gk_field_twistshift_enabled;
+    f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_enabled;
+    if (f->is_em)
+      f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_em_enabled;
   }
 
   f->solver_release_func = gk_field_fem_release_2x3x;

From b048256e127205fc838ebcdb2b8cbe0cf7b70ad1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 15:01:46 -0500
Subject: [PATCH 086/181] make sure that apar is acquired also when there is no
 collisionless term.

---
 gyrokinetic/apps/gk_species.c | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 6666dfb195..90d8a69316 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1518,7 +1518,8 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   }
 
   // We do not have FLR effects for EM yet.
-  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_ES)
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_NONE 
+    || gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_ES)
     gks->gyro_apar = gkyl_array_acquire(app->field->apar);
   else
     gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);

From 652c4b7fabf5dd32b83087a7a4ecc9c737f5d26a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 15:39:54 -0500
Subject: [PATCH 087/181] remove obsolete comment

---
 gyrokinetic/zero/gk_collisionless_flux.c | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 422024d157..e43e5123f4 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -9,11 +9,6 @@
 #include <gkyl_gk_collisionless_flux_priv.h>
 #include <gkyl_util.h>
 
-// TODO: remove add_em flag and replace by the collisionless enum type.
-// TODO: Combine apar and ES kernel together to allow the add Apardot only option.
-// TODO: In particular I have to have the same signature for each kernels regardless of whether they add EM terms or not,
-//       so that we can pass apar, or apardot if needed.
-
 gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 

From de94c1eaa1281c99ef1573d9704e0486bbb5b768 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 15:56:38 -0500
Subject: [PATCH 088/181] =?UTF-8?q?=F0=9F=94=A5=F0=9F=90=9B=F0=9F=94=A5=20?=
 =?UTF-8?q?the=202x2v=20flux=20surf=20y=20kernels=20were=20chosen=20in=20t?=
 =?UTF-8?q?he=203x2v=20case....?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 9300629745..3ff1e697f1 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -116,7 +116,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -124,7 +124,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, gk_em_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_em_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -137,7 +137,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   },
   {
@@ -145,7 +145,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 3
+      { NULL, gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };

From 1addd80c4b05ec3e93d5e683387ee834af147822 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 15:57:39 -0500
Subject: [PATCH 089/181] I don't know if it's needed but I find it scary to
 manipulate unallocated array with empty functions in the RK stepper so we
 allocate and release them to be sure.

---
 gyrokinetic/apps/gk_field_1x.c   | 12 ++++++------
 gyrokinetic/apps/gk_field_2x3x.c | 14 +++++++-------
 2 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index e6bb35444f..6677a71b6f 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -83,12 +83,12 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->phi_smooth);
   gkyl_array_release(f->phi_fem);
   gkyl_array_release(f->apar);
+  gkyl_array_release(f->apar_curr);
+  gkyl_array_release(f->apar1);
+  gkyl_array_release(f->aparnew);
   gkyl_array_release(f->apardot);
 
   if (f->is_em) {
-    gkyl_array_release(f->apar_curr);
-    gkyl_array_release(f->apar1);
-    gkyl_array_release(f->aparnew);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->currentDens_global);
@@ -133,13 +133,13 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->phi_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
   f->phi_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
   // Allocate additional arrays for EM case.
   if (f->is_em) {
-    f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index a111fb1276..a9ab09a5b6 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -205,11 +205,11 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->phi_smooth);
   gkyl_array_release(f->apar);
   gkyl_array_release(f->apardot);
+  gkyl_array_release(f->apar_curr);
+  gkyl_array_release(f->apar1);
+  gkyl_array_release(f->aparnew);
 
   if (f->is_em) {
-    gkyl_array_release(f->apar_curr);
-    gkyl_array_release(f->apar1);
-    gkyl_array_release(f->aparnew);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
@@ -245,7 +245,7 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_integrate_release(f->calc_em_energy);
 
   // Release TS BC and SSFG updater
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     if (app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_T_LU_lo);
     }
@@ -272,13 +272,13 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->phi_fem = mkarr(app->use_gpu, app->basis.num_basis, app->global_ext.volume);
   f->phi_smooth = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apar = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
   // Setup electromagnetic variables if needed.
   if (f->is_em) {
-    f->apar_curr = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
-    f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;

From 5eb779988b88ba253b53a08df01d1df8e9564e07 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 26 Dec 2025 16:16:15 -0500
Subject: [PATCH 090/181] Remove unused variable declaration in the
 electrostatic case.

---
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c | 26 -----------
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c | 46 -------------------
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c | 16 -------
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c | 16 -------
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c | 26 -----------
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c | 46 -------------------
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |  4 +-
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |  4 +-
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |  4 +-
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |  4 +-
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  4 +-
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  4 +-
 12 files changed, 12 insertions(+), 188 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index 46856edd2a..66d2f9ee5c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -45,17 +45,11 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -63,11 +57,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -93,11 +82,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -123,11 +107,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -153,11 +132,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 33349ec571..6213e03896 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -50,17 +50,11 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -68,11 +62,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -98,11 +87,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -128,11 +112,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -158,11 +137,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -188,11 +162,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -218,11 +187,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -248,11 +212,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
@@ -278,11 +237,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index 54c9a9bc01..c89bcda5a4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -38,17 +38,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -56,11 +50,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
 
@@ -77,11 +66,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 3b76a0d173..923cd51270 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -40,17 +40,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -58,11 +52,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
 
@@ -88,11 +77,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 45c4f44187..4d2b3e7f85 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -45,17 +45,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -63,11 +57,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
 
@@ -93,11 +82,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
 
@@ -123,11 +107,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
 
@@ -153,11 +132,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 462e705775..140ef97c8f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -50,17 +50,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
@@ -68,11 +62,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -98,11 +87,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -128,11 +112,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -158,11 +137,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -188,11 +162,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -218,11 +187,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -248,11 +212,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
@@ -278,11 +237,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index 8e77c3005b..4ff4b86d61 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -45,13 +45,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 8a4d7783c3..6876e3ddff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -50,13 +50,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
index d1d59d4fdb..1b99d93270 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -38,13 +38,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 806566190d..bac43c6b97 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -40,13 +40,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 70a81932f7..554172f189 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -45,13 +45,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
index bf11cf4394..ff0fdbdcca 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -50,13 +50,13 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   double B3_quad = 0.0; 
   double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
   double  g_13 = 0.0; 
   double  g_23 = 0.0; 
   double  g_33 = 0.0; 

From a5236a4fe181d0e33ea7b4b2994f069b86fa6bb1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 29 Dec 2025 12:03:25 -0500
Subject: [PATCH 091/181] We now smooth aparout which is apardot used to setp
 apar so that apar stays smooth. We also smooth apar after the IC ampere
 solve.

---
 gyrokinetic/apps/gk_field.c      |  7 ++++++-
 gyrokinetic/apps/gk_field_1x.c   | 12 ------------
 gyrokinetic/apps/gk_field_2x3x.c |  8 +++++---
 3 files changed, 11 insertions(+), 16 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index cc4084c76c..3774fe2c3e 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -222,7 +222,10 @@ static void
 gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
-  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);  
+  // Project inp (dApar/dt) onto FEM basis to make Apar continuous along z.
+  gk_field_fem_projection_par(app, field, out, out);
+  // Apar^{n+1} = Apar^{n} + dt*dApar/dt
+  gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
 }
 
 static void
@@ -456,6 +459,8 @@ void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field)
 {
   struct timespec wst = gkyl_wall_clock();
   field->ampere_solve(app, field);
+  // Smooth Apar after solving Ampere's law.
+  gk_field_fem_projection_par(app, field, field->apar, field->apar);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 6677a71b6f..0f67e5327e 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -41,17 +41,9 @@ static void
 gk_field_ampere_solve_1x_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
 
-
   // Weak division method Apar = sum_s q_s int dv vpar F_s / (k_perp^2/mu_0)
   gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apar, 0, field->currentDens, 
     0, field->lapWeightAmpere, &app->local);
-  
-  // gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->currentDens, field->currentDens_global);
-
-  // gkyl_fem_parproj_set_rhs(field->fem_apar_parproj, field->currentDens_global, field->currentDens_global);
-  // gkyl_fem_parproj_solve(field->fem_apar_parproj, field->phi_fem);
-
-  // gkyl_array_copy_range_to_range(field->apar, field->phi_fem, &app->local, &field->global_sub_range);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -96,7 +88,6 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_release(f->lapWeightAmpere);
     gkyl_array_release(f->dApartdtSlvr_kSq);
     gkyl_dg_bin_op_mem_release(f->div_mem);
-    gkyl_fem_parproj_release(f->fem_apar_parproj);
     if (app->use_gpu) {
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
@@ -166,9 +157,6 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     for (int d=0; d<app->num_periodic_dir; ++d)
       if (app->periodic_dirs[d] == app->cdim-1) f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_PERIODIC;
 
-    f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
-      f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
-
     assert(f->info.mu0 > 0.0);
     f->apar_energy_fac_1d = 0.5/f->info.mu0 * f->info.kperpSq;
     f->apar_energy_fac_1d *= -1.0; // the -1 is to be consistent with ES energy.
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index a9ab09a5b6..b782b654d7 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -238,7 +238,8 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
-  } else {
+  }
+  if (f->is_em || !(f->gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
     gkyl_fem_parproj_release(f->fem_parproj);
   }
 
@@ -279,7 +280,6 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
 
   // Setup electromagnetic variables if needed.
   if (f->is_em) {
-    
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
     if (app->use_gpu) {
@@ -427,13 +427,15 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       fem_parproj_bc_sol, 0, 0, app->use_gpu);
   } else {
     f->rhs_phi_func = gk_field_rhs_poisson_perp_2x3x;
+  }
+
+  if (f->is_em || !(f->gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
     enum gkyl_fem_parproj_bc_type fem_parproj_bc = GKYL_FEM_PARPROJ_NONE;
     for (int d=0; d<app->num_periodic_dir; ++d) {
       if (app->periodic_dirs[d] == app->cdim-1) {
         fem_parproj_bc = GKYL_FEM_PARPROJ_PERIODIC;
       }
     }
-
     f->fem_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
       fem_parproj_bc, 0, 0, app->use_gpu);
   }

From 7eec0e61b3e5a1ac8345a32998933a97a92be07b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 29 Dec 2025 13:40:56 -0500
Subject: [PATCH 092/181] the smoothing of apar here is a bad idea as it messes
 up with the 1x case. Will reintroduce it later in a better manner

---
 gyrokinetic/apps/gk_field.c | 2 --
 1 file changed, 2 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 3774fe2c3e..d9714a151b 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -222,8 +222,6 @@ static void
 gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double dt,
   const struct gkyl_array* inp)
 {
-  // Project inp (dApar/dt) onto FEM basis to make Apar continuous along z.
-  gk_field_fem_projection_par(app, field, out, out);
   // Apar^{n+1} = Apar^{n} + dt*dApar/dt
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
 }

From bf1079044cd351889b9e2d6a26fbb21c1bdadba1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 9 Feb 2026 11:34:27 -0500
Subject: [PATCH 093/181] Add the 3x2v alfven regression test

---
 gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c | 460 +++++++++++++++++++++
 1 file changed, 460 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
new file mode 100644
index 0000000000..4f6ac2d389
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
@@ -0,0 +1,460 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  double mu0;
+
+  // Geometry and magnetic field.
+  double R; // Major radius of the simulation box [m].
+  double a; // Minor radius at outboard midplane [m].
+  double r; // Minor radius of the simulation box [m].
+  double B; // Magnetic field magnitude in the simulation box [T].
+  double z_min;  double z_max;
+
+  double kperp;  // Perpendicular wavenumber.
+  double beta_hat; // Plasma beta parameter.
+
+  // Plasma parameters.
+  double me;  double qe;
+  double mi;  double qi;
+  double n0;  double Te0;  double Ti0; 
+
+  // Grid parameters.
+  double kz_min;
+  double x_min, x_max; // Min and max x-coordinates.
+  double y_min, y_max;
+  int Nx, Ny, Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc;  double mu_max_elc;
+  double vpar_max_ion;  double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Ion initial conditions.
+void density_init_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->n0;
+}
+void upar_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Ti0;
+}
+
+// Electron initial conditions.
+void density_init_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double z = xn[2];
+  fout[0] = app->n0 * (1 + 1e-6*cos(app->kz_min*z));
+}
+void upar_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = app->Te0;
+}
+
+// Slab magnetic equilibrium.
+static inline void
+mapc2p(double t, const double* xc, double* GKYL_RESTRICT xp, void* ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xc[0], y = xc[1], z = xc[2];
+  xp[0] = x; xp[1] = y; xp[2] = z;
+}
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  fout[0] = 0.0;
+  fout[1] = 0.0;
+  fout[2] = app->B;
+}
+
+void
+write_ctx_to_json(const struct gk_app_ctx *ctx)
+{
+  FILE *fp = fopen("ctx.json", "w");
+  if (!fp) {
+    perror("Error opening file for writing context");
+    return;
+  }
+
+  fprintf(fp, "{\n");
+  fprintf(fp, "  \"cdim\": %d,\n", ctx->cdim);
+  fprintf(fp, "  \"vdim\": %d,\n", ctx->vdim);
+  fprintf(fp, "  \"mu0\": %e,\n", ctx->mu0);
+  fprintf(fp, "  \"R\": %e,\n", ctx->R);
+  fprintf(fp, "  \"a\": %e,\n", ctx->a);
+  fprintf(fp, "  \"r\": %e,\n", ctx->r);
+  fprintf(fp, "  \"B\": %e,\n", ctx->B);
+  fprintf(fp, "  \"z_min\": %e,\n", ctx->z_min);
+  fprintf(fp, "  \"z_max\": %e,\n", ctx->z_max);
+  fprintf(fp, "  \"kperp\": %e,\n", ctx->kperp);
+  fprintf(fp, "  \"beta_hat\": %e,\n", ctx->beta_hat);
+  fprintf(fp, "  \"me\": %e,\n", ctx->me);
+  fprintf(fp, "  \"qe\": %e,\n", ctx->qe);
+  fprintf(fp, "  \"mi\": %e,\n", ctx->mi);
+  fprintf(fp, "  \"qi\": %e,\n", ctx->qi);
+  fprintf(fp, "  \"n0\": %e,\n", ctx->n0);
+  fprintf(fp, "  \"Te0\": %e,\n", ctx->Te0);
+  fprintf(fp, "  \"Ti0\": %e,\n", ctx->Ti0);
+  fprintf(fp, "  \"kz_min\": %e,\n", ctx->kz_min);
+  fprintf(fp, "  \"Nz\": %d,\n", ctx->Nz);
+  fprintf(fp, "  \"Nvpar\": %d,\n", ctx->Nvpar);
+  fprintf(fp, "  \"Nmu\": %d,\n", ctx->Nmu);
+  fprintf(fp, "  \"poly_order\": %d,\n", ctx->poly_order);
+  fprintf(fp, "  \"vpar_max_elc\": %e,\n", ctx->vpar_max_elc);
+  fprintf(fp, "  \"mu_max_elc\": %e,\n", ctx->mu_max_elc);
+  fprintf(fp, "  \"vpar_max_ion\": %e,\n", ctx->vpar_max_ion);
+  fprintf(fp, "  \"mu_max_ion\": %e,\n", ctx->mu_max_ion);
+  fprintf(fp, "  \"t_end\": %e,\n", ctx->t_end);
+  fprintf(fp, "  \"num_frames\": %d,\n", ctx->num_frames);
+  fprintf(fp, "  \"write_phase_freq\": %e,\n", ctx->write_phase_freq);
+  fprintf(fp, "  \"int_diag_calc_num\": %d,\n", ctx->int_diag_calc_num);
+  fprintf(fp, "  \"dt_failure_tol\": %e,\n", ctx->dt_failure_tol);
+  fprintf(fp, "  \"num_failures_max\": %d\n", ctx->num_failures_max);
+  fprintf(fp, "}\n");
+
+  fclose(fp);
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 3, vdim = 2; // Dimensionality.
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+  double me = GKYL_ELECTRON_MASS;
+  double mi = 2*GKYL_PROTON_MASS;
+  double mu0 = GKYL_MU0;
+  // Geometry, magnetic field and gradients.
+  double R0 = 1.313; // Major radius of the simulation box [m].
+  double a = 0.4701; // Minor radius at outboard midplane [m].
+  double B0 = 1.91; // Magnetic field magnitude in the simulation box [T].
+  double Ti0 = 2072*eV;
+  double eps_n = 0.2;
+  double kz_Ln = 1.0;
+
+  // EZ case:
+  // double beta_hat = 0.1; // gkylscan can parameter.
+  // double kperp_rhos = 0.5; // gkylscan can parameter.
+  // Damping hard to catch case:
+  double beta_hat = 0.1; // gkylscan can parameter.
+  double kperp_rhos = 0.5; // gkylscan can parameter.
+  double nperiod = 0.1;
+
+  double beta_e = beta_hat*2.0*me/mi;
+  double tau = 1.0; // Ti/Te.
+  // Derived paramters.
+  double r0 = 0.5*a; // Minor radius of the simulation box [m].
+  double R = R0 + r0; // Major radius at center of simulation box [m].
+  double B = B0 * R0/R; // Magnetic field at center of simulation box [T].
+  double Te0 = Ti0/tau; // Electron temperature [J].
+  double n0 = beta_e*B*B/(2*mu0*Te0); // Density [m^-3].
+  double vte = sqrt(Te0/me); // Electron thermal speed [m/s].
+  double vti = sqrt(Ti0/mi); // Ion thermal speed [m/s].
+  double c_s = sqrt(Te0/mi); // Sound speed [m/s].
+  double omega_ci = fabs(qi*B/mi); // Ion cyclotron frequency [rad/s].
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius [m]
+  double L_n = R*eps_n; // Density gradient scale length [m].
+  double kz_min = kz_Ln/L_n; // Minimum parallel wavenumber [1/m].
+  // Expected frequency from dispersion relation:
+  // double omega = kz_min*c_s*sqrt(2/beta_e/(1+beta_hat*pow(ky_rhos,2)));
+  double va = vte/sqrt(beta_hat); // Alfvén speed [m/s].
+  // double omega = kz_min*va; // Shear Alfvén wave frequency [rad/s].
+  double omega = sqrt(pow(kz_min*va,2)/(1+beta_hat*pow(kperp_rhos,2))); // KAW frequency [rad/s].
+  // double omega = sqrt(pow(kz_min,2)*2/beta_e*pow(c_s,2)/(1+beta_hat*pow(ky_rhos,2)));
+  
+  double kperp = kperp_rhos/rho_s; // Minimum perpendicular wavenumber [1/m].
+  double Lx = M_PI/kperp; // Domain length in x-direction [m].
+
+  // Grid parameters
+  int Nx = 8; // Number of cells in x-direction.
+  double x_min = -Lx/2;
+  double x_max = Lx/2;
+  int Ny = 8;
+  double y_min = -Lx/2;
+  double y_max = Lx/2;
+  int Nz = 12; // Reduce this to delay recurrence effect.
+  double z_min = -M_PI/kz_min;  // Min z-coordinate [m].
+  double z_max = M_PI/kz_min;   // Max z-coordinate [m].
+  int Nvpar = 24; // Increase this to delay recurrence effect.
+  double vpar_max_elc = 6.0*vte; // Max electron parallel velocity [m/s].
+  double vpar_min_elc = -vpar_max_elc; // Min electron parallel velocity [m/s].
+  double vpar_max_ion = 6.0*vti; // Max ion parallel velocity [m/s].
+  double vpar_min_ion = -vpar_max_ion; // Min ion parallel
+  int Nmu = 2;
+  double mu_max_elc = me*pow(4*vte,2)/(2*B); // Max electron mu [J/T].
+  double mu_max_ion = mi*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
+  int poly_order = 1;
+
+  double t_end = nperiod*2*M_PI/omega; // End time [s].
+  int num_frames = 1;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*1000;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .mu0 = mu0,
+    .R = R,
+    .B = B,
+    .beta_hat = beta_hat,
+    .me = me,  .qe = qe,
+    .mi = mi,  .qi = qi,
+    .n0 = n0,  .Te0 = Te0,  .Ti0 = Ti0,
+
+    .Nx = Nx,
+    .Ny = Ny,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .x_min = x_min,
+    .x_max = x_max,
+    .y_min = y_min,
+    .y_max = y_max,
+    .z_min = z_min,
+    .z_max = z_max,
+    .kperp = kperp,
+    .kz_min = kz_min,
+    .vpar_max_elc = vpar_max_elc,  .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion,  .mu_max_ion = mu_max_ion,
+    .cells = {Nx, Ny, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+
+    .t_end = t_end,  .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+int main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // Electrons.
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_elc, 0.0},
+    .upper = {  ctx.vpar_max_elc, ctx.mu_max_elc}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_elc,
+      .ctx_upar = &ctx,
+      .upar= upar_elc,
+      .ctx_temp = &ctx,
+      .temp = temp_elc,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+    },
+
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Ions.
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .is_static = false,
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = {  ctx.vpar_max_ion, ctx.mu_max_ion}, 
+    .cells = { cells_v[0], cells_v[1] },
+
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .density = density_init_ion,
+      .ctx_upar = &ctx,
+      .upar= upar_ion,
+      .ctx_temp = &ctx,
+      .temp = temp_ion,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+    },
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Field.
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .mu0 = ctx.mu0,
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .name = "gk_em_alfven_3x2v_p1",
+    .cfl_frac = 1.0,
+    .cfl_frac_omegaH = 1.0,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.y_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.y_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1], cells_x[2] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx
+    },
+
+    .num_periodic_dir = 2,
+    .periodic_dirs = {1,2},
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .cuts = { app_args.cuts[0], app_args.cuts[1], app_args.cuts[2] },
+      .comm = comm,
+    },
+  };
+
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  write_ctx_to_json(&ctx);
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+  return 0;
+}

From 41d8875bdeaf40f0c12a4b661509fef837d07c5f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 10 Feb 2026 14:29:56 -0500
Subject: [PATCH 094/181] Remove empty lines

---
 .../gkyl_gk_collisionless_flux_kernels.h      | 144 ------------------
 1 file changed, 144 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index f0cb7189da..982daf25ec 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -9,7 +9,6 @@ EXTERN_C_BEG
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -17,7 +16,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -25,7 +23,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -33,7 +30,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -49,7 +45,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -57,7 +52,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -65,7 +59,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -73,7 +66,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -89,7 +81,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -97,7 +88,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -105,7 +95,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -113,7 +102,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -129,7 +117,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -137,7 +124,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -145,7 +131,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -153,7 +138,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -169,7 +153,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -177,7 +160,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -185,7 +167,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -193,7 +174,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -201,7 +181,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -209,7 +188,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -217,7 +195,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -225,7 +202,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -241,7 +217,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -249,7 +224,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -257,7 +231,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -265,7 +238,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -273,7 +245,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -281,7 +252,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -289,7 +259,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -297,7 +266,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -313,7 +281,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -321,7 +288,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -329,7 +295,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -337,7 +302,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -345,7 +309,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -353,7 +316,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -361,7 +323,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -369,7 +330,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -385,7 +345,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -393,7 +352,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -401,7 +359,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -409,7 +366,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -417,7 +373,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -425,7 +380,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -433,7 +387,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -441,7 +394,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -457,7 +409,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -465,7 +416,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -473,7 +423,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -481,7 +430,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -489,7 +437,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -497,7 +444,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -505,7 +451,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -513,7 +458,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -521,7 +465,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -529,7 +472,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -537,7 +479,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -545,7 +486,6 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -561,7 +501,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -569,7 +508,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -577,7 +515,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -585,7 +522,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -593,7 +529,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -601,7 +536,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -609,7 +543,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -617,7 +550,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -625,7 +557,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -633,7 +564,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -641,7 +571,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -649,7 +578,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -665,7 +593,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -673,7 +600,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -681,7 +607,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -689,7 +614,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -705,7 +629,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -713,7 +636,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -721,7 +643,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -729,7 +650,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -745,7 +665,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p2(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -753,7 +672,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -761,7 +679,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -769,7 +686,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -785,7 +701,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -793,7 +708,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -801,7 +715,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -809,7 +722,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -825,7 +737,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p2(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -833,7 +744,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -841,7 +751,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -849,7 +758,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -857,7 +765,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -865,7 +772,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -873,7 +779,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -881,7 +786,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -897,7 +801,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -905,7 +808,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -913,7 +815,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -921,7 +822,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -929,7 +829,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -937,7 +836,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -945,7 +843,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -953,7 +850,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -969,7 +865,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -977,7 +872,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -985,7 +879,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -993,7 +886,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1001,7 +893,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1009,7 +900,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1017,7 +907,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1025,7 +914,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1041,7 +929,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p2(
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1049,7 +936,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1057,7 +943,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1065,7 +950,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1073,7 +957,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1081,7 +964,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1089,7 +971,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1097,7 +978,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1113,7 +993,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1121,7 +1000,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1129,7 +1007,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1137,7 +1014,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1145,7 +1021,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1153,7 +1028,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1161,7 +1035,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1169,7 +1042,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1177,7 +1049,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1185,7 +1056,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1193,7 +1063,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1201,7 +1070,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1217,7 +1085,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1225,7 +1092,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1233,7 +1099,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1241,7 +1106,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1249,7 +1113,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1257,7 +1120,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1265,7 +1127,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1273,7 +1134,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1281,7 +1141,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1289,7 +1148,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1297,7 +1155,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_, 
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
@@ -1305,7 +1162,6 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_
                   double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
                   const double *w, const double *dxv,
-                  
                   const double *vmap, const double *vmapSq, const double q_, const double m_,
                   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
                   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,

From 8528c0b6febf2488009a96b7777726093d80a3f0 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 10 Feb 2026 14:31:55 -0500
Subject: [PATCH 095/181] update calculation of alphavpar in the 1x1v case
 according to the latest state of the gkylcas routines.

---
 .../dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c              | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
index ab4e2f0517..c8f481cde2 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1.c
@@ -8,8 +8,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double *vmap,
   // out: output increment.
 
   double alphavpar[6] = {0.}; 
-  alphavpar[0] = -((1.4142135623730951*apardot[0]*q_)/m_); 
-  alphavpar[1] = -((1.4142135623730951*apardot[1]*q_)/m_); 
+  alphavpar[0] = -((1.1547005383792517*apardot[0]*q_)/(vmap[1]*m_)); 
+  alphavpar[1] = -((1.1547005383792517*apardot[1]*q_)/(vmap[1]*m_)); 
 
 
   out[2] += 0.8660254037844386*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 

From 2c4a660ff6a2174c5be28eb5af6856374443b2ef Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 10 Feb 2026 17:59:21 -0500
Subject: [PATCH 096/181] indentation fix

---
 gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 3ff1e697f1..9634cff95b 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -283,12 +283,12 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
 GKYL_CU_D
 static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[] = {
   {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      },
   },
   {
     .kernels_list = {

From 00f119288e75498c0234cd6339cc869a8e52666d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 11 Feb 2026 11:11:44 -0500
Subject: [PATCH 097/181] Benign bug fix. The conditions on colless_type was
 badly written. This is benign because it only activate the add_apar_term
 volume kernel in ES case, where Apar is 0 anyway but better to make it right.

---
 gyrokinetic/zero/dg_gyrokinetic.c     | 3 ++-
 gyrokinetic/zero/dg_gyrokinetic_cu.cu | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index b5c6f203d1..649ce45418 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -122,7 +122,8 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
-  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM || GKYL_GK_COLLISIONLESS_EM_BPERP ? 
+  gyrokinetic->vol_add_apar_term = 
+    (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 
     CK(vol_add_apar_kernels,cdim,vdim,poly_order) : dg_gyrokinetic_vol_return_zero;
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 52f1e81284..9185081a60 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -94,7 +94,8 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
   }
 
-  gyrokinetic->vol_add_apar_term = collless_type == GKYL_GK_COLLISIONLESS_EM || GKYL_GK_COLLISIONLESS_EM_BPERP ? 
+  gyrokinetic->vol_add_apar_term = 
+    ((collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 
     vol_add_apar_kernels[cv_index].kernels[poly_order] : dg_gyrokinetic_vol_return_zero;
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];

From 6ead1c6d430a91b79d80928282b6d49fe7c5bdd5 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 11 Feb 2026 11:12:43 -0500
Subject: [PATCH 098/181] Following the last commit, add extra parenthesis in
 logic to ensure that all the conditions on the collless_type are behaving
 correctly.

---
 gyrokinetic/apps/gk_field.c                  |   6 +-
 gyrokinetic/apps/gk_species.c                |   2 +-
 gyrokinetic/apps/gk_species_collisionless.c  |   4 +-
 gyrokinetic/apps/gyrokinetic.c               |   6 +
 gyrokinetic/creg/rt_gk_em_asdex_2x2v_p1.c    | 606 +++++++++++++++++++
 gyrokinetic/zero/gk_collisionless_flux.c     |   2 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu |   2 +-
 7 files changed, 620 insertions(+), 8 deletions(-)
 create mode 100644 gyrokinetic/creg/rt_gk_em_asdex_2x2v_p1.c

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index d9714a151b..cdc8361455 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -387,9 +387,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-    f->is_em = f->is_em || s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || 
-                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP ||
-                      s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPAR;
+    f->is_em = f->is_em || (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || 
+                      (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP) ||
+                      (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPAR);
   }
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 90d8a69316..83e3fba70e 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -981,7 +981,7 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
-  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM || gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)
+  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP))
     gks->add_apardot_rhs_func = gk_species_add_apardot_dynamic;
   else
     gks->add_apardot_rhs_func = gk_species_rhs_static;
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index ec938ff2f8..f6c3a83e95 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -177,7 +177,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
     }
     // Electromagnetic set up.
-    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+    if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
       only_apardot = true;
       // Create a special flux operator that only adds the AparDot contribution.
       gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
@@ -231,7 +231,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
-    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM || gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP) {
+    if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
       gkyl_gk_collisionless_flux_release(gkcls->add_apardot_surf_flux_op);
       gkyl_dg_updater_gyrokinetic_release(gkcls->add_apardot_slvr);
     }
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 7f58334f02..4cf56ad880 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1981,6 +1981,12 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
     gk_species_add_apardot_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+  }
+
+  // Update boundary fluxes and compute CFL condition.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *gk_s = &app->species[i];
+    // gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
     double dt1 = gk_species_get_cfl(app, gk_s, fin[i], fout[i], bflux_out[i]);
     dtmin = fmin(dtmin, dt1);
   }
diff --git a/gyrokinetic/creg/rt_gk_em_asdex_2x2v_p1.c b/gyrokinetic/creg/rt_gk_em_asdex_2x2v_p1.c
new file mode 100644
index 0000000000..5060913b9a
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_em_asdex_2x2v_p1.c
@@ -0,0 +1,606 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_tok_geo.h>
+
+#include <rt_arg_parse.h>
+
+struct gk_asdex_ctx {
+  int cdim, vdim; // Dimensionality
+
+  double chargeElc; // electron charge
+  double massElc; // electron mass
+  double chargeIon; // ion charge
+  double massIon; // ion mass
+  double Te; // electron temperature
+  double Ti; // ion temperature
+  double c_s; // sound speed
+  double nuElc; // electron collision frequency
+  double nuIon; // ion collision frequency
+  double B0; // reference magnetic field
+  double n0; // reference density
+  // Source parameters
+  double lambda_source;
+  double x_source;
+  // Domain parameters.            
+  int Nx, Nz; // Number of cells in x,y,z.
+  int Nvpar, Nmu; // Number of cells in vpar,mu.
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  double Lx; // Box size in x
+  double Lz; // Box size in z
+  // Physical velocity space limits
+  double vpar_max_elc; // Velocity space extents in vparallel for electrons
+  double mu_max_elc; // Velocity space extents in mu for electrons
+  double vpar_max_ion; // Velocity space extents in vparallel for ions
+  double mu_max_ion; // Velocity space extents in mu for ions
+  // Computational velocity space limits
+  double vpar_min_elc_c, vpar_max_elc_c;
+  double mu_min_elc_c, mu_max_elc_c;
+  double vpar_min_ion_c, vpar_max_ion_c;
+  double mu_min_ion_c, mu_max_ion_c;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+double random0to1() 
+{
+  return (double)rand() / (double)RAND_MAX;
+}
+
+void
+eval_density(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double floor = 0.01;
+
+  fout[0] = fmax(exp(-128.48398224*x+62.52416972), floor); // The coefficients from fitting the data points on Fig. 7 Carralero 2017 Nuclear Fusion.
+}
+
+void
+eval_upar(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+
+void
+eval_temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double eV = GKYL_ELEMENTARY_CHARGE;
+
+  //fout[0] = (-2000.0*x + 360.0)*eV;   // [16, 40] eV
+  fout[0] = (-50*tanh((x-0.15)/0.022) + 40) * eV;
+}
+
+void
+eval_temp_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double eV = GKYL_ELEMENTARY_CHARGE;
+
+  //fout[0] = (-3000.0*x + 552.0)*eV;   // [36, 72] eV
+  fout[0] = (-90*tanh((x-0.15)/0.022) + 72) * eV;
+}
+
+void
+eval_density_source(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double lambda_source = app->lambda_source;
+  double x_source = app->x_source;
+  double z_source = 0.0;
+  double Lz = app->Lz;
+  double source_floor = 1e-10;
+
+  if (x < x_source + 3*lambda_source)
+    source_floor = 1e-2;
+  if (fabs(z) < Lz/4)
+    fout[0] = 6.0e21*fmax(exp(-(x-x_source)*(x-x_source)/((2*lambda_source)*(2*lambda_source))), source_floor);
+  else
+    fout[0] = 6.0e21*1e-40;
+}
+
+void
+eval_upar_source(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+
+void
+eval_temp_elc_source(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double lambda_source = app->lambda_source;
+  double x_source = app->x_source;
+  double Lz = app->Lz;
+  double eV = GKYL_ELEMENTARY_CHARGE;
+  if ((x < x_source + 3*lambda_source) && (fabs(z) < Lz/4))
+    fout[0] = 40.0*eV;
+  else
+    fout[0] = 1.920292202211762*eV;
+}
+
+void
+eval_temp_ion_source(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double x = xn[0], z = xn[1];
+  double lambda_source = app->lambda_source;
+  double x_source = app->x_source;
+  double Lz = app->Lz;
+  double eV = GKYL_ELEMENTARY_CHARGE;
+  if ((x < x_source + 3*lambda_source) && (fabs(z) < Lz/4))
+    fout[0] = 72.0*eV;
+  else
+    fout[0] = 3.4565259639811785*eV;
+}
+
+void
+diffusion_D_func(double t, const double* GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void* ctx)
+{
+  struct sheath_ctx *app = ctx;
+
+  fout[0] = 0.1; // Diffusivity [m^2/s].
+}
+
+// Velocity space mappings.
+void mapc2p_vel_elc(double t, const double *vc, double* GKYL_RESTRICT vp, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double vpar_max_elc = app->vpar_max_elc;
+  double mu_max_elc = app->mu_max_elc;
+
+  double cvpar = vc[0], cmu = vc[1];
+  // Linear map up to vpar_max/2, then quadratic.
+  if (fabs(cvpar) <= 0.5)
+    vp[0] = vpar_max_elc*cvpar;
+  else if (cvpar < -0.5)
+    vp[0] = -vpar_max_elc*2.0*pow(cvpar,2);
+  else
+    vp[0] =  vpar_max_elc*2.0*pow(cvpar,2);
+
+  // Quadratic map in mu.
+  vp[1] = mu_max_elc*pow(cmu,2);
+}
+
+void mapc2p_vel_ion(double t, const double *vc, double* GKYL_RESTRICT vp, void *ctx)
+{
+  struct gk_asdex_ctx *app = ctx;
+  double vpar_max_ion = app->vpar_max_ion;
+  double mu_max_ion = app->mu_max_ion;
+
+  double cvpar = vc[0], cmu = vc[1];
+  // Linear map up to vpar_max/2, then quadratic.
+  if (fabs(cvpar) <= 0.5)
+    vp[0] = vpar_max_ion*cvpar;
+  else if (cvpar < -0.5)
+    vp[0] = -vpar_max_ion*2.0*pow(cvpar,2);
+  else
+    vp[0] =  vpar_max_ion*2.0*pow(cvpar,2);
+
+  // Quadratic map in mu.
+  vp[1] = mu_max_ion*pow(cmu,2);
+}
+
+struct gk_asdex_ctx
+create_ctx(void)
+{
+  int cdim = 2, vdim = 2; // Dimensionality.
+
+  double eps0 = GKYL_EPSILON0;
+  double eV = GKYL_ELEMENTARY_CHARGE;
+  double mi = 2.014*GKYL_PROTON_MASS; // ion mass
+  double me = GKYL_ELECTRON_MASS;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+
+  double Te = 40.0*eV;
+  double Ti = 72.0*eV;
+  double B0 = 2.57; // Magnetic field magnitude in Tesla
+  double n0 = 6.0e18; // Particle density in 1/m^3
+
+  // Derived parameters.
+  double vtIon = sqrt(Ti/mi);
+  double vtElc = sqrt(Te/me);
+  double c_s = sqrt(Te/mi);
+  double omega_ci = fabs(qi*B0/mi);
+  double rho_s = c_s/omega_ci;
+
+
+  // Collision parameters.
+  double nuFrac = 1.0;  
+  double logLambdaElc = 6.6 - 0.5*log(n0/1e20) + 1.5*log(Te/eV);
+  double nuElc = nuFrac*logLambdaElc*pow(eV, 4.0)*n0/(6.0*sqrt(2.0)*M_PI*sqrt(M_PI)*eps0*eps0*sqrt(me)*(Te*sqrt(Te)));  // collision freq
+
+  double logLambdaIon = 6.6 - 0.5*log(n0/1e20) + 1.5*log(Ti/eV);
+  double nuIon = nuFrac*logLambdaIon*pow(eV, 4.0)*n0/(12.0*M_PI*sqrt(M_PI)*eps0*eps0*sqrt(mi)*(Ti*sqrt(Ti)));
+
+  // Simulation box size (psi, theta).
+  double Lx = 0.172 - 0.150;
+  double Lz = (M_PI-1.0e-14)*2;
+
+  // Source parameters.
+  double x_source = 0.160;   // changed from 0.16167
+  double lambda_source = 0.0004;   // Changed from 0.00034, characteristic length scale of n and T
+
+  // Physical velocity space limits
+  double vpar_max_elc = 6.0*vtElc;
+  double mu_max_elc = me*(4.0*vtElc)*(4.0*vtElc)/(2.0*B0);
+
+  double vpar_max_ion = 6.0*vtIon;
+  double mu_max_ion = mi*(4.0*vtIon)*(4.0*vtIon)/(2.0*B0);
+
+  // Computational velocity space limits.
+  double vpar_min_ion_c = -1.0/sqrt(2.0);
+  double vpar_max_ion_c = 1.0/sqrt(2.0);
+  double mu_min_ion_c = 0.;
+  double mu_max_ion_c = 1.;
+  // Computational velocity space limits.
+  double vpar_min_elc_c = -1.0/sqrt(2.0);
+  double vpar_max_elc_c = 1.0/sqrt(2.0);
+  double mu_min_elc_c = 0.;
+  double mu_max_elc_c = 1.;
+
+  int Nx = 16; // Number of cells in x.
+  int Nz = 16; // Number of cells in z, originally 8.
+  int Nvpar = 16; // Number of cells in vpar.
+  int Nmu = 8; // Number of cells in mu.
+
+  double t_end = 10.0e-6;
+  double num_frames = 20;
+  double write_phase_freq = 0.2; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*100;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 20; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_asdex_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .chargeElc = qe, 
+    .massElc = me, 
+    .chargeIon = qi, 
+    .massIon = mi,
+    .Te = Te, 
+    .Ti = Ti, 
+    .c_s = c_s, 
+    .nuElc = nuElc, 
+    .nuIon = nuIon, 
+    .B0 = B0, 
+    .n0 = n0, 
+    .Lx = Lx, 
+    .Lz = Lz, 
+    .lambda_source = lambda_source,
+    .x_source = x_source,
+    // Physical velocity space limits
+    .vpar_max_elc = vpar_max_elc, 
+    .mu_max_elc = mu_max_elc, 
+    .vpar_max_ion = vpar_max_ion, 
+    .mu_max_ion = mu_max_ion, 
+    // Computational velocity space limits
+    .vpar_min_elc_c = vpar_min_elc_c,
+    .vpar_max_elc_c = vpar_max_elc_c,
+    .mu_min_elc_c = mu_min_elc_c,
+    .mu_max_elc_c = mu_max_elc_c,
+    .vpar_min_ion_c = vpar_min_ion_c,
+    .vpar_max_ion_c = vpar_max_ion_c,
+    .mu_min_ion_c = mu_min_ion_c,
+    .mu_max_ion_c = mu_max_ion_c,
+    .Nx = Nx,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .cells = {Nx, Nz, Nvpar, Nmu},
+    .t_end = t_end, 
+    .num_frames = num_frames, 
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+int
+main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_asdex_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // electrons
+  struct gkyl_gyrokinetic_projection elc_ic = {
+    .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+    .ctx_density = &ctx,
+    .density = eval_density,
+    .ctx_upar = &ctx,
+    .upar= eval_upar,
+    .ctx_temp = &ctx,
+    .temp = eval_temp_elc,      
+  };
+
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.chargeElc, .mass = ctx.massElc,
+    .vdim = ctx.vdim,
+    .lower = { ctx.vpar_min_elc_c, ctx.mu_min_elc_c},
+    .upper = { ctx.vpar_max_elc_c, ctx.mu_max_elc_c},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .mapc2p = {
+      .mapping = mapc2p_vel_elc,
+      .ctx = &ctx,
+    },
+
+    .projection = elc_ic,
+  
+    .correct = {
+      .correct_all_moms = true, 
+      .use_last_converged = true, 
+      .iter_eps = 1e-12,
+      .max_iter = 10,
+    }, 
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_BGK_COLLISIONS,
+      .den_ref = ctx.n0, // Density used to calculate coulomb logarithm
+      .temp_ref = ctx.Te, // Temperature used to calculate coulomb logarithm
+      .num_cross_collisions = 1,
+      .collide_with = { "ion" },
+      .write_diagnostics = true, 
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      //.write_source = true,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+        .ctx_density = &ctx,
+        .density = eval_density_source,
+        .ctx_upar = &ctx,
+        .upar= eval_upar_source,
+        .ctx_temp = &ctx,
+        .temp = eval_temp_elc_source,      
+      }, 
+    },
+
+    .anomalous_diffusion = {
+      .anomalous_diff_id = GKYL_GK_ANOMALOUS_DIFF_D,
+      .D_profile = diffusion_D_func,
+      .D_profile_ctx = &ctx,
+//      .write_diagnostics = true,
+    },
+      
+    .positivity = {
+      .type = GKYL_GK_POSITIVITY_SHIFT,
+      .write_diagnostics = true,
+      .quasineutrality_rescale = true,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_FIXED_FUNC, .projection = elc_ic, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB, },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH, },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH, },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP, GKYL_F_MOMENT_BIMAXWELLIAN, GKYL_F_MOMENT_MAXWELLIAN },
+  };
+
+  // ions
+  struct gkyl_gyrokinetic_projection ion_ic = {
+    .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+    .ctx_density = &ctx,
+    .density = eval_density,
+    .ctx_upar = &ctx,
+    .upar= eval_upar,
+    .ctx_temp = &ctx,
+    .temp = eval_temp_ion,      
+  };
+
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.chargeIon, .mass = ctx.massIon,
+    .vdim = ctx.vdim,
+    .lower = { ctx.vpar_min_ion_c, ctx.mu_min_ion_c},
+    .upper = { ctx.vpar_max_ion_c, ctx.mu_max_ion_c},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .mapc2p = {
+      .mapping = mapc2p_vel_ion,
+      .ctx = &ctx,
+    },
+
+    .projection = ion_ic,
+
+    .correct = {
+      .correct_all_moms = true, 
+      .use_last_converged = true, 
+      .iter_eps = 1e-12,
+      .max_iter = 10,
+    }, 
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_BGK_COLLISIONS,
+      .den_ref = ctx.n0, // Density used to calculate coulomb logarithm
+      .temp_ref = ctx.Ti, // Temperature used to calculate coulomb logarithm
+      .num_cross_collisions = 1,
+      .collide_with = { "elc" },
+      .write_diagnostics = true, 
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      //.write_source = true,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+        .ctx_density = &ctx,
+        .density = eval_density_source,
+        .ctx_upar = &ctx,
+        .upar= eval_upar_source,
+        .ctx_temp = &ctx,
+        .temp = eval_temp_ion_source,      
+      }, 
+    },
+
+    .anomalous_diffusion = {
+      .anomalous_diff_id = GKYL_GK_ANOMALOUS_DIFF_D,
+      .D_profile = diffusion_D_func,
+      .D_profile_ctx = &ctx,
+//      .write_diagnostics = true,
+    },
+    
+    .positivity = {
+      .type = GKYL_GK_POSITIVITY_SHIFT,
+      .write_diagnostics = true,
+      .quasineutrality_rescale = true,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_FIXED_FUNC, .projection = ion_ic, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB, },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH, },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH, },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP, GKYL_F_MOMENT_BIMAXWELLIAN, GKYL_F_MOMENT_MAXWELLIAN },
+  };
+
+  // field
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .mu0 = GKYL_MU0,
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+  };
+
+  struct gkyl_efit_inp efit_inp = {
+    // psiRZ and related inputs
+    .filepath = "asdex.geqdsk", // equilibrium to use
+    .rz_poly_order = 2,                      // polynomial order for psi(R,Z) used for field line tracing
+    .flux_poly_order = 1,                    // polynomial order for fpol(psi)
+  };
+
+  struct gkyl_tok_geo_grid_inp grid_inp = {
+    .ftype = GKYL_LSN_SOL,                     // type of geometry
+    .rclose = 2.5,                             // closest R to region of interest
+    .rright = 2.5,                             // Closest R to outboard SOL
+    .rleft = 0.7,                              // closest R to inboard SOL
+    .rmax = 2.5,                               // largest R in machine
+    .rmin = 0.7,                               // smallest R in machine
+    .zmin = -1.3,                              // Lower Z boundary 
+    .zmax = 1.0,                               // Upper Z boundary
+    .zmin_left = -1.0,                         // Z of inboard divertor plate
+    .zmin_right = -1.0,                        // Z of outboard divertor plate
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .name = "wk/em_gk_bgk_asdex_2x2v_p1",
+
+    .cdim = ctx.cdim,
+    .lower = { 0.15, -ctx.Lz/2.0 },   // Originally 0.16
+    .upper = { 0.172, ctx.Lz/2.0 },   // Originally 0.175
+    .cells = { cells_x[0], cells_x[1] },
+    .poly_order = 1,
+    .basis_type = app_args.basis_type,
+    .cfl_frac = 0.03,
+
+    .geometry = {
+      .geometry_id = GKYL_TOKAMAK,
+      .efit_info = efit_inp,
+      .tok_grid_info = grid_inp,
+    },
+
+    .num_periodic_dir = 0,
+    .periodic_dirs = {  },
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .cuts = { app_args.cuts[0], app_args.cuts[1] },
+      .comm = comm,
+    },
+  };
+
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+  
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+
+  return 0;
+}
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index e43e5123f4..e9af9a8813 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -51,7 +51,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
     }
     up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
   } else {
-    int em = (type == GKYL_GK_COLLISIONLESS_EM || type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 1 : 0;
+    int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
     if (no_by) {
       for (int d=0; d<cdim; ++d) {
         // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index fa2ef0a8aa..4af0b95b54 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -259,7 +259,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
-  int em = (type == GKYL_GK_COLLISIONLESS_EM || type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 1 : 0;
+  int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
 
   // Acquire pointers to on_dev objects so memcpy below copies those too.
   struct gk_geometry *geom_ho = gkyl_gk_geometry_acquire(gk_geom);

From 7b819c054360f0a8ff6a153c1b93af9026aeb92b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 12 Feb 2026 15:20:32 -0500
Subject: [PATCH 099/181] remove unused kernel

---
 .../gk_collisionless_flux_surfvpar_return_zero.c      | 11 -----------
 1 file changed, 11 deletions(-)
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
deleted file mode 100644
index b47331bf64..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
+++ /dev/null
@@ -1,11 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-    return 0.0; 
-}
\ No newline at end of file

From ac10eb7e0f228fd1eccb9077013e20c6e9181321 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 12 Feb 2026 15:31:58 -0500
Subject: [PATCH 100/181] remove unused return zero vpar kernel and handle
 improve spacing

---
 .../gk_collisionless_flux_surf_return_zero.c  |    2 +-
 .../gkyl_gk_collisionless_flux_kernels.h      | 2072 ++++++++---------
 2 files changed, 1033 insertions(+), 1041 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
index 5f1299df4e..95196d3239 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
@@ -8,4 +8,4 @@ GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   return 0.0; 
-}
\ No newline at end of file
+}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index 982daf25ec..bf3aa0d71e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -8,1240 +8,1232 @@
 EXTERN_C_BEG
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_, 
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-                  const double *w, const double *dxv,
-                  const double *vmap, const double *vmapSq, const double q_, const double m_,
-                  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-                  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-                  const double *phi, const double *apar, const double *JfL, const double *JfR, 
-                  double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-              const double *w, const double *dxv,
-              const double *vmap_prime_l, const double *vmap_prime_r, 
-              const double *vmap, const double *vmapSq, const double q_, const double m_, 
-              const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-              const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR, 
-              double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p2(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p2(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p2(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
-            const double *w, const double *dxv,
-            const double *vmap_prime_l, const double *vmap_prime_r, 
-            const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-            const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR, 
-            double* GKYL_RESTRICT flux_surf); 
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf);
-
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf);
+  const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf);
 
 EXTERN_C_END

From e5a0cf6df4be367a2e3c79cf8b5e665e4081fd15 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 09:52:19 -0500
Subject: [PATCH 101/181] =?UTF-8?q?=F0=9F=90=9B*=20Rehandling=20of=20the?=
 =?UTF-8?q?=20EM=20workflow.=20Now,=20we=20call=20the=20RHS=20species=20fu?=
 =?UTF-8?q?nction=20twice=20in=20gyrokinetic.c:=20once=20to=20build=20RHS*?=
 =?UTF-8?q?=20which=20is=20used=20to=20solve=20Ohm's=20law=20and=20get=20A?=
 =?UTF-8?q?pardot,=20once=20to=20build=20the=20total=20RHS.=20The=20goal?=
 =?UTF-8?q?=20is=20to=20be=20sure=20that=20the=20upwind=20direction=20is?=
 =?UTF-8?q?=20chosen=20w.r.t.=20the=20total=20advection=20(the=20other=20e?=
 =?UTF-8?q?m=20branch=20upwind=20first=20ES+Apar,=20then=20Apardot=20only)?=
 =?UTF-8?q?.=20*:=20this=20branch=20may=20contain=20a=20bug,=20the=20alfve?=
 =?UTF-8?q?n=20wave=20test=20is=20no=20giving=20very=20clean=20results=20a?=
 =?UTF-8?q?s=20the=20get=5Fem=5Fback=20branch=20does.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Details:
- We replace the `add_apardot` flag by an `em_star` flag, which tells the dg vol and flux updaters if we are computing the full RHS or the RHS_star (no Apardot contribution).
- The surface flux kernels are now split in three cases: vanilla (electrostatic), em_star (ES+Apar RHS for solving Ohm's law), and em (full ES+Apar+Apardot).
- The volume kernels are now all called through a unified kernel function that calls pointers to function to get electrostatic, Apar and Apardot terms. These pointers to function are used to activate or not the em terms.
---
 gyrokinetic/apps/gk_species.c                 |   56 +-
 gyrokinetic/apps/gk_species_collisionless.c   |   62 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |   40 +-
 gyrokinetic/apps/gyrokinetic.c                |   27 +-
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |    3 +-
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |    3 +-
 ...sionless_flux_em_edge_surfx_1x1v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfx_1x2v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfx_2x2v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfx_3x2v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfy_2x2v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfy_3x2v_ser_p1.c} |    5 +-
 ...sionless_flux_em_edge_surfz_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_1x1v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_1x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfx_1x1v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfx_1x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfx_2x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfx_3x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfy_2x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfy_3x2v_ser_p1.c} |    5 +-
 ...ux_em_multib_boundary_surfz_3x2v_ser_p1.c} |    5 +-
 ...ss_flux_em_no_by_edge_surfx_2x2v_ser_p1.c} |    5 +-
 ...ss_flux_em_no_by_edge_surfx_3x2v_ser_p1.c} |    5 +-
 ...ss_flux_em_no_by_edge_surfy_2x2v_ser_p1.c} |    5 +-
 ...ss_flux_em_no_by_edge_surfy_3x2v_ser_p1.c} |    5 +-
 ...ss_flux_em_no_by_edge_surfz_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_2x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfx_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfy_2x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfy_3x2v_ser_p1.c} |    5 +-
 ..._multib_boundary_edge_surfz_3x2v_ser_p1.c} |    5 +-
 ...no_by_multib_boundary_surfx_2x2v_ser_p1.c} |    5 +-
 ...no_by_multib_boundary_surfx_3x2v_ser_p1.c} |    5 +-
 ...no_by_multib_boundary_surfy_2x2v_ser_p1.c} |    5 +-
 ...no_by_multib_boundary_surfy_3x2v_ser_p1.c} |    5 +-
 ...no_by_multib_boundary_surfz_3x2v_ser_p1.c} |    5 +-
 ...less_flux_em_no_by_surfvpar_2x2v_ser_p1.c} |  142 +-
 ...less_flux_em_no_by_surfvpar_3x2v_ser_p1.c} |  250 +-
 ...ionless_flux_em_no_by_surfx_2x2v_ser_p1.c} |    5 +-
 ...ionless_flux_em_no_by_surfx_3x2v_ser_p1.c} |    5 +-
 ...ionless_flux_em_no_by_surfy_2x2v_ser_p1.c} |    5 +-
 ...ionless_flux_em_no_by_surfy_3x2v_ser_p1.c} |    5 +-
 ...ionless_flux_em_no_by_surfz_3x2v_ser_p1.c} |    5 +-
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c |   98 +
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c |  126 +
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c |  217 ++
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c |  372 +++
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c |  217 ++
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c |  374 +++
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c |  372 +++
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c |  100 +
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c |  128 +
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c |  231 ++
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c |  398 +++
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c |  231 ++
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c |  400 +++
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c |  398 +++
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c |  100 +
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c |  128 +
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c |  231 ++
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c |  398 +++
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c |  231 ++
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c |  400 +++
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c |  398 +++
 ...lux_em_star_no_by_edge_surfx_2x2v_ser_p1.c |  193 ++
 ...lux_em_star_no_by_edge_surfx_3x2v_ser_p1.c |  324 +++
 ...lux_em_star_no_by_edge_surfy_2x2v_ser_p1.c |  193 ++
 ...lux_em_star_no_by_edge_surfy_3x2v_ser_p1.c |  326 +++
 ...lux_em_star_no_by_edge_surfz_3x2v_ser_p1.c |  324 +++
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  207 ++
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  350 +++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  207 ++
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  352 +++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  350 +++
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  207 ++
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  350 +++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  207 ++
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  352 +++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  350 +++
 ...flux_em_star_no_by_surfvpar_2x2v_ser_p1.c} |   15 +-
 ...flux_em_star_no_by_surfvpar_3x2v_ser_p1.c} |   15 +-
 ...ess_flux_em_star_no_by_surfx_2x2v_ser_p1.c |  193 ++
 ...ess_flux_em_star_no_by_surfx_3x2v_ser_p1.c |  324 +++
 ...ess_flux_em_star_no_by_surfy_2x2v_ser_p1.c |  193 ++
 ...ess_flux_em_star_no_by_surfy_3x2v_ser_p1.c |  326 +++
 ...ess_flux_em_star_no_by_surfz_3x2v_ser_p1.c |  324 +++
 ...nless_flux_em_star_surfvpar_1x1v_ser_p1.c} |   15 +-
 ...nless_flux_em_star_surfvpar_1x2v_ser_p1.c} |   15 +-
 ...nless_flux_em_star_surfvpar_2x2v_ser_p1.c} |   15 +-
 ...nless_flux_em_star_surfvpar_3x2v_ser_p1.c} |   15 +-
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c |   98 +
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c |  126 +
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c |  217 ++
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c |  372 +++
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c |  217 ++
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c |  374 +++
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c |  372 +++
 ...llisionless_flux_em_surfvpar_1x1v_ser_p1.c |  105 +
 ...llisionless_flux_em_surfvpar_1x2v_ser_p1.c |  129 +
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  226 ++
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  423 ++++
 ...collisionless_flux_em_surfx_1x1v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfx_1x2v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfx_2x2v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfx_3x2v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfy_2x2v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfy_3x2v_ser_p1.c} |    5 +-
 ...collisionless_flux_em_surfz_3x2v_ser_p1.c} |    5 +-
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c |    3 +-
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c |    3 +-
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c |    3 +-
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |    3 +-
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |    3 +-
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |    3 +-
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |    3 +-
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |    3 +-
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |    3 +-
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |    3 +-
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |    3 +-
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |    3 +-
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |    3 +-
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |    3 +-
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |    3 +-
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |    3 +-
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |    3 +-
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |    3 +-
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |   13 +-
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |   13 +-
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |    3 +-
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |    3 +-
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |    3 +-
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |    3 +-
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surf_return_zero.c  |    2 +-
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |   13 +-
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |   13 +-
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |   13 +-
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |   13 +-
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |    3 +-
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |    3 +-
 ...ss_flux_add_apardot_surfvpar_1x1v_ser_p1.c |   65 -
 ...ss_flux_add_apardot_surfvpar_1x2v_ser_p1.c |   83 -
 .../gkyl_gk_collisionless_flux_kernels.h      | 2167 ++++++++---------
 gyrokinetic/zero/dg_gyrokinetic.c             |   34 +-
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         |   24 +-
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |    4 +-
 gyrokinetic/zero/gk_collisionless_flux.c      |   66 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  |   23 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  373 +--
 .../zero/gkyl_dg_updater_gyrokinetic.h        |   17 +-
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h |    6 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  360 ++-
 179 files changed, 16048 insertions(+), 2164 deletions(-)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c => gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c} (95%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c} (97%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c} (95%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c} (96%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c} (95%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c} (96%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c} (66%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c} (77%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c} (99%)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c => gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c} (96%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c => gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c} (98%)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c => gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c} (88%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c => gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c} (93%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c => gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c} (98%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c => gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c} (99%)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfx_1x1v_ser_p1.c => gk_collisionless_flux_em_surfx_1x1v_ser_p1.c} (95%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfx_1x2v_ser_p1.c => gk_collisionless_flux_em_surfx_1x2v_ser_p1.c} (97%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfx_2x2v_ser_p1.c => gk_collisionless_flux_em_surfx_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfx_3x2v_ser_p1.c => gk_collisionless_flux_em_surfx_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfy_2x2v_ser_p1.c => gk_collisionless_flux_em_surfy_2x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfy_3x2v_ser_p1.c => gk_collisionless_flux_em_surfy_3x2v_ser_p1.c} (99%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_em_collisionless_flux_surfz_3x2v_ser_p1.c => gk_collisionless_flux_em_surfz_3x2v_ser_p1.c} (99%)
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 83e3fba70e..aaead547ee 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -162,14 +162,45 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 static void
-gk_species_add_apardot_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_star_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  struct timespec wst = gkyl_wall_clock();
+  // Gyroaverage the potential if needed.
+  species->gyroaverage(app, species, app->field->phi_smooth, species->gyro_phi);
+
+  gkyl_array_clear(species->cflrate, 0.0);
+  gkyl_array_clear(rhs, 0.0);
+
+  // Collisionless terms.
+  gk_species_collisionless_rhs_star(app, species, &species->collisionless, fin, rhs);
+
+  // Damping term.
+  gk_species_damping_advance(app, species, &species->damping, app->field->phi_smooth, fin,
+    species->lte.f_lte, rhs, species->cflrate);
 
-  gk_species_collisionless_add_apardot_rhs(app, species, &species->collisionless, fin, rhs);
+  // LBO Collisions.
+  gk_species_lbo_rhs(app, species, &species->lbo, fin, rhs);
 
-  app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
+  // BGK collisions.
+  gk_species_bgk_rhs(app, species, &species->bgk, fin, rhs);
+  
+  // Anomalous diffusion.
+  gk_species_anomalous_diff_rhs(app, species, &species->anom_diff, fin, rhs);
+
+  // Line radiation.
+  gk_species_radiation_rhs(app, species, &species->rad, fin, rhs);
+
+  // Reactions with charged species.
+  gk_species_react_rhs(app, species, &species->react, fin, rhs);
+
+  // Reactions with neutral species.
+  gk_species_react_rhs(app, species, &species->react_neut, fin, rhs);
+
+  // Heating source.
+  gk_species_heating_rhs(app, species, &species->heat_src, fin, rhs);
+
+  // Particle + heat source terms.
+  gk_species_source_rhs(app, species, &species->src, fin, rhs);
 }
 
 static double
@@ -979,12 +1010,13 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   }
 
   // Set function pointers.
-  gks->rhs_func = gk_species_rhs_dynamic;
+  gks->rhs_func = gk_species_rhs_static;
+  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
+    gks->rhs_star_func = gk_species_rhs_star_dynamic;
+  } else {
+    gks->rhs_star_func = gk_species_rhs_static;
+  }
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
-  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP))
-    gks->add_apardot_rhs_func = gk_species_add_apardot_dynamic;
-  else
-    gks->add_apardot_rhs_func = gk_species_rhs_static;
   gks->bflux_update = gk_species_update_bflux_dynamic;
   gks->get_cfl = gk_species_get_cfl_dynamic;
   gks->bc_func = gk_species_apply_bc_dynamic;
@@ -1020,8 +1052,8 @@ gk_species_init_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
   
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
+  gks->rhs_star_func = gk_species_rhs_static;
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
-  gks->add_apardot_rhs_func = gk_species_rhs_static;
   gks->bflux_update = gk_species_rhs_static;
   gks->get_cfl = gk_species_get_cfl_static;  
   gks->bc_func = gk_species_apply_bc_static;
@@ -1819,10 +1851,10 @@ gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 void
-gk_species_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  species->add_apardot_rhs_func(app, species, fin, rhs, bflux_moms);
+  species->rhs_star_func(app, species, fin, rhs, bflux_moms);
 }
 
 void 
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index f6c3a83e95..2cd5fba41c 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -20,9 +20,20 @@ gk_species_collisionless_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_speci
   // where they are not defined.
   gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, species->gyro_apar, fin, gkcls->flux_surf, species->cflrate);
+    species->gyro_phi, species->gyro_apar, species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
 }
 
+static void
+gk_species_collisionless_flux_star_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  struct gk_collisionless *gkcls, const struct gkyl_array *fin)
+{
+  // Compute the surface expansion of the phase space flux for ES + Apar contributions.
+  gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_em_star_op, 
+    &app->local, &species->local, &app->local_ext, &species->local_ext, 
+    species->gyro_phi, species->gyro_apar, species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
+}
+
+
 static void
 gk_species_collisionless_rhs_disabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
@@ -45,22 +56,19 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
-static void gk_species_collisionless_add_apardot_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+static void
+gk_species_collisionless_rhs_star_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
   struct timespec wst = gkyl_wall_clock();
 
-  // First remove the current ES+Apar contribution from the flux_surf array.
-  // Otherwise it will be counted twice in the gkyl_dg update.
-  gkyl_array_clear(gkcls->flux_surf, 0.0);
-  gkyl_gk_collisionless_flux_surf(gkcls->add_apardot_surf_flux_op, 
-    &app->local, &species->local, &app->local_ext, &species->local_ext, 
-    species->gyro_phi, species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
+  gkcls->flux_func_star(app, species, gkcls, fin);
 
-  // Advance the rhs adding only the Apardot volume contribution.
-  gkyl_dg_updater_gyrokinetic_advance(gkcls->add_apardot_slvr, &species->local,
+  gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_em_star, &species->local, 
     fin, species->cflrate, rhs);
 
+  gkcls->fdot_scaling(app, species, gkcls, rhs, species->cflrate, &species->local);
+
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -106,7 +114,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
-  gkcls->add_apardot_rhs_func = gk_species_collisionless_rhs_disabled;
+  gkcls->rhs_star_func = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -150,9 +158,9 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       bctype_conf[GKYL_MAX_CDIM+d] = gks->upper_bc[d].type;
     }
 
-    bool only_apardot = false;
+    bool em_star = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-      gks->info.charge, gks->info.mass, gkcls->collisionless_id,  gkcls->no_by, only_apardot, app->gk_geom, 
+      gks->info.charge, gks->info.mass, gkcls->collisionless_id,  gkcls->no_by, em_star, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -160,7 +168,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, gks->vel_map, 
+      gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     gkcls->scale_fac = -1.0; // Not used if scale_factor in input file is not given.
@@ -178,18 +186,18 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     }
     // Electromagnetic set up.
     if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
-      only_apardot = true;
-      // Create a special flux operator that only adds the AparDot contribution.
-      gkcls->add_apardot_surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-        gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, 
+      // Set up ES + Apar contributions to flux and solver.
+      em_star = true;
+      gkcls->surf_flux_em_star_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+        gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, 
         app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
-      // Create solver that only adds AparDot terms.
-      gkcls->add_apardot_slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+      gkcls->slvr_em_star = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
         &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, only_apardot, app->gk_geom, gks->vel_map, 
+        gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
         &aux_inp, app->use_gpu);
       // Methods chosen at runtime.
-      gkcls->add_apardot_rhs_func = gk_species_collisionless_add_apardot_rhs_enabled;
+      gkcls->flux_func_star = gk_species_collisionless_flux_star_enabled; // ES + Apar.
+      gkcls->rhs_star_func = gk_species_collisionless_rhs_star_enabled; // ES + Apar.
     }
   }
 }
@@ -208,11 +216,11 @@ gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *speci
   gkcls->rhs_func(app, species, gkcls, fin, rhs);
 }
 
-void 
-gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void
+gk_species_collisionless_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
-  gkcls->add_apardot_rhs_func(app, species, gkcls, fin, rhs);
+  gkcls->rhs_star_func(app, species, gkcls, fin, rhs);
 }
 
 void
@@ -232,8 +240,8 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
     if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
-      gkyl_gk_collisionless_flux_release(gkcls->add_apardot_surf_flux_op);
-      gkyl_dg_updater_gyrokinetic_release(gkcls->add_apardot_slvr);
+      gkyl_gk_collisionless_flux_release(gkcls->surf_flux_em_star_op);
+      gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_em_star);
     }
 
     if (gkcls->write_diagnostics) {
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index ab1ba821fb..71758f9500 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -296,13 +296,15 @@ struct gk_collisionless {
     struct {
       struct gkyl_array *flux_surf; // Array for surface phase space flux
       struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
-  struct gkyl_gk_collisionless_flux *add_apardot_surf_flux_op; // Updater to add Apardot terms to fluxes.
+      struct gkyl_gk_collisionless_flux *surf_flux_em_star_op; // EM collisionless fluxes without Apardot contribution.
       gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.
-  gkyl_dg_updater_gyrokinetic *add_apardot_slvr; // Solver to add Apardot terms to RHS.
+      gkyl_dg_updater_gyrokinetic *slvr_em_star; // EM without Apardot contribution.
 
       // Methods chosen at runtime.
       void (*flux_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
         struct gk_collisionless *gkcls, const struct gkyl_array *fin);
+      void (*flux_func_star)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+        struct gk_collisionless *gkcls, const struct gkyl_array *fin);
     };
     // Neutral (Vlasov) species ............................................ //
     struct {
@@ -321,7 +323,7 @@ struct gk_collisionless {
   };
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
-  void (*add_apardot_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*rhs_star_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
   void (*fdot_scaling)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, struct gkyl_array *rhs, struct gkyl_array *cflrate, struct gkyl_range *rng);
@@ -1037,10 +1039,11 @@ struct gk_species {
 
   struct gk_positivity positivity; // Positivity enforcing operator.
 
-  // Pointer to various functions selected at runtime.
+  // Pointer to full RHS (ES + [Apar + Apardot]).
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
-  void (*add_apardot_rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  // Pointer to RHS star function (ES + [Apar]).
+  void (*rhs_star_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
   void (*bflux_update)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
@@ -1821,27 +1824,15 @@ void gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
- * @brief Add Apardot electromagnetic contribution to the collisionless RHS.
- * 
- * @param app Gyrokinetic app object.
- * @param species Pointer to species.
- * @param gkcls Species collisionless object.
- * @param fin Input distribution function.
- * @param rhs On output, the RHS from collisionless terms including EM contribution.
- */
-void gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
-  struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
-
-/**
- * @brief Add Apardot electromagnetic contribution to the collisionless RHS.
- * 
+ * Compute RHS star (ES + Aparallel).
+ *
  * @param app Gyrokinetic app object.
- * @param species Pointer to species.
+ * @param gks Pointer to species.
  * @param gkcls Species collisionless object.
  * @param fin Input distribution function.
- * @param rhs On output, the RHS from collisionless terms including EM contribution.
+ * @param rhs collisionless contribution to df/dt.
  */
-void gk_species_collisionless_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_collisionless_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *gks,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
@@ -3099,16 +3090,15 @@ void gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
- * Add the Apardot electromagnetic part of the RHS from species distribution function
+ * Compute RHS star (ES + Apar) from species distribution function.
  *
  * @param app gyrokinetic app object.
  * @param species Pointer to species.
  * @param fin Input distribution function.
  * @param rhs On output, the RHS from the species object.
  * @param bflux_moms Output boundary flux moments.
- * @return Maximum stable time-step.
  */
-void gk_species_add_apardot_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 4cf56ad880..3b764403a7 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1950,7 +1950,19 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_recycle_react_scale_cross_moms(app, gk_ns, &gk_ns->rrs, fin, fin_neut);
   }
 
-  // Compute df/dt (not including sources).
+  // Compute df/dt^* for Ohm's law.
+  for (int i=0; i<app->num_species; ++i) {
+    struct gk_species *gk_s = &app->species[i];
+    gk_species_rhs_star(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
+  }
+
+  // Compute Apardot (solves Ohm's law using the previously built df/dt^*).
+  gk_field_em_rhs(app, app->field, fin, fout);
+  // Update aparout.
+  gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
+
+  // Compute the total RHS.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
     gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
@@ -1972,21 +1984,10 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
       &app->neut_species[i].src, fin_neut[i], fout_neut[i]);
   }
 
-  // Compute Apardot (solves Ohm's law using the previously built RHS).
-  gk_field_em_rhs(app, app->field, fin, fout);
-  // Update aparout.
-  gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
-
-  // Add Apardot contributions to the collisionless update of charged species.
-  for (int i=0; i<app->num_species; ++i) {
-    struct gk_species *gk_s = &app->species[i];
-    gk_species_add_apardot_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
-  }
-
   // Update boundary fluxes and compute CFL condition.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
-    // gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
     double dt1 = gk_species_get_cfl(app, gk_s, fin[i], fout[i], bflux_out[i]);
     dtmin = fmin(dtmin, dt1);
   }
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index d238da4c5a..21395c014a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 8b28a452a8..39e7d6f8f4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 92e198ca2b..b42929a7c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 88ca99e273..6ffcb3b181 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 9bd473b754..54f701c4de 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 0b8ed9317d..1fb10c7e31 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 498a277666..07e496557a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
similarity index 95%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
index 90a6185dbe..c523120459 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
similarity index 97%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
index abb643af57..5b1a91cf59 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index d481398725..543122e6e1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index 74dab01d37..21cd3f2031 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 3fcfb15e9a..457ae57c6e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index b53afc39d6..0fe90bc65a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index cfa071a002..7a83ba0f4b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
similarity index 95%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 86bf858c8b..3d0b9f5171 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
similarity index 96%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 9178775b0d..38f15344ea 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 78f56ea7d7..34004a4621 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 82f5835ad3..e78f7c7f70 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 828c96be5f..035985c9ac 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index a1d2929177..2c43901ca5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 22ca3cba66..563eb0d645 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
similarity index 95%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
index fde3592231..0d6428a5b3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
similarity index 96%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
index cae67f7f34..1d4dd33bbf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index 2a7d13cc5b..f1e0ed2e6f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index 061695ebcb..a08bcb0502 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index d145fcb87e..c789feeaab 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index 20b2a9a8c2..312892cec8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index f708659280..0fe30219a5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
index 92c1484678..922a2d2a11 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
index 236d9d116b..84adee49a6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
index 8a8c643afc..3e5463c316 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
index d780f7c162..a6fd2411df 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
index 3897256920..594123ddf8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index ed70213a63..16d1b0bd97 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index a8379b1fee..982a3c1806 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index fd55d64a51..a8a7840a32 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 012b22e263..bda9e10f3c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 34e8b51d8b..221bf629fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 43866b33a1..9def8c690a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 5398b50f5a..20ad12619b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 8a9f94a5f3..40266505b0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 5441d7d138..bb62460cf2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 3c063d47f0..a9227a6401 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
similarity index 66%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
index cc5236dc31..9960f87ece 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -17,7 +17,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
-  // apar: parallel component of vector potential (here it will be apardot).
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -27,94 +28,163 @@ GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
   double rdz2 = 2.0/dxv[1];
   double rdvpar2 = 2.0/dxv[2];
 
+  double hamil[24] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
+  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-
-
-
-  alpha_quad = -q_/m_*(0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0]); 
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0]); 
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
 
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
similarity index 77%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
index 57d3645f56..f17e7210c7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -17,7 +17,8 @@ GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
   // gkdgv: gyrokinetic volume DG geometry.
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
-  // apar: parallel component of vector potential (here it will be apardot).
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
@@ -28,174 +29,295 @@ GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
   double rdz2 = 2.0/dxv[2];
   double rdvpar2 = 2.0/dxv[3];
 
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_; 
+  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[4] = 2.0*vmapSq[1]*m_; 
+  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[6] = 2.0*phi[4]*q_; 
+  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
+  hamil[8] = 2.0*phi[6]*q_; 
+  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 2.0*phi[7]*q_; 
+  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
+  hamil[32] = 2.0*vmapSq[2]*m_; 
 
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-
-
-
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[4].bmag; 
+  B3_quad = gkdgv[4].B3; 
+  Jc_quad = dgv[4].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[8] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[9] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[5].bmag; 
+  B3_quad = gkdgv[5].B3; 
+  Jc_quad = dgv[5].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[10] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[11] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[6].bmag; 
+  B3_quad = gkdgv[6].B3; 
+  Jc_quad = dgv[6].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[12] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[13] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[7].bmag; 
+  B3_quad = gkdgv[7].B3; 
+  Jc_quad = dgv[7].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[14] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -q_/m_*(0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0]); 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
   JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
   Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[15] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
 
   double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
index 2a75acf281..37fe20dca7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
index 01f69a0ccf..4eafcb85af 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
index 3f3ae1c87f..25e5751268 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
index 5e9589a976..f7b24b2131 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
index f42556cfd1..61bfba4e75 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..78f68add35
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,98 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..43bae49e46
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,126 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..82c9d44359
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,217 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..644327770f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,372 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..166f58b19f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,217 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..70fa8792a5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,374 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..dde338cae6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,372 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..ba2f277224
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -0,0 +1,100 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double JRatfR[3] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..6c6e3762ce
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -0,0 +1,128 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double JRatfR[6] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.0; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..3e7ca37c52
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,231 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..aaa1f5f526
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,398 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..9742dac181
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,231 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..cd9733339a
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,400 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..7e945d1213
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,398 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..f605e8c5e5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
@@ -0,0 +1,100 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double JRatfL[3] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..00ac69d1b9
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
@@ -0,0 +1,128 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double JRatfL[6] = {0.}; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.0; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..0d08c4712f
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,231 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..91ce1d5dc3
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,398 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..72d8bee3db
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,231 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..19a1a165f5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,400 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..14e533ab79
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,398 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..59f6d3cadc
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,193 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..0a0a8600a3
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,324 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..2cc04c4882
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,193 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..3b47a467d8
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,326 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..d7c0ae209c
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,324 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..0ddae0edea
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -0,0 +1,207 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..8aa9ab8802
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -0,0 +1,350 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
+  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
+  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..cebf6859ea
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -0,0 +1,207 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
+  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfR[12] = {0.}; 
+  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
+  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
+  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
+  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
+  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
+  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
+  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
+  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..b4b1e0d722
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -0,0 +1,352 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..f9f93ebcf3
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -0,0 +1,350 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
+  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
+  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
+  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfR[24] = {0.}; 
+  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
+  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
+  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
+  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
+  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
+  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
+  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
+  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
+  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
+  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
+  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
+  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
+  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
+  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
+  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
+  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
+  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
+  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
+  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
+  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
+  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
+  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
+  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
+  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..0be6a0fa4e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -0,0 +1,207 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..bbb398d1f5
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -0,0 +1,350 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..25dc5aa761
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -0,0 +1,207 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double JRatfL[12] = {0.}; 
+  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
+  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
+  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
+  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
+  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
+  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
+  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
+  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
+  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
+  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
+  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
+  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..2f56cf6794
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -0,0 +1,352 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..3f88a65d7c
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -0,0 +1,350 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double JRatfL[24] = {0.}; 
+  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
+  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
+  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
+  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
+  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
+  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
+  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
+  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
+  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
+  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
+  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
+  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
+  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
+  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
+  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
+  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
+  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
+  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
+  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
+  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
+  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
+  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
+  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
+  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
similarity index 96%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
index 4ff4b86d61..aa09067e70 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
index 6876e3ddff..7c16b44bc7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..4c11b54983
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
@@ -0,0 +1,193 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..37c9f0661e
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
@@ -0,0 +1,324 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..facf04d3db
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
@@ -0,0 +1,193 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..8392c9d227
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
@@ -0,0 +1,326 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = 0.0; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..735a25a7e4
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
@@ -0,0 +1,324 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
similarity index 88%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
index 1b99d93270..3f7f1533e1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
similarity index 93%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
index bac43c6b97..ca427e16b1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
similarity index 98%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index 554172f189..4ae855d703 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index ff0fdbdcca..6357925048 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
new file mode 100644
index 0000000000..49283bbf91
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
@@ -0,0 +1,98 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
+  hamil[1] = 0.5*vmapSq[1]*m_; 
+  hamil[2] = 0.5*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
+  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
new file mode 100644
index 0000000000..1aae86a624
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
@@ -0,0 +1,126 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
+  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
new file mode 100644
index 0000000000..92557904d8
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -0,0 +1,217 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
new file mode 100644
index 0000000000..d2112db809
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -0,0 +1,372 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
+  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[0]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdx2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
new file mode 100644
index 0000000000..5e84833bd1
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -0,0 +1,217 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
+  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[12]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
+  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
new file mode 100644
index 0000000000..9b5f6282d9
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -0,0 +1,374 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
+  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = bmag[0]*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
+  hamil[8] = bmag[1]*vmap[3]; 
+  hamil[9] = bmag[3]*vmap[3]; 
+  hamil[12] = vmap[3]*bmag[5]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdy2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
new file mode 100644
index 0000000000..80deed09d6
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -0,0 +1,372 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot,
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgs: surface DG geometry.
+  // gkdgs: gyrokinetic surface DG geometry.
+  // bmag: bmag represented on the surface.
+  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
+  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
+  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
+  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
+  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[48]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double normcurlbhat_quad = 0.0; 
+  double area_elem_quad = 0.0; 
+  double bhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double mvpar_quad[3] = {0.0}; 
+  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double mvparsq_quad[3] = {0.0}; 
+  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
+  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
+  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+
+  bmag_quad = gkdgs[0].bmag; 
+  Jc_quad = gkdgs[0].Jc; 
+  B3_quad = gkdgs[0].B3; 
+  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
+  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
+  area_elem_quad = dgs[0].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[1].bmag; 
+  Jc_quad = gkdgs[1].Jc; 
+  B3_quad = gkdgs[1].B3; 
+  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
+  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
+  area_elem_quad = dgs[1].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
+  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[2].bmag; 
+  Jc_quad = gkdgs[2].Jc; 
+  B3_quad = gkdgs[2].B3; 
+  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
+  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
+  area_elem_quad = dgs[2].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  bmag_quad = gkdgs[3].bmag; 
+  Jc_quad = gkdgs[3].Jc; 
+  B3_quad = gkdgs[3].B3; 
+  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
+  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
+  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
+  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
+  area_elem_quad = dgs[3].area_elem; 
+
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
+  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
+  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
+  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
+
+
+  return cfl*1.5*rdz2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
new file mode 100644
index 0000000000..2989bfd7d0
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
@@ -0,0 +1,105 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[6] = {0.}; 
+  hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
+  hamil[1] = 1.4142135623730951*phi[1]*q_; 
+  hamil[2] = 0.7071067811865475*vmapSq[1]*m_; 
+  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[3]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
new file mode 100644
index 0000000000..d248598c35
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
@@ -0,0 +1,129 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdvpar2 = 2.0/dxv[1];
+
+  double hamil[12] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = vmapSq[1]*m_; 
+  hamil[3] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[8] = vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[6]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
new file mode 100644
index 0000000000..626389a2ec
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -0,0 +1,226 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdz2 = 2.0/dxv[1];
+  double rdvpar2 = 2.0/dxv[2];
+
+  double hamil[24] = {0.}; 
+  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
+  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
+  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
+  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[24]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
new file mode 100644
index 0000000000..638edf4c49
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -0,0 +1,423 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
+{ 
+  // w[NDIM]: cell-center.
+  // dxv[NDIM]: cell length.
+  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
+  // vmap: velocity space mapping.
+  // vmapSq: velocity space mapping squared.
+  // q_,m_: species charge and mass.
+  // dgv: volume DG geometry.
+  // gkdgv: gyrokinetic volume DG geometry.
+  // bmag: magnetic field amplitude.
+  // phi: electrostatic potential.
+  // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
+  // JfL: distribution times total jacobian in left cell.
+  // JfR: distribution times total jacobian in right cell.
+  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
+  //            Note: Each cell owns their *lower* edge surface evaluation.
+
+  double rdx2 = 2.0/dxv[0];
+  double rdy2 = 2.0/dxv[1];
+  double rdz2 = 2.0/dxv[2];
+  double rdvpar2 = 2.0/dxv[3];
+
+  double hamil[48] = {0.}; 
+  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
+  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
+  hamil[2] = 2.0*phi[2]*q_; 
+  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
+  hamil[4] = 2.0*vmapSq[1]*m_; 
+  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
+  hamil[6] = 2.0*phi[4]*q_; 
+  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
+  hamil[8] = 2.0*phi[6]*q_; 
+  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
+  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
+  hamil[16] = 2.0*phi[7]*q_; 
+  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
+  hamil[32] = 2.0*vmapSq[2]*m_; 
+
+  double *flux_surf_nodal = &flux_surf[72]; 
+  double cfl = 0.0; 
+  double bmag_quad = 0.0; 
+  double B3_quad = 0.0; 
+  double Jc_quad = 0.0; 
+  double dualcurlbhat_quad[3] = {0.0}; 
+  double alpha_quad = 0.0; 
+  double JfL_quad = 0.0; 
+  double JfR_quad = 0.0; 
+  double Jfavg_quad = 0.0; 
+  double Jfjump_quad = 0.0; 
+  double m_bmag_inv = 0.0; 
+  double mvpar_over_q = 0.0; 
+  double  g_13 = 0.0; 
+  double  g_23 = 0.0; 
+  double  g_33 = 0.0; 
+  double  mag_e_3 = 0.0; 
+
+  bmag_quad = gkdgv[0].bmag; 
+  B3_quad = gkdgv[0].B3; 
+  Jc_quad = dgv[0].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[0].g_13; 
+  g_23 = gkdgv[0].g_23; 
+  g_33 = gkdgv[0].g_33; 
+  mag_e_3 = gkdgv[0].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[1].bmag; 
+  B3_quad = gkdgv[1].B3; 
+  Jc_quad = dgv[1].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[1].g_13; 
+  g_23 = gkdgv[1].g_23; 
+  g_33 = gkdgv[1].g_33; 
+  mag_e_3 = gkdgv[1].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[2].bmag; 
+  B3_quad = gkdgv[2].B3; 
+  Jc_quad = dgv[2].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[2].g_13; 
+  g_23 = gkdgv[2].g_23; 
+  g_33 = gkdgv[2].g_33; 
+  mag_e_3 = gkdgv[2].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[3].bmag; 
+  B3_quad = gkdgv[3].B3; 
+  Jc_quad = dgv[3].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[3].g_13; 
+  g_23 = gkdgv[3].g_23; 
+  g_33 = gkdgv[3].g_33; 
+  mag_e_3 = gkdgv[3].mag_e_3; 
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[4].bmag; 
+  B3_quad = gkdgv[4].B3; 
+  Jc_quad = dgv[4].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[4].g_13; 
+  g_23 = gkdgv[4].g_23; 
+  g_33 = gkdgv[4].g_33; 
+  mag_e_3 = gkdgv[4].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[5].bmag; 
+  B3_quad = gkdgv[5].B3; 
+  Jc_quad = dgv[5].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[5].g_13; 
+  g_23 = gkdgv[5].g_23; 
+  g_33 = gkdgv[5].g_33; 
+  mag_e_3 = gkdgv[5].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[6].bmag; 
+  B3_quad = gkdgv[6].B3; 
+  Jc_quad = dgv[6].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[6].g_13; 
+  g_23 = gkdgv[6].g_23; 
+  g_33 = gkdgv[6].g_33; 
+  mag_e_3 = gkdgv[6].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  bmag_quad = gkdgv[7].bmag; 
+  B3_quad = gkdgv[7].B3; 
+  Jc_quad = dgv[7].Jc; 
+  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
+  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
+  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  m_bmag_inv = 1.0/(m_*bmag_quad); 
+  g_13 = gkdgv[7].g_13; 
+  g_23 = gkdgv[7].g_23; 
+  g_33 = gkdgv[7].g_33; 
+  mag_e_3 = gkdgv[7].mag_e_3; 
+
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
+
+  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
+  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
+  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
+  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
+  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
+  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
+
+
+  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
+
+  return cfl/vmap_prime_min*2.5*rdvpar2; 
+
+} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
similarity index 95%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
index 9529bc93d9..850f927129 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
similarity index 97%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
index 5a925e02bf..ea0b519c46 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index cf64cd51ba..dbf9971dc9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index fd7dc2c76a..b1570cade8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index b93ef24d68..f23c376835 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index 19536db253..11bfc03e8e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
similarity index 99%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index d3b9aa1639..d95b14e1e5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -1,10 +1,10 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 9839938bde..b5fadd95ca 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 59741c6716..ec1c2e82f7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 4d2caaa586..ecd3ba844a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 654ae35df3..da7d97aeb6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index d6718fe837..3b707055bf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 5d062b6954..5ca2d688a4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index e0bf10f4f3..9ae1961330 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 3e0e9a58ee..048bd3237b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 57462146c1..5f4580602c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 6cf635577b..c1cc0f5020 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 1abad940db..5c61b1f8a9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index f850648838..b7c585f799 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index 13cc478df5..e8bf6132d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index 988d136907..da17447f50 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 6184d536a3..221b5d1423 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index a2da499294..443f043456 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index 4ca93d910c..82e53feddc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index 43d4ce97f4..369c86f08b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 403e5afe85..fcaca72bb8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 55a1af88c1..f994230a51 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index a71b45ec40..cbc6b5b929 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index a9079ef2ed..e45ee49e08 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 6646198205..4d7217100b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 6284a429d7..80d5ed0ce3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 944529819a..63e9a1f60e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index b45acf2030..0c955575e9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 1be9740d4c..ea60efd4fd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index b2df2b4cc8..7381fcb251 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 9ccf675e30..cefe23f089 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index 66d2f9ee5c..e9cd2a02a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 6213e03896..80f1415fb5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index c6fa855f0b..6a5dd6206d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index 8e0df1984a..b9284c26fd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index a602b33749..355ac1a61b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index 8907a70957..e82df8b127 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index a7d42b1e38..c32a86f42e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
index 95196d3239..abf19ca158 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot, 
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   return 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index c89bcda5a4..d7d9e3ffbc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 923cd51270..2605f00d88 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 4d2b3e7f85..40b8d09f56 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 140ef97c8f..515d1b1f98 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -1,11 +1,11 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
+  const double *w, const double *dxv, 
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
   // dxv[NDIM]: cell length.
@@ -18,6 +18,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   // bmag: magnetic field amplitude.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 8351564ace..21823e2e6d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index afb03ca1e1..eb9c4c7812 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index 46e83b07d7..dba5b7cb2d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 1e92b3a798..00d228fa69 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index c176ec2db1..528b7070de 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 5c178c9917..359e2550e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 9a58c63c81..192ec8bdf9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -4,7 +4,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
     const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar,
+    const double *phi, const double *apar, const double *apardot,
     const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
 { 
   // w[NDIM]: cell-center.
@@ -19,6 +19,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
   // phi: electrostatic potential.
   // apar: parallel component of vector potential.
+  // apardot: time derivative of parallel component of vector potential.
   // JfL: distribution times total jacobian in left cell.
   // JfR: distribution times total jacobian in right cell.
   // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index 12e52528d6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,65 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential (here it will be apardot).
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-
-  double *flux_surf_nodal = &flux_surf[3]; 
-  double cfl = 0.0; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-
-
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index e9c19092a9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,83 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
-    const double *w, const double *dxv, 
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-    const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential (here it will be apardot).
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-
-  double *flux_surf_nodal = &flux_surf[6]; 
-  double cfl = 0.0; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-
-
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -q_/m_*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] += alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index bf3aa0d71e..c908ee160b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -8,1224 +8,1155 @@
 EXTERN_C_BEG
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
 GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p2(
+
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-  const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p2(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p2(
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1(
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
+    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+    double* GKYL_RESTRICT flux_surf); 
+GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apardot, const double *JfL, const double *JfR,
+  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
 GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
@@ -1233,7 +1164,7 @@ GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *JfL, const double *JfR,
+  const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf);
 
 EXTERN_C_END
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 649ce45418..3fef766c90 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -47,14 +47,14 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
-      charge, mass, skip_cell_threshold, collless_type, no_by, only_apardot, gk_geom, vel_map);
+      charge, mass, skip_cell_threshold, collless_type, no_by, em_star, gk_geom, vel_map);
 #endif
 
   struct dg_gyrokinetic *gyrokinetic = gkyl_malloc(sizeof(struct dg_gyrokinetic));
@@ -78,9 +78,9 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   gyrokinetic->eqn.boundary_surf_term = boundary_surf;
   gyrokinetic->eqn.boundary_diag_term = boundary_diag;
 
-  const gkyl_dg_gyrokinetic_vol_kern_list *vol_kernels, *vol_no_by_kernels;
+  const gkyl_dg_gyrokinetic_vol_es_kern_list *vol_kernels, *vol_no_by_kernels;
   const gkyl_dg_gyrokinetic_vol_add_apar_kern_list *vol_add_apar_kernels;
-  const gkyl_dg_gyrokinetic_vol_kern_list *vol_add_apardot_kernels;
+  const gkyl_dg_gyrokinetic_vol_add_apardot_kern_list *vol_add_apardot_kernels;
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_x_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_y_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_z_kernels; 
@@ -92,7 +92,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
 
   switch (cbasis->b_type) {
     case GKYL_BASIS_MODAL_SERENDIPITY:
-      vol_kernels = ser_vol_kernels;
+      vol_kernels = ser_vol_es_kernels;
       vol_add_apar_kernels = ser_add_apar_vol_kernels;
       vol_add_apardot_kernels = ser_add_apardot_vol_kernels;
       surf_x_kernels = ser_surf_x_kernels;
@@ -104,7 +104,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       boundary_surf_z_kernels = ser_boundary_surf_z_kernels;
       boundary_surf_vpar_kernels = ser_boundary_surf_vpar_kernels;
 
-      vol_no_by_kernels = ser_no_by_vol_kernels;
+      vol_no_by_kernels = ser_no_by_vol_es_kernels;
       break;
 
     default:
@@ -112,19 +112,25 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
       break;
   }
 
+  gyrokinetic->eqn.vol_term = kernel_dg_gyrokinetic_vol;
+
   if (no_by) {
-    gyrokinetic->eqn.vol_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    if (only_apardot)
-      gyrokinetic->eqn.vol_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
-    else
-      gyrokinetic->eqn.vol_term = CK(vol_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
-  gyrokinetic->vol_add_apar_term = 
-    (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP) ? 
-    CK(vol_add_apar_kernels,cdim,vdim,poly_order) : dg_gyrokinetic_vol_return_zero;
+  // Setup electromagnetic terms if needed.
+  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
+  gyrokinetic->vol_add_apar_term = dg_gyrokinetic_add_apar_vol_return_zero;
+  gyrokinetic->vol_add_apardot_term = dg_gyrokinetic_add_apardot_vol_return_zero;
+  if (is_em) {
+    gyrokinetic->vol_add_apar_term = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+    // Apardot is removed if we want to compute RHS star (ES + Apardot).
+    if (em_star)
+      gyrokinetic->vol_add_apardot_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+  }
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
   if (cdim>1)
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 9185081a60..4b2122f6dc 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -83,20 +83,26 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       assert(false);
       break;    
   }  
+  
+  gyrokinetic->eqn.vol_term = kernel_dg_gyrokinetic_vol;
 
   if (no_by) {
-    gyrokinetic->eqn.vol_term = vol_no_by_kernels[cv_index].kernels[poly_order];
+    gyrokinetic->vol_es_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    if (only_apardot)
-      gyrokinetic->eqn.vol_term = vol_add_apardot_kernels[cv_index].kernels[poly_order];
-    else
-      gyrokinetic->eqn.vol_term = vol_kernels[cv_index].kernels[poly_order];
+    gyrokinetic->vol_es_term = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
-  gyrokinetic->vol_add_apar_term = 
-    ((collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 
-    vol_add_apar_kernels[cv_index].kernels[poly_order] : dg_gyrokinetic_vol_return_zero;
+  // Setup electromagnetic terms if needed.
+  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
+  gyrokinetic->vol_add_apar_term = dg_gyrokinetic_add_apar_vol_return_zero;
+  gyrokinetic->vol_add_apardot_term = dg_gyrokinetic_add_apardot_vol_return_zero;
+  if (is_em) {
+    gyrokinetic->vol_add_apar_term = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+    // Apardot is removed if we want to compute RHS star (ES + Apardot).
+    if (em_star)
+      gyrokinetic->vol_add_apardot_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+  }
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
   if (cdim>1)
@@ -118,7 +124,7 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
+  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
 {
   struct dg_gyrokinetic *gyrokinetic = (struct dg_gyrokinetic*) gkyl_malloc(sizeof(*gyrokinetic));
 
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 80e204c622..9f17b2d46d 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -22,7 +22,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, 
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -30,7 +30,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, skip_cell_threshold, collless_type, no_by, only_apardot, gk_geom, vel_map, up->use_gpu);
+    charge, mass, skip_cell_threshold, collless_type, no_by, em_star, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index e9af9a8813..22d5cd2e27 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -13,14 +13,14 @@ gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type type,
-  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
 {
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis, 
-      charge, mass, type, no_by, only_apardot, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, type, no_by, only_apardot, em_star, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
@@ -35,44 +35,34 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
-  up->only_apardot = only_apardot;
   up->gk_geom = gkyl_gk_geometry_acquire(gk_geom);
   up->dg_geom = gkyl_dg_geom_acquire(dg_geom);
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
   // Choose appropriate kernels.
-  if (only_apardot){
-    // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
+  int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
+  em = em_star ? 2 : em; // If em_star is true, use EM kernels without Apardot contribution.
+  if (no_by) {
     for (int d=0; d<cdim; ++d) {
-      up->flux_surf[d] = gk_collisionless_flux_surf_return_zero;
-      up->flux_surf_edge_lo[d] = gk_collisionless_flux_surf_return_zero;
-      up->flux_surf_edge_up[d] = gk_collisionless_flux_surf_return_zero;
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
-  } else {
-    int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
-    if (no_by) {
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
-    } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
+  } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
+    for (int d=0; d<cdim; ++d) {
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
   }
 
   up->flags = 0;
@@ -85,13 +75,13 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
-  const struct gkyl_array *phi, const struct gkyl_array *apar,
+  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *apardot,
   const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 {
 #ifdef GKYL_HAVE_CUDA
   if (gkyl_array_is_cu_dev(flux_surf)) {
     return gkyl_gk_collisionless_flux_surf_cu(up, conf_range, phase_range,
-      conf_ext_range, phase_ext_range, phi, apar, fin, flux_surf, cflrate);
+      conf_ext_range, phase_ext_range, phi, apar, apardot, fin, flux_surf, cflrate);
   }
 #endif
   int pdim = up->pdim;
@@ -123,6 +113,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
     const double *bmag_d = gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = gkyl_array_cfetch(phi, loc_conf);
     const double *apar_d = gkyl_array_cfetch(apar, loc_conf);
+    const double *apardot_d = gkyl_array_cfetch(apardot, loc_conf);
     const double *vmap_d = gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -146,11 +137,11 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
       if (idx[dir] == phase_range->lower[dir]) {
         // Lower domain/block boundary.
         cflrate_d[0] += up->flux_surf_edge_lo[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
       } else {
         // Interior, lower cell surface.
         cflrate_d[0] += up->flux_surf[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
       }
 
       // Upper domain/block boundary.
@@ -177,7 +168,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
         double* flux_surf_ext_d = gkyl_array_fetch(flux_surf, loc_phase_ext);
 
         cflrate_ext_d[0] += up->flux_surf_edge_up[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_ext_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_ext_d);
       }  
     }
   }
@@ -197,6 +188,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
     const double *bmag_d = gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = gkyl_array_cfetch(phi, loc_conf);
     const double *apar_d = gkyl_array_cfetch(apar, loc_conf);
+    const double *apardot_d = gkyl_array_cfetch(apardot, loc_conf);
     const double *vmap_d = gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -219,7 +211,7 @@ void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up,
     const struct gkyl_dg_vol_geom *dgv = gkyl_dg_geom_get_vol(up->dg_geom, idx);
     const struct gkyl_gk_dg_vol_geom *gkdgv = gkyl_gk_dg_geom_get_vol(up->gk_dg_geom, idx);
     cflrate_d[0] += up->flux_surfvpar[0](xc, up->phase_grid.dx, vpL, vpR, vmap_d, vmapSq_d, up->charge, up->mass,
-      dgv, gkdgv, bmag_d, phi_d, apar_d, fL, fR, flux_surf_d);
+      dgv, gkdgv, bmag_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
   }
 }
 
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 4af0b95b54..1b13d8c2f0 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -18,7 +18,8 @@ __global__ void
 gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux *up, 
   struct gkyl_range conf_range, struct gkyl_range phase_range,
   struct gkyl_range conf_ext_range, struct gkyl_range phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array *apar, const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
+  const struct gkyl_array *apar, const struct gkyl_array *apardot,
+  const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 { 
   int pdim = up->pdim;
   int cdim = up->cdim;
@@ -48,6 +49,7 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
     const double *bmag_d = (const double*) gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = (const double*) gkyl_array_cfetch(phi, loc_conf);
     const double *apar_d = (const double*) gkyl_array_cfetch(apar, loc_conf);
+    const double *apardot_d = (const double*) gkyl_array_cfetch(apardot, loc_conf);
     const double *vmap_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -71,11 +73,11 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
       if (idx[dir] == phase_range.lower[dir]) {
         // Lower domain/block boundary.
         cflrate_d[0] += up->flux_surf_edge_lo[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
       } else {
         // Interior, lower cell surface.
         cflrate_d[0] += up->flux_surf[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
       }
 
       // If the phase space index is at the local configuration space upper value, we
@@ -101,7 +103,7 @@ gkyl_gk_collisionless_flux_surf_conf_cu_kernel(struct gkyl_gk_collisionless_flux
         double* flux_surf_ext_d = (double*) gkyl_array_fetch(flux_surf, loc_phase_ext);
 
         cflrate_ext_d[0] = up->flux_surf_edge_up[dir](xc, up->phase_grid.dx, vmap_d, vmapSq_d, up->charge, up->mass,
-          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, fL, fR, flux_surf_ext_d);
+          dgs, gkdgs, bmag_d, jacgeo_rat_surfL_d, jacgeo_rat_surfR_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_ext_d);
       }  
     }
   }
@@ -111,8 +113,8 @@ __global__ void
 gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_flux *up, 
   struct gkyl_range conf_range, struct gkyl_range phase_range,
   struct gkyl_range conf_ext_range, struct gkyl_range phase_ext_range, struct gkyl_range vpar_range,
-  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *fin, 
-  struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
+  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *apardot,
+  const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate)
 { 
   int pdim = up->pdim;
   int cdim = up->cdim;
@@ -143,6 +145,7 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
     const double *bmag_d = (const double*) gkyl_array_cfetch(up->gk_geom->geo_corn.bmag, loc_conf);
     const double *phi_d = (const double*) gkyl_array_cfetch(phi, loc_conf);
     const double *apar_d = (const double*) gkyl_array_cfetch(apar, loc_conf);
+    const double *apardot_d = (const double*) gkyl_array_cfetch(apardot, loc_conf);
     const double *vmap_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap, loc_vel);
     const double *vmapSq_d = (const double*) gkyl_array_cfetch(up->vel_map->vmap_sq, loc_vel);
 
@@ -168,7 +171,7 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
     cflrate_d[0] += up->flux_surfvpar[0](xc, up->phase_grid.dx, 
       vpL, vpR,
       vmap_d, vmapSq_d, up->charge, up->mass,
-      dgv, gkdgv, bmag_d, phi_d, apar_d,  fL, fR, flux_surf_d);
+      dgv, gkdgv, bmag_d, phi_d, apar_d, apardot_d, fL, fR, flux_surf_d);
   }
 }
 
@@ -176,10 +179,10 @@ gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel(struct gkyl_gk_collisionless_
 void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array *apar, const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate)
+  const struct gkyl_array *apar, const struct gkyl_array *apardot, const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate)
 {
   gkyl_gk_collisionless_flux_surf_conf_cu_kernel<<<phase_range->volume, GKYL_DEFAULT_NUM_THREADS>>>(up->on_dev, 
-    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, phi->on_dev, apar->on_dev, fin->on_dev,
+    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, phi->on_dev, apar->on_dev, apardot->on_dev, fin->on_dev,
     flux_surf->on_dev, cflrate->on_dev);
 
   struct gkyl_range vpar_range;
@@ -192,7 +195,7 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
   sublower[up->cdim] += 1;
   gkyl_sub_range_init(&vpar_range, phase_ext_range, sublower, subupper);
   gkyl_gk_collisionless_flux_surf_surfvpar_cu_kernel<<<vpar_range.volume, GKYL_DEFAULT_NUM_THREADS>>>(up->on_dev, 
-    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, vpar_range, phi->on_dev, apar->on_dev, fin->on_dev,
+    *conf_range, *phase_range, *conf_ext_range, *phase_ext_range, vpar_range, phi->on_dev, apar->on_dev, apardot->on_dev, fin->on_dev,
     flux_surf->on_dev, cflrate->on_dev);
 
 }
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 62687abb43..dd93dd2039 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -12,15 +12,21 @@
 #include <gkyl_dg_gyrokinetic.h>
 
 // Types for various kernels.
+
+typedef double (*dg_gyrokinetic_vol_es_t)(const double *w, const double *dxv,
+  const double *vmap, const double *vmapSq, const double q_, const double m_,
+  const double *bmag, const double *phi,
+  const double *dualcurlbhatoverB, const double *rtg33inv, const double* bioverJB,
+  const double *fin, double* GKYL_RESTRICT out); 
+
 typedef double (*dg_gyrokinetic_vol_add_apar_t)(const double *w, const double *dxv, 
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
   const double *bmag, const double *jacobtot_inv, const double *b_i, const double *phi, 
   const double *apar, const double *fin, double* GKYL_RESTRICT out);
 
-typedef double (*dg_gyrokinetic_vol_add_apardot_t)(const double *w, const double *dxv, 
-  const double *vmap, const double *vmapSq,const double q_, const double m_, 
-  const double *bmag, const double *jacobtot_inv, const double *b_i, const double *phi, 
-  const double *apardot, const double *fin, double* GKYL_RESTRICT out);
+typedef double (*dg_gyrokinetic_vol_add_apardot_t)(const double *vmap, 
+  const double q_, const double m_,
+  const double *apardot, const double *fin, double* GKYL_RESTRICT out); 
 
 typedef double (*dg_gyrokinetic_surf_t)( const double *w, const double *dxv,
   const double *vmap_prime_l, const double *vmap_prime_c, const double *vmap_prime_r, 
@@ -43,7 +49,9 @@ static struct { int vdim[3]; } cv_index[] = {
 
 // for use in kernel tables
 typedef struct { vol_termf_t kernels[3]; } gkyl_dg_gyrokinetic_vol_kern_list;
+typedef struct { dg_gyrokinetic_vol_es_t kernels[3]; } gkyl_dg_gyrokinetic_vol_es_kern_list;
 typedef struct { dg_gyrokinetic_vol_add_apar_t kernels[3]; } gkyl_dg_gyrokinetic_vol_add_apar_kern_list;
+typedef struct { dg_gyrokinetic_vol_add_apardot_t kernels[3]; } gkyl_dg_gyrokinetic_vol_add_apardot_kern_list;
 typedef struct { dg_gyrokinetic_surf_t kernels[3]; } gkyl_dg_gyrokinetic_surf_kern_list;
 typedef struct { dg_gyrokinetic_boundary_surf_t kernels[3]; } gkyl_dg_gyrokinetic_boundary_surf_kern_list;
 
@@ -51,7 +59,9 @@ struct dg_gyrokinetic {
   struct gkyl_dg_eqn eqn; // Base object.
   int cdim; // Config-space dimensions.
   int pdim; // Phase-space dimensions.
+  dg_gyrokinetic_vol_es_t vol_es_term; // Electrostatic contribution to volume term.
   dg_gyrokinetic_vol_add_apar_t vol_add_apar_term; // Additional volume term for Apar contribution.
+  dg_gyrokinetic_vol_add_apardot_t vol_add_apardot_term; // Additional volume term for Apar contribution.
   dg_gyrokinetic_surf_t surf[4]; // Surface terms.
   dg_gyrokinetic_boundary_surf_t boundary_surf[4]; // Surface terms for velocity boundary.
   struct gkyl_range conf_range; // Configuration space range.
@@ -70,7 +80,7 @@ struct dg_gyrokinetic {
 
 GKYL_CU_DH
 static double
-kernel_dg_gyrokinetic_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
+kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
   const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
 {
   
@@ -87,7 +97,7 @@ kernel_dg_gyrokinetic_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
   double cfl = 0.0;
-  cfl = dg_gyrokinetic_vol_1x1v_ser_p1(xc, dx,
+  cfl = gyrokinetic->vol_es_term(xc, dx,
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
@@ -107,365 +117,84 @@ kernel_dg_gyrokinetic_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const doubl
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
     (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
     qIn, qRhsOut);
-  return cfl;
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  double cfl = 0.0;
-  cfl = dg_gyrokinetic_vol_1x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
+  cfl += gyrokinetic->vol_add_apardot_term(
     (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
     gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
+    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
     qIn, qRhsOut);
   return cfl;
 }
 
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  double cfl = 0.0;
-  cfl = dg_gyrokinetic_vol_2x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
-    qIn, qRhsOut);
-  return cfl;
+// To turn off EM effects:
+GKYL_CU_DH 
+static double 
+dg_gyrokinetic_add_apar_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+{ 
+  return 0.; 
 }
 
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
+GKYL_CU_DH 
+static double 
+dg_gyrokinetic_add_apardot_vol_return_zero(const double *vmap, const double q_, const double m_,
+            const double *apardot, const double *fin, double* GKYL_RESTRICT out)
+{ 
+  return 0.; 
+} 
 
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
 
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  double cfl = 0.0;
-  cfl = dg_gyrokinetic_vol_3x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
-    qIn, qRhsOut);
-  return cfl;
-}
-
-// Volume kernel list.
+// Volume electrostatic kernel list.
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_vol_kern_list ser_vol_kernels[] = {
+static const gkyl_dg_gyrokinetic_vol_es_kern_list ser_vol_es_kernels[] = {
   // 1x kernels
-  { NULL, kernel_dg_gyrokinetic_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, kernel_dg_gyrokinetic_vol_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, kernel_dg_gyrokinetic_vol_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, kernel_dg_gyrokinetic_vol_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_vol_3x2v_ser_p1, NULL }, // 3
 };
 
 //
 // Serendipity volume kernels general geometry, no toroidal field (by=0)
 // Need to be separated like this for GPU build
 //
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_no_by_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_no_by_vol_2x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_no_by_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
-  return dg_gyrokinetic_no_by_vol_3x2v_ser_p1(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-}
-
-// Volume kernel list.
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_vol_kern_list ser_no_by_vol_kernels[] = {
+static const gkyl_dg_gyrokinetic_vol_es_kern_list ser_no_by_vol_es_kernels[] = {
   // 1x kernels
-  { NULL, kernel_dg_gyrokinetic_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, kernel_dg_gyrokinetic_vol_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, kernel_dg_gyrokinetic_no_by_vol_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_no_by_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, kernel_dg_gyrokinetic_no_by_vol_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_no_by_vol_3x2v_ser_p1, NULL }, // 3
 };
 
 // Electromagnetic serendipity volume kernels general geometry.
 GKYL_CU_D
 static const gkyl_dg_gyrokinetic_vol_add_apar_kern_list ser_add_apar_vol_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_apar_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_apar_vol_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_add_apar_vol_return_zero, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_apar_vol_return_zero, NULL }, // 1
   // 2x kernels
   { NULL, dg_gyrokinetic_add_apar_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
   { NULL, dg_gyrokinetic_add_apar_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  return dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
-    qIn, qRhsOut);
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  return dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
-    qIn, qRhsOut);
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  return dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
-    qIn, qRhsOut);
-}
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  return dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
-    qIn, qRhsOut);
-}
-
 // Electromagnetic volume kernel list (apardot).
 GKYL_CU_D
-static const gkyl_dg_gyrokinetic_vol_kern_list ser_add_apardot_vol_kernels[] = {
+static const gkyl_dg_gyrokinetic_vol_add_apardot_kern_list ser_add_apardot_vol_kernels[] = {
   // 1x kernels
-  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1, NULL }, // 0
-  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1, NULL }, // 1
+  { NULL, dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
-  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1, NULL }, // 2
+  { NULL, dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels
-  { NULL, kernel_dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1, NULL }, // 3
+  { NULL, dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1, NULL }, // 3
 };
 
-// To turn off EM effects:
-GKYL_CU_DH 
-static double 
-dg_gyrokinetic_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
-    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
-{ 
-  return 0.; 
-} 
-
-GKYL_CU_DH
-static double
-kernel_dg_gyrokinetic_vol_return_zero(const struct gkyl_dg_eqn *eqn, const double* xc, const double* dx, 
-  const int* idx, const double* qIn, double* GKYL_RESTRICT qRhsOut)
-{
-  struct dg_gyrokinetic *gyrokinetic = container_of(eqn, struct dg_gyrokinetic, eqn);
-
-  if (fabs(qIn[0]) < gyrokinetic->skip_cell_thresh) {
-    return 0.;
-  }
-  
-  int vel_idx[2];
-  for (int d=gyrokinetic->cdim; d<gyrokinetic->pdim; d++) vel_idx[d-gyrokinetic->cdim] = idx[d];
-
-  long cidx = gkyl_range_idx(&gyrokinetic->conf_range, idx);
-  long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
-  return dg_gyrokinetic_vol_return_zero(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-}
-
 //
 // Serendipity surface kernels general geometry
 //
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 619bfed7d5..3d664f73c4 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -31,7 +31,7 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param only_apardot Whether we want to only add the apardot term.
+ * @param em_star Whether it computes (ES + [Apar]) or [ES + [Apar + Apardot]).
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -42,7 +42,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, double skip_cell_threshold,
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, 
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, 
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
@@ -71,19 +71,6 @@ void gkyl_dg_updater_gyrokinetic_advance(gkyl_dg_updater_gyrokinetic *gyrokineti
   const struct gkyl_range *update_rng, const struct gkyl_array* GKYL_RESTRICT fIn,
   struct gkyl_array* GKYL_RESTRICT cflrate, struct gkyl_array* GKYL_RESTRICT rhs);
 
-/**
- * Add Apardot electromagnetic contribution to the RHS.
- * 
- * @param gyrokinetic 
- * @param update_rng 
- * @param fIn 
- * @param cflrate 
- * @param rhs 
- */
-void gkyl_dg_updater_gyrokinetic_add_apardot(gkyl_dg_updater_gyrokinetic *gyrokinetic,
-  const struct gkyl_range *update_rng, const struct gkyl_array* GKYL_RESTRICT fIn,
-  struct gkyl_array* GKYL_RESTRICT cflrate, struct gkyl_array* GKYL_RESTRICT rhs);
-
 /**
  * Return total time spent in gyrokinetic equation
  *
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index efe8da3aaa..28e7cbda2e 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -24,7 +24,7 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * @param mass Species mass
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param only_apardot Whether to only add Apardot terms to the flux.
+ * @param em_star Whether to compute fstar for Ohm's law.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
@@ -36,7 +36,7 @@ struct gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, 
+  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, 
   const struct gkyl_dg_geom *dg_geom, const struct gkyl_gk_dg_geom *gk_dg_geom, 
   const struct gkyl_velocity_map *vel_map, const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
 
@@ -61,7 +61,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 void gkyl_gk_collisionless_flux_surf(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
-  const struct gkyl_array *phi, const struct gkyl_array *apar,
+  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *apardot,
   const struct gkyl_array *fin, struct gkyl_array* flux_surf, struct gkyl_array *cflrate);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 9634cff95b..8cf9212fa7 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -14,14 +14,14 @@ typedef double (*gk_collisionless_flux_surf_t)(const double *w, const double *dx
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, const double *phi,
-  const double *apar, const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
+  const double *apar, const double *apardot, const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
 
 typedef double (*gk_collisionless_flux_surfvpar_t)( 
   const double *w, const double *dxv, 
   const double *vmap_prime_l, const double *vmap_prime_r,
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
   const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-  const double *bmag, const double *phi, const double *apar,
+  const double *bmag, const double *phi, const double *apar, const double *apardot,
   const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf); 
 
 // The cv_index[cd].vdim[vd] is used to index the various list of
@@ -53,7 +53,6 @@ struct gkyl_gk_collisionless_flux {
   
   double charge, mass;
   bool is_em; // Whether it is electromagnetic.
-  bool only_apardot; // Whether it is meant to only add Apardot terms.
   const struct gk_geometry *gk_geom; // Pointer to geometry struct.
   const struct gkyl_dg_geom *dg_geom; // Pointer to vol dg geometry struct.
   const struct gkyl_gk_dg_geom *gk_dg_geom; // Pointer to vol gk dg geometry struct.
@@ -79,10 +78,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -100,10 +107,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -123,8 +138,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -144,8 +167,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -166,7 +197,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -187,7 +226,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -205,10 +252,18 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -229,10 +284,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -250,10 +313,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list= {
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list= {
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -273,8 +344,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -294,8 +373,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -316,7 +403,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -337,7 +432,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -359,10 +462,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -380,10 +491,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -403,8 +522,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -424,8 +551,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -446,8 +581,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1, NULL }, // 3
     },  
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+    },
   }
 };
 
@@ -467,7 +610,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -485,10 +636,18 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -509,10 +668,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -530,10 +697,18 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_em_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -553,8 +728,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -574,8 +757,16 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -596,7 +787,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -617,7 +816,15 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_em_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+    },
+  },
+  {
+    .kernels_list = {
+      { NULL, NULL, NULL }, // 0
+      { NULL, NULL, NULL }, // 1
+      { NULL, NULL, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -740,25 +947,6 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int em, int cdim, int vdim, in
   return ser_gk_collisionless_flux_no_by_surfvpar_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
-
-//
-// Electromagnetic serendipity surface kernels.
-// Parallel electric field term.
-GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_add_apardot_surfvpar_kernels[] = {
-  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_1x1v_ser_p1, NULL }, // 0
-  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_1x2v_ser_p1, NULL }, // 1
-  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_2x2v_ser_p1, NULL }, // 2
-  { NULL, gk_em_collisionless_flux_add_apardot_surfvpar_3x2v_ser_p1, NULL }, // 3
-};
-
-GKYL_CU_D
-static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(int cdim, int vdim, int poly_order)
-{
-  return ser_gk_collisionless_flux_add_apardot_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
-}
-
 #ifdef GKYL_HAVE_CUDA
 /**
  * Create new updater to compute gyrokinetic variables on

From b5874bdaec4ebc55060d88b5b77cd36032138430 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 11:48:03 -0500
Subject: [PATCH 102/181] I don't think we need fdot scaling in the rhs star

---
 gyrokinetic/apps/gk_species_collisionless.c | 1 +
 1 file changed, 1 insertion(+)

diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 2cd5fba41c..3b98e06a94 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -67,6 +67,7 @@ gk_species_collisionless_rhs_star_enabled(gkyl_gyrokinetic_app *app, struct gk_s
   gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_em_star, &species->local, 
     fin, species->cflrate, rhs);
 
+  // AH Note: I'm not sure we need this here.
   gkcls->fdot_scaling(app, species, gkcls, rhs, species->cflrate, &species->local);
 
   app->stat.species_collisionless_tm += gkyl_time_diff_now_sec(wst);

From 183d7edb8326c8cb9a1d00fad8f9513e32e34617 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 11:48:19 -0500
Subject: [PATCH 103/181] regroup the lines that are meant to compute Apardot

---
 gyrokinetic/apps/gyrokinetic.c | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 3b764403a7..09b07daca7 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1950,14 +1950,13 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_recycle_react_scale_cross_moms(app, gk_ns, &gk_ns->rrs, fin, fin_neut);
   }
 
-  // Compute df/dt^* for Ohm's law.
+  // Compute Apardot (solves Ohm's law using the previously built df/dt^*).
+  // Compute df/dt^* (ES + Apar)
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
     gk_species_rhs_star(app, gk_s, fin[i], fout[i], bflux_out[i]);
     gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
   }
-
-  // Compute Apardot (solves Ohm's law using the previously built df/dt^*).
   gk_field_em_rhs(app, app->field, fin, fout);
   // Update aparout.
   gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);

From 8da594c3c5cdc7650bb11bb90d99d2b247d1a5e6 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 11:49:33 -0500
Subject: [PATCH 104/181] Refactor dg volume pointer to function naming to
 differentiate between poiting to a kernel and the one pointing to a higher
 level routine.

---
 gyrokinetic/zero/dg_gyrokinetic.c           | 14 ++---
 gyrokinetic/zero/dg_gyrokinetic_cu.cu       | 12 ++---
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h | 57 ++++++++++-----------
 3 files changed, 40 insertions(+), 43 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 3fef766c90..08b3eaf1d5 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -115,21 +115,21 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   gyrokinetic->eqn.vol_term = kernel_dg_gyrokinetic_vol;
 
   if (no_by) {
-    gyrokinetic->vol_es_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    gyrokinetic->vol_es_term = CK(vol_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
   // Setup electromagnetic terms if needed.
   bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
-  gyrokinetic->vol_add_apar_term = dg_gyrokinetic_add_apar_vol_return_zero;
-  gyrokinetic->vol_add_apardot_term = dg_gyrokinetic_add_apardot_vol_return_zero;
+  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_return_zero;
+  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_return_zero;
   if (is_em) {
-    gyrokinetic->vol_add_apar_term = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_add_apar_kernel = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
     // Apardot is removed if we want to compute RHS star (ES + Apardot).
-    if (em_star)
-      gyrokinetic->vol_add_apardot_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_add_apardot_kernel = em_star ? 
+      dg_gyrokinetic_add_apardot_vol_return_zero : CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
   }
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 4b2122f6dc..1df3ea9f0b 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -87,21 +87,21 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->eqn.vol_term = kernel_dg_gyrokinetic_vol;
 
   if (no_by) {
-    gyrokinetic->vol_es_term = CK(vol_no_by_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = CK(vol_no_by_kernels,cdim,vdim,poly_order);
   }
   else {
-    gyrokinetic->vol_es_term = CK(vol_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = CK(vol_kernels,cdim,vdim,poly_order);
   }
 
   // Setup electromagnetic terms if needed.
   bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
-  gyrokinetic->vol_add_apar_term = dg_gyrokinetic_add_apar_vol_return_zero;
-  gyrokinetic->vol_add_apardot_term = dg_gyrokinetic_add_apardot_vol_return_zero;
+  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_return_zero;
+  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_return_zero;
   if (is_em) {
-    gyrokinetic->vol_add_apar_term = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_add_apar_kernel = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
     // Apardot is removed if we want to compute RHS star (ES + Apardot).
     if (em_star)
-      gyrokinetic->vol_add_apardot_term = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+      gyrokinetic->vol_add_apardot_kernel = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
   }
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index dd93dd2039..4832cbb08a 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -59,9 +59,9 @@ struct dg_gyrokinetic {
   struct gkyl_dg_eqn eqn; // Base object.
   int cdim; // Config-space dimensions.
   int pdim; // Phase-space dimensions.
-  dg_gyrokinetic_vol_es_t vol_es_term; // Electrostatic contribution to volume term.
-  dg_gyrokinetic_vol_add_apar_t vol_add_apar_term; // Additional volume term for Apar contribution.
-  dg_gyrokinetic_vol_add_apardot_t vol_add_apardot_term; // Additional volume term for Apar contribution.
+  dg_gyrokinetic_vol_es_t vol_es_kernel; // Electrostatic contribution to volume term.
+  dg_gyrokinetic_vol_add_apar_t vol_add_apar_kernel; // Additional volume term for Apar contribution.
+  dg_gyrokinetic_vol_add_apardot_t vol_add_apardot_kernel; // Additional volume term for Apar contribution.
   dg_gyrokinetic_surf_t surf[4]; // Surface terms.
   dg_gyrokinetic_boundary_surf_t boundary_surf[4]; // Surface terms for velocity boundary.
   struct gkyl_range conf_range; // Configuration space range.
@@ -97,31 +97,28 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
   long vidx = gkyl_range_idx(&gyrokinetic->vel_map->local_vel, vel_idx);
   long pidx = gkyl_range_idx(&gyrokinetic->phase_range, idx);
   double cfl = 0.0;
-  cfl = gyrokinetic->vol_es_term(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx),
-    qIn, qRhsOut);
-  cfl += gyrokinetic->vol_add_apar_term(xc, dx,
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx),
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx),
-    qIn, qRhsOut);
-  cfl += gyrokinetic->vol_add_apardot_term(
-    (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx),
-    gyrokinetic->charge, gyrokinetic->mass,
-    (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx),
-    qIn, qRhsOut);
+
+  const double *phi = (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.phi, cidx);
+  const double *apar = (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apar, cidx);
+  const double *apardot = (const double*) gkyl_array_cfetch(gyrokinetic->auxfields.apardot, cidx);
+  const double *vm = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx);
+  const double *vm_sq = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx);
+  const double *bmag = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx);
+  const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx);
+  const double *b_i = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx);
+  const double *dualcurlbhatoverB = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx);
+  const double *rtg33inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx);
+  const double *bioverJB = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx);
+  
+  // Electrostatic contribution to volume term.
+  cfl = gyrokinetic->vol_es_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
+    bmag, phi, dualcurlbhatoverB, rtg33inv, bioverJB, qIn, qRhsOut);
+  // Add Apar contribution to volume term if needed.
+  cfl += gyrokinetic->vol_add_apar_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
+    bmag, jacobtot_inv, b_i, phi, apar, qIn, qRhsOut);
+  // Add Apardot contribution to volume term if needed.
+  cfl += gyrokinetic->vol_add_apardot_kernel( vm, gyrokinetic->charge, gyrokinetic->mass, 
+    apardot, qIn, qRhsOut);
   return cfl;
 }
 
@@ -175,8 +172,8 @@ static const gkyl_dg_gyrokinetic_vol_es_kern_list ser_no_by_vol_es_kernels[] = {
 GKYL_CU_D
 static const gkyl_dg_gyrokinetic_vol_add_apar_kern_list ser_add_apar_vol_kernels[] = {
   // 1x kernels
-  { NULL, dg_gyrokinetic_add_apar_vol_return_zero, NULL }, // 0
-  { NULL, dg_gyrokinetic_add_apar_vol_return_zero, NULL }, // 1
+  { NULL, dg_gyrokinetic_add_apar_vol_1x1v_ser_p1, NULL }, // 0
+  { NULL, dg_gyrokinetic_add_apar_vol_1x2v_ser_p1, NULL }, // 1
   // 2x kernels
   { NULL, dg_gyrokinetic_add_apar_vol_2x2v_ser_p1, NULL }, // 2
   // 3x kernels

From 4bb87174981654793bec2e2b97805383dc162ca7 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 11:53:45 -0500
Subject: [PATCH 105/181] =?UTF-8?q?=F0=9F=94=A5=F0=9F=90=9B=F0=9F=94=A5=20?=
 =?UTF-8?q?the=20rhs=20was=20always=20static,=20bug=20introduce=20during?=
 =?UTF-8?q?=20the=20logic=20rehandling.=20the=20alfven=20tests=20are=20giv?=
 =?UTF-8?q?ing=20the=20correct=20frequencies=20and=20conserve=20energy=20a?=
 =?UTF-8?q?nd=20particle=20now=20for=201x2v,=202x2v=20and=203x2v.=20The=20?=
 =?UTF-8?q?3x2v=20case=20takes=201min30s=20agains=201min=20for=20the=20get?=
 =?UTF-8?q?=5Fem=5Fback=20branch=20due=20to=20the=20double=20RHS=20evaluat?=
 =?UTF-8?q?ion...?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/apps/gk_species.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index aaead547ee..8c9487a35c 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1010,7 +1010,7 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   }
 
   // Set function pointers.
-  gks->rhs_func = gk_species_rhs_static;
+  gks->rhs_func = gk_species_rhs_dynamic;
   if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
     gks->rhs_star_func = gk_species_rhs_star_dynamic;
   } else {

From 0c48925ffb8b8adb2c5fd8541542c76061f6b88b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 13:55:32 -0500
Subject: [PATCH 106/181] small bug fix of the collisionless type

---
 gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c b/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
index a520d0502d..a2412585c3 100644
--- a/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_bgk_cross_relax_1x2v_p1.c
@@ -390,7 +390,7 @@ main(int argc, char **argv)
     },      
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES_NO,
+      .type = GKYL_GK_COLLISIONLESS_ES,
       .no_by = true,
     },
 

From 7ab32681e41307fb8dbe27bda964d6e75bf773f6 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 17 Feb 2026 10:58:29 -0800
Subject: [PATCH 107/181] =?UTF-8?q?finish=20GPU=20implementation=20of=20fu?=
 =?UTF-8?q?ll=20upwind=20em=20scheme.=20Tested=20in=20all=20alfven=20cases?=
 =?UTF-8?q?=20and=20one=20TCV=20with=20multi=20GPU=20all=20looks=20to=20wo?=
 =?UTF-8?q?rk=20fine.=20The=20results=20though=20are=20exactly=20the=20sam?=
 =?UTF-8?q?e=20as=20the=20get=5Fem=5Fback=20implementation...=20so=20we=20?=
 =?UTF-8?q?do=20not=20see=20any=20improvement=20of=20the=20discontinuity?=
 =?UTF-8?q?=20build=20up=20observed=20in=20ne=20and=20Te=20when=20using=20?=
 =?UTF-8?q?the=20full=20upwind=20advection=20instead=20of=20the=20partial?=
 =?UTF-8?q?=20one=20=F0=9F=98=94?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         | 22 ++++----
 gyrokinetic/zero/gk_collisionless_flux.c      |  2 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  | 52 ++++++++-----------
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |  4 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  2 +-
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h |  3 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    |  7 +--
 7 files changed, 43 insertions(+), 49 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 1df3ea9f0b..4be7c2b899 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -38,7 +38,7 @@ gkyl_gyrokinetic_set_auxfields_cu(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_
 __global__ static void 
 dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_basis_type b_type,
   int cv_index, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type collless_type, 
-  bool no_by, bool only_apardot)
+  bool no_by, bool em_star)
 {
   gyrokinetic->auxfields.flux_surf = 0; 
   gyrokinetic->auxfields.phi = 0; 
@@ -49,9 +49,9 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->eqn.boundary_surf_term = boundary_surf;
   gyrokinetic->eqn.boundary_diag_term = boundary_diag;
 
-  const gkyl_dg_gyrokinetic_vol_kern_list *vol_kernels, *vol_no_by_kernels;
+  const gkyl_dg_gyrokinetic_vol_es_kern_list *vol_kernels, *vol_no_by_kernels;
   const gkyl_dg_gyrokinetic_vol_add_apar_kern_list *vol_add_apar_kernels;
-  const gkyl_dg_gyrokinetic_vol_kern_list *vol_add_apardot_kernels;
+  const gkyl_dg_gyrokinetic_vol_add_apardot_kern_list *vol_add_apardot_kernels;
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_x_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_y_kernels; 
   const gkyl_dg_gyrokinetic_surf_kern_list *surf_z_kernels; 
@@ -63,7 +63,7 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   
   switch (b_type) {
     case GKYL_BASIS_MODAL_SERENDIPITY:
-      vol_kernels = ser_vol_kernels;
+      vol_kernels = ser_vol_es_kernels;
       vol_add_apar_kernels = ser_add_apar_vol_kernels;
       vol_add_apardot_kernels = ser_add_apardot_vol_kernels;
       surf_x_kernels = ser_surf_x_kernels;
@@ -75,7 +75,7 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
       boundary_surf_z_kernels = ser_boundary_surf_z_kernels;
       boundary_surf_vpar_kernels = ser_boundary_surf_vpar_kernels;
 
-      vol_no_by_kernels = ser_no_by_vol_kernels;
+      vol_no_by_kernels = ser_no_by_vol_es_kernels;
       
       break;
 
@@ -87,10 +87,10 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->eqn.vol_term = kernel_dg_gyrokinetic_vol;
 
   if (no_by) {
-    gyrokinetic->vol_es_kernel = CK(vol_no_by_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = vol_no_by_kernels[cv_index].kernels[poly_order];
   }
   else {
-    gyrokinetic->vol_es_kernel = CK(vol_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_es_kernel = vol_kernels[cv_index].kernels[poly_order];
   }
 
   // Setup electromagnetic terms if needed.
@@ -98,10 +98,10 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_return_zero;
   gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_return_zero;
   if (is_em) {
-    gyrokinetic->vol_add_apar_kernel = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_add_apar_kernel = vol_add_apar_kernels[cv_index].kernels[poly_order];
     // Apardot is removed if we want to compute RHS star (ES + Apardot).
-    if (em_star)
-      gyrokinetic->vol_add_apardot_kernel = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+    gyrokinetic->vol_add_apardot_kernel = em_star ?
+      dg_gyrokinetic_add_apardot_vol_return_zero : vol_add_apardot_kernels[cv_index].kernels[poly_order];
   }
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
@@ -162,7 +162,7 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gkyl_cu_memcpy(gyrokinetic_cu, gyrokinetic, sizeof(struct dg_gyrokinetic), GKYL_CU_MEMCPY_H2D);
 
   dg_gyrokinetic_set_cu_dev_ptrs<<<1,1>>>(gyrokinetic_cu, cbasis->b_type, cv_index[cdim].vdim[vdim],
-    cdim, vdim, poly_order, collless_type, no_by, only_apardot);
+    cdim, vdim, poly_order, collless_type, no_by, em_star);
 
   // set parent on_dev pointer
   gyrokinetic->eqn.on_dev = &gyrokinetic_cu->eqn;
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 22d5cd2e27..3ecf356485 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -20,7 +20,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis, 
-      charge, mass, type, no_by, only_apardot, em_star, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, type, no_by, em_star, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 1b13d8c2f0..2f887bf2f4 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -205,39 +205,31 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
   bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, 
-  bool no_by, bool only_apardot,
+  bool no_by, bool em_star,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
-  if (only_apardot){
-    // If we only add Apardot terms to the flux, the only non zero kernel is the vpar one.
+  // Choose appropriate kernels.
+  em = em_star ? 2 : em; // If em_star is true, use EM kernels without Apardot contribution.
+  if (no_by) {
     for (int d=0; d<cdim; ++d) {
-      up->flux_surf[d] = gk_collisionless_flux_surf_return_zero;
-      up->flux_surf_edge_lo[d] = gk_collisionless_flux_surf_return_zero;
-      up->flux_surf_edge_up[d] = gk_collisionless_flux_surf_return_zero;
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_add_apardot_surf_vpar_kern(cdim, vdim, poly_order);
-  } else {
-    if (no_by) {
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
-    } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
-      for (int d=0; d<cdim; ++d) {
-        // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-        up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-        up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[d]);
-        up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
-          poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
-      }
-      up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
+  } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
+    for (int d=0; d<cdim; ++d) {
+      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
+      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[d]);
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
+        poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
   }
 }
 
@@ -245,7 +237,7 @@ gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type type, 
-  const bool no_by, const bool only_apardot,
+  const bool no_by, const bool em_star,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
@@ -284,7 +276,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   struct gkyl_gk_collisionless_flux *up_cu = (struct gkyl_gk_collisionless_flux*) gkyl_cu_malloc(sizeof(*up_cu));
   gkyl_cu_memcpy(up_cu, up, sizeof(gkyl_gk_collisionless_flux), GKYL_CU_MEMCPY_H2D);
 
-  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, no_by, only_apardot, bctype_conf_dev);
+  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, no_by, em_star, bctype_conf_dev);
 
   gkyl_cu_free(bctype_conf_dev);
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index fe5581fa6d..8dbbd24ca0 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -29,7 +29,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param skip_cell_threshold Threshold for skipping cells in the gyrokinetic equation
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param only_apardot Whether we want to only add the apardot term.
+ * @param em_star Whether to compute RHS star (i.e. ES + Apardot) RHS for electromagnetic simulations.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -38,7 +38,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_cell_threshold, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 4832cbb08a..08566c6227 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -402,7 +402,7 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, double skip_if_smaller_than, enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool only_apardot, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
+  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**
  * CUDA device function to set the auxiliary fields (e.g. geometry & EM fields)
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index 28e7cbda2e..2c70c74a84 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -53,7 +53,8 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
  * @param conf_ext_range Extended configuration space range (so we obtain geo quantities at all the needed surfaces).
  * @param phase_ext_range Extended Phase space range (so we obtain alpha_surf at all the needed surfaces).
  * @param phi Electrostatic potential.
- * @param apar Parallel component of vector potential OR should be Apardot if only_apardot is true.
+ * @param apar Parallel component of vector potential.
+ * @param apardot Time derivative of parallel component of vector potential.
  * @param fin Distribution function.
  * @param flux_surf Output surface expansion in a cell on the *lower* edge in each direction.
  * @param clfrate Output CFL rate.
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 8cf9212fa7..db8b8269e2 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -955,7 +955,7 @@ choose_gk_collisionless_flux_no_by_surf_vpar_kern(int em, int cdim, int vdim, in
 struct gkyl_gk_collisionless_flux* 
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
-  double charge, double mass, enum gkyl_gk_collisionless_type type, const bool no_by, const bool only_apardot,
+  double charge, double mass, enum gkyl_gk_collisionless_type type, const bool no_by, const bool em_star,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf);
@@ -965,6 +965,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
  */
 void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
-  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, const struct gkyl_array *phi, 
-  const struct gkyl_array *apar, const struct gkyl_array* fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate);
+  const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
+  const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *apardot, 
+  const struct gkyl_array* fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate);
 #endif

From 33731ed2396a5ca7a29b02f91966b86b39afb10d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 18 Feb 2026 09:21:30 -0500
Subject: [PATCH 108/181] These new apar volume kernels use the product rule to
 compute ``` curl(Apar b)/mB ``` as ``` Apar/m curl(b)/B + grad(Apar)/m x b/B
 ``` so that we make full use of predefined geometric quantities used in the
 electrostatic volume kernel, i.e. - `dualcurlbhatoverB` for curl(b)/B -
 `bioverJB` for the cross product with b/B

---
 .../dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c |  25 +++-
 .../dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c |  34 ++++-
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c |  60 ++++----
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c | 140 ++++++++++--------
 .../gkyl_dg_gyrokinetic_kernels.h             |   8 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  11 +-
 6 files changed, 177 insertions(+), 101 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
index 16e90e0188..889648f0c1 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
@@ -1,6 +1,6 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
@@ -10,6 +10,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   // q_,m_: species charge and mass.
   // bmag: magnetic field amplitude.
   // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // dualcurlbhatoverB: dual curl of bhat over B.
+  // bioverJB: b_i over J times B.
   // b_i: covariant components of the field aligned unit vector.
   // apar: parallel component of magnetic vector potential.
   // phi: electrostatic potential .
@@ -26,6 +28,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   const double *b_y = &b_i[2];
   const double *b_z = &b_i[4];
 
+  const double *bioverJB_x = &bioverJB[0]; 
+  const double *bioverJB_y = &bioverJB[2]; 
+  const double *bioverJB_z = &bioverJB[4]; 
+
+  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+
   double hamil[6] = {0.}; 
   hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
   hamil[1] = 1.4142135623730951*phi[1]*q_; 
@@ -39,12 +49,25 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   hamil2[1] = hamil[4]*hamil[4]; 
 
   double alphax[6] = {0.}; 
+  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+1.5811388300841895*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdx2)/(vmap[1]*m_); 
+  alphax[3] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+1.5811388300841895*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdx2)/(vmap[1]*m_); 
 
 
+  out[1] += 0.8660254037844386*(alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[3] += 0.7745966692414834*alphax[3]*fin[5]+0.7745966692414833*alphax[2]*fin[4]+0.8660254037844386*(alphax[1]*fin[3]+fin[1]*alphax[3]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[5] += 0.8660254037844386*alphax[1]*fin[5]+0.8660254037844387*alphax[0]*fin[4]+0.7745966692414834*(alphax[3]*fin[3]+alphax[2]*fin[2]); 
 
   double alphavpar[6] = {0.}; 
+  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
 
 
+  out[2] += 0.8660254037844386*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[3] += 0.8660254037844386*(alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[4] += 1.9364916731037085*(alphavpar[1]*fin[3]+alphavpar[0]*fin[2]); 
+  out[5] += 1.9364916731037085*(alphavpar[0]*fin[3]+alphavpar[1]*fin[2]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
index 459582a12d..491eab8b83 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
@@ -1,6 +1,6 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
@@ -10,6 +10,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   // q_,m_: species charge and mass.
   // bmag: magnetic field amplitude.
   // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // dualcurlbhatoverB: dual curl of bhat over B.
+  // bioverJB: b_i over J times B.
   // b_i: covariant components of the field aligned unit vector.
   // apar: parallel component of magnetic vector potential.
   // phi: electrostatic potential .
@@ -27,6 +29,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   const double *b_y = &b_i[2];
   const double *b_z = &b_i[4];
 
+  const double *bioverJB_x = &bioverJB[0]; 
+  const double *bioverJB_y = &bioverJB[2]; 
+  const double *bioverJB_z = &bioverJB[4]; 
+
+  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+
   double hamil[12] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
   hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
@@ -42,12 +52,34 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[8]*hamil[8]; 
 
   double alphax[12] = {0.}; 
+  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]+1.5811388300841895*apar[0]*dualcurlbhatoverB_z[0]*hamil[8])*rdx2)/(vmap[1]*m_); 
+  alphax[4] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]+1.5811388300841895*dualcurlbhatoverB_z[0]*apar[1]*hamil[8])*rdx2)/(vmap[1]*m_); 
 
 
+  out[1] += 0.6123724356957944*(alphax[4]*fin[4]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[4] += 0.5477225575051661*(alphax[4]*fin[9]+alphax[2]*fin[8])+0.6123724356957944*(alphax[1]*fin[4]+fin[1]*alphax[4]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[5] += 0.6123724356957944*(alphax[4]*fin[7]+alphax[2]*fin[6]+alphax[1]*fin[5]+alphax[0]*fin[3]); 
+  out[7] += 0.5477225575051661*(alphax[4]*fin[11]+alphax[2]*fin[10])+0.6123724356957944*(alphax[1]*fin[7]+alphax[0]*fin[6]+alphax[4]*fin[5]+alphax[2]*fin[3]); 
+  out[9] += 0.6123724356957944*(alphax[1]*fin[9]+alphax[0]*fin[8])+0.5477225575051661*(alphax[4]*fin[4]+alphax[2]*fin[2]); 
+  out[11] += 0.6123724356957944*(alphax[1]*fin[11]+alphax[0]*fin[10])+0.5477225575051661*(alphax[4]*fin[7]+alphax[2]*fin[6]); 
 
   double alphavpar[12] = {0.}; 
+  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[3] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[5])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[5])*rdx2)/(vmap[1]*m_); 
+  alphavpar[5] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[5])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[5])*rdx2)/(vmap[1]*m_); 
 
 
+  out[2] += 0.6123724356957944*(alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[4] += 0.6123724356957944*(alphavpar[3]*fin[5]+fin[3]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[6] += 0.6123724356957944*(alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[7] += 0.6123724356957944*(alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[8] += 1.369306393762915*(alphavpar[5]*fin[7]+alphavpar[3]*fin[6]+alphavpar[1]*fin[4]+alphavpar[0]*fin[2]); 
+  out[9] += 1.369306393762915*(alphavpar[3]*fin[7]+alphavpar[5]*fin[6]+alphavpar[0]*fin[4]+alphavpar[1]*fin[2]); 
+  out[10] += 1.369306393762915*(alphavpar[1]*fin[7]+alphavpar[0]*fin[6]+fin[4]*alphavpar[5]+fin[2]*alphavpar[3]); 
+  out[11] += 1.369306393762915*(alphavpar[0]*fin[7]+alphavpar[1]*fin[6]+fin[2]*alphavpar[5]+alphavpar[3]*fin[4]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index 7b32a1eb31..0b083c62b0 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -1,6 +1,6 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
@@ -10,6 +10,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   // q_,m_: species charge and mass.
   // bmag: magnetic field amplitude.
   // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // dualcurlbhatoverB: dual curl of bhat over B.
+  // bioverJB: b_i over J times B.
   // b_i: covariant components of the field aligned unit vector.
   // apar: parallel component of magnetic vector potential.
   // phi: electrostatic potential .
@@ -28,6 +30,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   const double *b_y = &b_i[4];
   const double *b_z = &b_i[8];
 
+  const double *bioverJB_x = &bioverJB[0]; 
+  const double *bioverJB_y = &bioverJB[4]; 
+  const double *bioverJB_z = &bioverJB[8]; 
+
+  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[8]; 
+
   double hamil[24] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
   hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
@@ -47,14 +57,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = ((-(0.6123724356957944*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]-0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[1] = ((-(1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*apar[2]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]-0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[2] = ((-(0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[3] = ((-(1.369306393762915*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[5] = ((-(0.5511351921262146*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.5511351921262146*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[2]*hamil[3]*jacobtot_inv[3]-1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[6] = ((-(2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.232375754386623*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]-1.369306393762915*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]-1.232375754386623*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[7] = ((-(0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16])-0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[11] = ((-(1.232375754386623*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.232375754386623*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[16]-2.4647515087732463*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -71,14 +81,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = ((0.6123724356957944*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[1] = ((0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[2] = ((1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[3] = ((1.369306393762915*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[5] = ((0.5511351921262146*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[6] = ((0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[7] = ((2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+1.232375754386623*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+1.232375754386623*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[11] = ((1.232375754386623*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.232375754386623*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+2.4647515087732463*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]+0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[0] = ((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/(vmap[1]*m_); 
+  alphaz[1] = ((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/(vmap[1]*m_); 
+  alphaz[2] = ((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/(vmap[1]*m_); 
+  alphaz[3] = ((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdz2)/(vmap[1]*m_); 
+  alphaz[5] = ((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/(vmap[1]*m_); 
+  alphaz[6] = ((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdz2)/(vmap[1]*m_); 
+  alphaz[7] = ((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdz2)/(vmap[1]*m_); 
+  alphaz[11] = ((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdz2)/(vmap[1]*m_); 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -95,14 +105,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[5])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[5]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[5]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[5]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[5]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3]-0.6123724356957944*b_y[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*b_y[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*jacobtot_inv[2]*apar[3]*b_y[3]-0.6123724356957944*jacobtot_inv[1]*hamil[2]*apar[3]*b_y[3]-0.3061862178478971*apar[0]*hamil[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[0]*apar[2]*hamil[2]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]-0.3061862178478971*b_y[0]*hamil[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*hamil[2]*apar[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[2]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[2]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[2]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[2]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[2]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[1] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[5])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[5]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[5]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[5]+1.1022703842524295*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*hamil[2]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*hamil[2]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*hamil[2]*apar[3]*b_y[3]-0.6123724356957944*apar[1]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.6123724356957944*hamil[1]*apar[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[1]*apar[2]*hamil[2]*b_y[3]+0.5511351921262146*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]-0.6123724356957944*b_y[1]*hamil[2]*jacobtot_inv[2]*apar[3]+0.6123724356957944*hamil[1]*b_y[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*hamil[2]*apar[3]+0.5511351921262146*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[2]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[2]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[2]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[2] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[5]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[5]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[5]-1.1022703842524295*hamil[2]*apar[3]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3]-0.5511351921262146*apar[2]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.6123724356957944*apar[1]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[2]*b_y[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3]-0.5511351921262146*b_y[2]*hamil[2]*jacobtot_inv[2]*apar[3]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[2]*apar[3]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*b_y[2]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[2]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[2]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[4] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[12])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[12]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[12]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[12]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[12]-0.6123724356957944*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[9]+0.6123724356957944*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[5] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[5]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[5]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[5]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[5]-0.5511351921262146*apar[2]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.5511351921262146*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]-0.5511351921262146*b_y[2]*hamil[2]*apar[3]*jacobtot_inv[3]+0.5511351921262146*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[3]-1.1022703842524295*hamil[2]*jacobtot_inv[2]*apar[3]*b_y[3]+1.1022703842524295*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.6123724356957944*jacobtot_inv[0]*apar[1]*hamil[2]*b_y[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*hamil[2]*apar[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*b_y[2]*apar[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[2]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[2]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[8] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[12]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[12]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[12]-0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[9]+1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[8]+0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[8]+0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[9] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[12]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[12]-1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[9]-0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[9]+0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[12] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[12]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[12]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[9]-1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[9]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[9]+0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[8]+1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_x[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
index 705fe962bd..100d9568df 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -1,6 +1,6 @@
 #include <gkyl_dg_gyrokinetic_kernels.h> 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   // w[NDIM]: cell-center.
@@ -10,6 +10,8 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   // q_,m_: species charge and mass.
   // bmag: magnetic field amplitude.
   // jacobtot_inv: reciprocal of the conf-space jacobian time the guiding center coordinate Jacobian.
+  // dualcurlbhatoverB: dual curl of bhat over B.
+  // bioverJB: b_i over J times B.
   // b_i: covariant components of the field aligned unit vector.
   // apar: parallel component of magnetic vector potential.
   // phi: electrostatic potential .
@@ -29,6 +31,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   const double *b_y = &b_i[8];
   const double *b_z = &b_i[16];
 
+  const double *bioverJB_x = &bioverJB[0]; 
+  const double *bioverJB_y = &bioverJB[8]; 
+  const double *bioverJB_z = &bioverJB[16]; 
+
+  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[16]; 
+
   double hamil[48] = {0.}; 
   hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
   hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
@@ -52,22 +62,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (((-(0.21650635094610965*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]-0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]+0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*apar[3]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_z[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]+0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[2] = ((-(0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]-0.21650635094610965*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[3] = (((-(0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[4] = (((-(0.4841229182759271*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[6] = ((-(0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7])-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[7] = (((-(0.19485571585149863*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.19485571585149863*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[3]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]+0.19485571585149863*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[2]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[8] = ((-(0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[9] = (((-(0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.43571062644833425*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]+0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[10] = ((-(0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]-0.4841229182759271*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[11] = (((-(0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]+0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[16] = ((-(0.19485571585149863*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[17] = ((-(0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[18] = (((-(0.43571062644833425*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.7842791276070014*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]+0.43571062644833425*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[19] = ((-(0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[26] = ((-(0.43571062644833425*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -96,22 +106,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (((0.21650635094610965*apar[3]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*b_x[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[5]+0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[4]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*apar[1]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*b_z[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[1] = (((0.38971143170299727*hamil[4]*apar[5]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*apar[3]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_x[5]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[0]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.10825317547305482*b_z[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_z[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[2] = (((0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]+0.21650635094610965*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[3] = (((0.10825317547305482*apar[0]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*apar[5]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*apar[1]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_z[5]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[4] = (((0.4841229182759271*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[6] = (((0.38971143170299727*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[7] = (((0.19485571585149863*apar[1]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[3]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[3]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.19485571585149863*b_z[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*apar[1]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[5]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[8] = (((0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]-0.21650635094610965*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[9] = (((0.8714212528966685*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.43571062644833425*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[10] = (((0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]+0.4841229182759271*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[11] = (((0.24206145913796356*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[32]-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[16] = (((0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[17] = (((0.8714212528966685*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[18] = (((0.43571062644833425*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[19] = (((0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]-0.4841229182759271*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[26] = (((0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]-0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
 
 
   out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -140,22 +150,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (((-(0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[4]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.21650635094610965*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((-(0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[2] = ((0.21650635094610965*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[3] = (((-(0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[4] = (((-(0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.4841229182759271*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[6] = ((0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[7] = (((-(0.35074028853269745*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]-0.19485571585149863*b_x[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*apar[2]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*apar[1]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[8] = ((0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]+0.21650635094610965*b_y[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[9] = (((-(0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]-0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[10] = ((0.4841229182759271*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[11] = (((-(0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]-0.43571062644833425*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[16] = ((0.19485571585149863*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_y[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[17] = ((0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[18] = (((-(0.7842791276070014*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]-0.43571062644833425*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.43571062644833425*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[19] = ((0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]+0.4841229182759271*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[26] = ((0.43571062644833425*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]+0.43571062644833425*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
 
 
   out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -184,22 +194,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (((-(0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[7]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[6]+0.10825317547305482*apar[2]*hamil[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*b_x[3]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[5]*b_x[5]+0.10825317547305482*hamil[3]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[4]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[3]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[3]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[3]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[8]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[6]*apar[7]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[6]-0.21650635094610965*apar[1]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*b_y[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*apar[5]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*hamil[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[3]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[16]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.38971143170299727*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.21650635094610965*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[8]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[7]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[7]+0.10825317547305482*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[6]+0.21650635094610965*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[6]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[6]+0.21650635094610965*apar[1]*hamil[2]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[5]*jacobtot_inv[5]+0.21650635094610965*b_z[1]*hamil[2]*apar[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[5]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[3]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[4]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[3]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[3]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[2]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[2]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[1] = (((-(0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[16]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[7]+0.19485571585149863*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[6]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[6]-0.38971143170299727*hamil[2]*apar[5]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*hamil[3]*apar[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_x[5]-0.21650635094610965*hamil[2]*apar[3]*jacobtot_inv[3]*b_x[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[5]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[5]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[5]+0.10825317547305482*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[4]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[3]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[16]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]-0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[7]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[6]*apar[7]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[6]+0.38971143170299727*hamil[1]*apar[5]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[5]*b_y[5]-0.21650635094610965*apar[1]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.21650635094610965*hamil[1]*apar[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[3]*b_y[5]+0.19485571585149863*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[5]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[16]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[7]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[6]-0.19485571585149863*hamil[1]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_z[5]+0.21650635094610965*apar[1]*hamil[2]*jacobtot_inv[3]*b_z[5]-0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*apar[3]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[4]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[2]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[2]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[16])-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[8]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*hamil[6]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[6]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[7]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.21650635094610965*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[6]-0.21650635094610965*hamil[3]*apar[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_y[5]-0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[4]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[16]+0.38971143170299727*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[8]+0.21650635094610965*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[2]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[4]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[3] = (((-(0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[16]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[16]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[7]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[6]-0.10825317547305482*apar[0]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[1]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[16]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[16]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[8]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[7]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[6]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[6]-0.38971143170299727*hamil[3]*apar[5]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[5]*jacobtot_inv[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[5]*b_y[5]-0.19485571585149863*apar[3]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[3]*b_y[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[5]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[5]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[5]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[16]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[8]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[7]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[7]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[6]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[6]+0.38971143170299727*hamil[2]*apar[5]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[4]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_z[5]+0.19485571585149863*hamil[2]*apar[3]*jacobtot_inv[3]*b_z[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[5]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[5]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[5]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[3]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[3]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[3]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[5] = (((0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[21]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[14]+0.10825317547305482*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[21]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[14]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[21]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[12]-0.10825317547305482*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[6] = (((-(0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[16])-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[3]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*hamil[6]*apar[7]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*hamil[6]*apar[7]-0.38971143170299727*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[6]-0.19485571585149863*jacobtot_inv[1]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[8]-0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[7]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[7]+0.38971143170299727*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[6]-0.10825317547305482*apar[2]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[3]*jacobtot_inv[3]*apar[4]*b_y[5]+0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[4]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[16]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[8]+0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[8]+0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*apar[2]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*hamil[2]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[4]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[7] = (((-(0.7014805770653949*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.7014805770653949*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.7014805770653949*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[16]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[16]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[8]+0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[7]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[7]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[7]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[7]+0.35074028853269745*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[7]-0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[6]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[6]-0.19485571585149863*apar[1]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.19485571585149863*b_x[1]*hamil[2]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*apar[5]*b_x[5]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[16]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[8]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[8]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[8]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[7]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[7]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.19485571585149863*apar[3]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*apar[1]*hamil[1]*b_y[5]*jacobtot_inv[5]-0.19485571585149863*b_y[3]*hamil[3]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_y[1]*hamil[1]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[5]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*apar[5]*b_y[5]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[3]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[16]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[16]+0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[8]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[8]-0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[7]-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[7]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[7]-0.35074028853269745*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[6]+0.19485571585149863*hamil[2]*apar[3]*b_z[5]*jacobtot_inv[5]+0.19485571585149863*hamil[2]*b_z[3]*apar[5]*jacobtot_inv[5]-0.19485571585149863*b_z[1]*hamil[1]*apar[4]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[5]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*apar[5]*b_z[5]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[4]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[3]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[3]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[8] = (((-(0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[16])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[6]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[6]-0.10825317547305482*apar[2]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*b_x[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[16]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[7]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[7]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[7]-0.38971143170299727*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[7]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[6]+0.10825317547305482*hamil[1]*apar[2]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*b_y[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[4]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[8]+0.38971143170299727*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[6]*apar[7]+0.38971143170299727*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[6]+0.21650635094610965*b_z[1]*hamil[2]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[4]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[12] = (((0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[14]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[14]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[21])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[21]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[14]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[12]-0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[12]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[13] = ((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[14]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[14]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[12]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[14] = (((0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[14]+0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[21]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[21]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[14]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[21]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[12]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[16] = (((-(0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[16])-0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[0]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[0]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[7]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[6]-0.19485571585149863*hamil[2]*apar[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_x[5]-0.10825317547305482*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[16]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[7]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[7]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[6]-0.19485571585149863*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[6]+0.19485571585149863*hamil[1]*apar[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[4]*b_y[5]+0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[16]+0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[16]+0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.35074028853269745*b_z[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[5]*apar[7]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[6]+0.10825317547305482*b_z[0]*hamil[2]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[20] = ((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[21]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[12]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[21] = (((0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[21]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[21]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[14]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[21]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[21]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[21]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[14]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[21])-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[21]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[21]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[12]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[22] = ((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[21]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[21]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[14]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[14]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[12]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[27] = ((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[21]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[14]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[14]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[14]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[12]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[4])*rdx2)/vmap[1])/m_; 
+  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
 
 
   out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
index e8225e1740..00b7369710 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
+++ b/gyrokinetic/ker/dg_gyrokinetic/gkyl_dg_gyrokinetic_kernels.h
@@ -230,7 +230,7 @@ GKYL_CU_DH double dg_gyrokinetic_boundary_surfvpar_3x2v_ser_p1(const double *w,
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
+            const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double *vmap, const double q_, const double m_,
@@ -238,7 +238,7 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x1v_ser_p1(const double *vmap,
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
+            const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double *vmap, const double q_, const double m_,
@@ -246,7 +246,7 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_1x2v_ser_p1(const double *vmap,
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
+            const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double *vmap, const double q_, const double m_,
@@ -254,7 +254,7 @@ GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_2x2v_ser_p1(const double *vmap,
 
 GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const double *dxv, 
             const double *vmap, const double *vmapSq, const double q_, const double m_, 
-            const double *bmag, const double *jacobtot_inv,
+            const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
             const double *b_i, const double *phi, const double *apar,
             const double *fin, double* GKYL_RESTRICT out); 
 GKYL_CU_DH double dg_gyrokinetic_add_apardot_vol_3x2v_ser_p1(const double *vmap, const double q_, const double m_,
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 08566c6227..569574c836 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -21,8 +21,8 @@ typedef double (*dg_gyrokinetic_vol_es_t)(const double *w, const double *dxv,
 
 typedef double (*dg_gyrokinetic_vol_add_apar_t)(const double *w, const double *dxv, 
   const double *vmap, const double *vmapSq, const double q_, const double m_, 
-  const double *bmag, const double *jacobtot_inv, const double *b_i, const double *phi, 
-  const double *apar, const double *fin, double* GKYL_RESTRICT out);
+  const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB, const double *b_i, 
+  const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out); 
 
 typedef double (*dg_gyrokinetic_vol_add_apardot_t)(const double *vmap, 
   const double q_, const double m_,
@@ -104,7 +104,8 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
   const double *vm = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx);
   const double *vm_sq = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx);
   const double *bmag = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx);
-  const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx);
+  // const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx);gk_geom->geo_int.bmag_nodal
+  const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bmag_inv, cidx);
   const double *b_i = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx);
   const double *dualcurlbhatoverB = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx);
   const double *rtg33inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx);
@@ -115,7 +116,7 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
     bmag, phi, dualcurlbhatoverB, rtg33inv, bioverJB, qIn, qRhsOut);
   // Add Apar contribution to volume term if needed.
   cfl += gyrokinetic->vol_add_apar_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
-    bmag, jacobtot_inv, b_i, phi, apar, qIn, qRhsOut);
+    bmag, jacobtot_inv, dualcurlbhatoverB, bioverJB, b_i, phi, apar, qIn, qRhsOut);
   // Add Apardot contribution to volume term if needed.
   cfl += gyrokinetic->vol_add_apardot_kernel( vm, gyrokinetic->charge, gyrokinetic->mass, 
     apardot, qIn, qRhsOut);
@@ -126,7 +127,7 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
 GKYL_CU_DH 
 static double 
 dg_gyrokinetic_add_apar_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
     const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   return 0.; 

From 3ffc48538b151975278431871c4aba1cc6a6d85a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 27 Feb 2026 08:41:31 -0500
Subject: [PATCH 109/181] add a coputation of the EM fiels at initial condition
 to write out Apardot and Apar at IC

---
 gyrokinetic/apps/gyrokinetic.c | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 09b07daca7..60be812ff9 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -926,10 +926,12 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
 
   // Compute the fields and apply BCs.
   struct gkyl_array *distf[app->num_species];
+  struct gkyl_array *distfdot[app->num_species];
   struct gkyl_array **bflux[app->num_species];
   struct gkyl_array *distf_neut[app->num_neut_species];
   for (int i=0; i<app->num_species; ++i) {
     distf[i] = app->species[i].f;
+    distfdot[i] = app->species[i].f1;
     bflux[i] = app->species[i].bflux.f;
   }
   for (int i=0; i<app->num_neut_species; ++i) {
@@ -956,6 +958,18 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
       // MF 2024/09/27/: Need the cast here for consistency. Fixing
       // this may require removing 'const' from a lot of places.
       gyrokinetic_calc_field_enabled(app, t0, (const struct gkyl_array **) distf, bflux);
+
+      // This does not seem to work well when using multiple MPI processes.
+      // It benign because this will be overwritten by the first RHS calls.
+      if (app->field->is_em) {
+        gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
+        gk_field_calc_apar_ic(app, app->field);
+        for (int i=0; i<app->num_species; ++i) {
+          struct gk_species *gk_s = &app->species[i];
+          gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+        }
+        gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
+      }
     else {
       if (app->field->info.init_field_profile == 0)
         // Read the field.

From 7fcc669444b61dd1b972ac18108f93bc713421f4 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 27 Feb 2026 08:54:33 -0500
Subject: [PATCH 110/181] set the kernel back to their original format (without
 zeroing out the problematic conf surf flux and vpar vol terms).

---
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c | 130 +++++++++---------
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c |  84 +++++------
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  84 +++++------
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |   4 +-
 4 files changed, 150 insertions(+), 152 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
index 100d9568df..d2f445577a 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -24,8 +24,6 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   double rdvpar2 = 2.0/dxv[3];
   double rdmu2 = 2.0/dxv[4];
 
-  double rdvpar2Sq = rdvpar2*rdvpar2;
-  double dvparSq = dxv[3]*dxv[3];
 
   const double *b_x = &b_i[0];
   const double *b_y = &b_i[8];
@@ -62,22 +60,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -106,22 +104,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
 
 
   out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -150,22 +148,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
 
 
   out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -194,22 +192,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[4])*rdx2)/vmap[1])/m_; 
-  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_z[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_z[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_z[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_x[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_z[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[4])*rdx2)/vmap[1])/m_; 
+  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
 
 
   out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index 6357925048..c9f2ca2ad9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -118,9 +118,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -133,9 +133,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -160,9 +160,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -175,9 +175,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -202,9 +202,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -217,9 +217,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -244,9 +244,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[4].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -259,9 +259,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -286,9 +286,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[5].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -301,9 +301,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -328,9 +328,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[6].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -343,9 +343,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -370,9 +370,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[7].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -385,9 +385,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index 638edf4c49..3dd040864b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -120,9 +120,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[1].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -136,9 +136,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -164,9 +164,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[2].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -180,9 +180,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -208,9 +208,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[3].mag_e_3; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -224,9 +224,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -252,9 +252,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[4].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -268,9 +268,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -296,9 +296,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[5].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -312,9 +312,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -340,9 +340,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[6].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -356,9 +356,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -384,9 +384,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   mag_e_3 = gkdgv[7].mag_e_3; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -400,9 +400,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 569574c836..4d84488a12 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -104,8 +104,8 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
   const double *vm = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap, vidx);
   const double *vm_sq = (const double*) gkyl_array_cfetch(gyrokinetic->vel_map->vmap_sq, vidx);
   const double *bmag = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_corn.bmag, cidx);
-  // const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx);gk_geom->geo_int.bmag_nodal
-  const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bmag_inv, cidx);
+  // The jacobtot_inv is not used anymore.
+  const double *jacobtot_inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.jacobtot_inv, cidx);
   const double *b_i = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.b_i, cidx);
   const double *dualcurlbhatoverB = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.dualcurlbhatoverB, cidx);
   const double *rtg33inv = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.rtg33inv, cidx);

From da74b08e524a17754c85cf11ea961888a6d400a4 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 27 Feb 2026 08:56:51 -0500
Subject: [PATCH 111/181] create a unit test for the helmholtz perp solver
 (Poisson perp with kSq). The test checks are not set up yet. The setup works
 well and convergence of order 2 is observed in various cases.

---
 gyrokinetic/unit/ctest_fem_helmholtz_perp.c | 715 ++++++++++++++++++++
 1 file changed, 715 insertions(+)
 create mode 100644 gyrokinetic/unit/ctest_fem_helmholtz_perp.c

diff --git a/gyrokinetic/unit/ctest_fem_helmholtz_perp.c b/gyrokinetic/unit/ctest_fem_helmholtz_perp.c
new file mode 100644
index 0000000000..25ffb0b0ed
--- /dev/null
+++ b/gyrokinetic/unit/ctest_fem_helmholtz_perp.c
@@ -0,0 +1,715 @@
+// Test the perpendicular FEM Helmholtz solver with a nonzero kSq,
+// essentially solving the Helmholtz equation:
+//   - nabla . (epsilon * nabla phi) + kSq * phi = rho
+// using the gkyl_fem_poisson_perp struct.
+//
+#include <acutest.h>
+#include <assert.h>
+#include <math.h>
+#include <stdlib.h>
+#include <gkyl_proj_on_basis.h>
+#include <gkyl_range.h>
+#include <gkyl_rect_decomp.h>
+#include <gkyl_rect_grid.h>
+#include <gkyl_array_rio.h>
+#include <gkyl_fem_poisson_perp.h>
+#include <gkyl_array_reduce.h>
+#include <gkyl_dg_bin_ops.h>
+
+static double error_L2norm(struct gkyl_rect_grid grid, struct gkyl_range range,
+  struct gkyl_basis basis, struct gkyl_array* field1, struct gkyl_array* field2)
+{
+  // Compute the L2 norm of the difference between 2 fields.
+  assert(field1->ncomp == field2->ncomp);
+  assert(field1->size == field2->size);
+
+  struct gkyl_array *diff = gkyl_array_new(GKYL_DOUBLE, field1->ncomp, field1->size);
+  gkyl_array_copy(diff, field1);
+  gkyl_array_accumulate(diff, -1.0, field2);
+
+  struct gkyl_array *l2_cell = gkyl_array_new(GKYL_DOUBLE, 1, field1->size);
+  gkyl_dg_calc_l2_range(basis, 0, l2_cell, 0, diff, range);
+  gkyl_array_scale_range(l2_cell, grid.cellVolume, &range);
+
+  double l2[1];
+  gkyl_array_reduce_range(l2, l2_cell, GKYL_SUM, &range);
+
+  gkyl_array_release(diff);
+  gkyl_array_release(l2_cell);
+  return sqrt(l2[0]);
+}
+
+static struct gkyl_array*
+mkarr(bool use_gpu, long nc, long size)
+{
+  // allocate array (filled with zeros)
+  struct gkyl_array* a = use_gpu? gkyl_array_cu_dev_new(GKYL_DOUBLE, nc, size)
+                                : gkyl_array_new(GKYL_DOUBLE, nc, size);
+  return a;
+}
+
+// We want to test the solution to the Helmholtz equation: -d^2(phi)/dx^2 - kSq*phi = rho
+
+static double ksquare() { return 20.0; }  // To get kSq everywhere in one place for easy editing.
+static double x_dirichletbc_lo() { return 0.0; } // to set BC values in one place for easy editing.
+static double x_dirichletbc_up() { return 0.5; } // Only effective for 2x problem.
+
+static double p1_func(double x)
+{
+  // This is a linear polynomial that is compatible with the BCs above. (assumes domain is [0,1])
+  double a = -ksquare()*x_dirichletbc_lo();
+  double b = -ksquare()*x_dirichletbc_up();
+  return (b - a)*x + a;
+}
+
+static void evalFunc_ksquare(double t, const double *xn, double* restrict fout, void *ctx) 
+{ 
+  double x = xn[0], y = xn[1], z = xn[2];
+  fout[0] = ksquare();
+  // fout[0] *= cos(2*M_PI*x); 
+  // fout[0] *= exp(4*M_PI*y); 
+  // fout[0] *= sin(z)+2;  
+  // noise:
+  fout[0] *= 1. + 1e-7*cos(2*M_PI*x)*exp(4*M_PI*y)*(sin(z)+2);
+}
+
+// RHS: rho(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m sin(2*pi*m*x)
+void evalFunc_rhs_dirichletx_2x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  // These values have to match those in the test below.
+  double bmn[] = {1.5, 1.5, -0.5};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double b = bmn[m-1];
+    double t2 = b*sin(2*M_PI*m*x);
+    fout[0] += t2;
+  }
+  double kz = 1.;
+  fout[0] *= (1.+kz*z+0.5*pow(z,2));
+  
+  // fout[0] *= 0.0; // To test exact integration (linear polynomial)
+  fout[0] += p1_func(x);
+}
+// Solution: phi(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m*sin(2*pi*m*x)/( (2*pi*m)^2 - kSq )
+void evalFunc_sol_dirichletx_2x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  // These values have to match those in the test below.
+  double bmn[] = {1.5, 1.5, -0.5};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double b = bmn[m-1];
+    double kx = 2*M_PI*m;
+    double t2 = b*sin(kx*x)/(kx*kx - ksquare());
+    fout[0] += t2;
+  }
+  double kz = 1.;
+  fout[0] *= (1.+kz*z+0.5*pow(z,2));
+  
+  // fout[0] *= 0.0; // To test exact integration (linear polynomial)
+  fout[0] += -p1_func(x)/ksquare();
+}
+// Periodic case (This is not suitable for convergence test as it leaves a constant offset in the solution)
+void evalFunc_rhs_periodicx_2x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  // These values have to match those in the test below.
+  double gxx = 1.0;
+  double amn[] = {-0.6, -2., 1.5};
+  double bmn[] = { 1.,  0.7, -0.3};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double a = amn[m-1];
+    double b = bmn[m-1];
+    double kx = 2*M_PI*m;
+    double t1 = a*cos(kx*x);
+    double t2 = b*sin(kx*x);
+    fout[0] += t1+t2;
+  }
+  double kz = 0.;
+  fout[0] *= (1.+kz*z);
+
+}
+void evalFunc_sol_periodicx_2x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  // These values have to match those in the test below.
+  double amn[] = {-0.6, -2., 1.5};
+  double bmn[] = { 1.,  0.7, -0.3};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double a = amn[m-1];
+    double b = bmn[m-1];
+    double kx = 2*M_PI*m;
+    double t1 = a*cos(kx*x)/(kx*kx - ksquare());
+    double t2 = b*sin(kx*x)/(kx*kx - ksquare());
+    fout[0] += t1+t2;
+  }
+  double kz = 0.;
+  fout[0] *= (1.+kz*z);
+}
+
+// 3x cases
+// RHS: rho(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m sin(2*pi*m*x)
+void evalFunc_rhs_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  // These values have to match those in the test below.
+  double bmn[] = {0.2, 0.5, -0.5};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double b = bmn[m-1];
+    double kx = 2*M_PI*m;
+    double ky = 2*M_PI;
+    double t2 = b*sin(kx*x) * sin(ky*y);
+    fout[0] += t2;
+  }
+  double kz = 1.;
+ fout[0] *= (1.+kz*z+0.5*pow(z,2));
+}
+// Solution: phi(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m*sin(2*pi*m*x)/( (2*pi*m)^2 - kSq )
+void evalFunc_sol_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  // These values have to match those in the test below.
+  double bmn[] = {0.2, 0.5, -0.5};
+  fout[0] = 0.;
+  for (int m=1; m<3; m++) {
+    double b = bmn[m-1];
+    double kx = 2*M_PI*m;
+    double ky = 2*M_PI;
+    double t2 = b*sin(kx*x) * sin(ky*y)/(kx*kx + ky*ky - ksquare());
+    fout[0] += t2;
+  }
+  double kz = 1.;
+ fout[0] *= (1.+kz*z+0.5*pow(z,2));
+}
+
+double trig_func(double x, double y, bool laplacian)
+{
+  double amn[] = {0.0, -1., 0., -0.0};
+  double out = 0.;
+  for (int m=0; m<4; m++) {
+    double a = amn[m];
+    double kx = M_PI*m;
+    double ky = 2*M_PI*m*0;
+    double t2 = a*cos(ky*y);
+    if (m > 0)
+      t2 *= sin(kx*x);
+
+    if (laplacian) {
+      t2 *= -(kx*kx + ky*ky);
+    }
+    out += t2;
+  }
+  return out;
+}
+
+double z_envelope(double z)
+{
+  double kz = 1.;
+  return 1.0;
+}
+
+void evalFunc_sol_dirichletx_periodicy_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  fout[0] = trig_func(x,y,false);
+  fout[0] *= z_envelope(z);
+}
+
+// Periodic case (This is not suitable for convergence test as it leaves a constant offset in the solution)
+void evalFunc_rhs_dirichletx_periodicy_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  double kSq[1];
+  evalFunc_ksquare(t, xn, kSq, ctx);
+  double fsol[1];
+  evalFunc_sol_dirichletx_periodicy_3x(t, xn, fsol, ctx);
+  fout[0] = -trig_func(x,y,true)*z_envelope(z) - kSq[0]*fsol[0];
+}
+
+void
+test_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson_bc bcs, bool use_gpu)
+{
+  double epsilon_0 = 1.0;
+  double kSq = ksquare();  // Helmholtz wave number squared.
+
+  double lower[] = {0.0, -M_PI}, upper[] = {1.0, M_PI};
+  int dim = sizeof(lower)/sizeof(lower[0]);
+  int dim_perp = dim - 1;
+
+  // Grids.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, dim, lower, upper, cells);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, dim, poly_order);
+
+  int ghost[] = { 1, 1 };
+  struct gkyl_range localRange, localRange_ext; // local, local-ext ranges.
+  gkyl_create_grid_ranges(&grid, ghost, &localRange_ext, &localRange);
+
+  // Projection updater for DG field.
+  gkyl_proj_on_basis *projob = NULL, *projob_sol = NULL;
+  if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET)) {
+    projob = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_rhs_dirichletx_2x, NULL);
+    projob_sol = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_sol_dirichletx_2x, NULL);
+  } else if ((bcs.lo_type[0] == GKYL_POISSON_PERIODIC && bcs.up_type[0] == GKYL_POISSON_PERIODIC)) {
+    projob = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_rhs_periodicx_2x, NULL);
+    projob_sol = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_sol_periodicx_2x, NULL);
+  }
+
+  // Create DG field we wish to make continuous.
+  struct gkyl_array *rho = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Create array holding continuous field we'll compute.
+  struct gkyl_array *phi = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Create DG field for permittivity tensor (1 component for 1D perp).
+  int epsnum = dim_perp + (int)ceil((pow(3., dim_perp - 1) - dim_perp) / 2);
+  struct gkyl_array *eps = mkarr(use_gpu, epsnum * basis.num_basis, localRange_ext.volume);
+  // Create DG field for kSq.
+  struct gkyl_array *kSqFld = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Analytic solution.
+  struct gkyl_array *phisol_ho = mkarr(false, basis.num_basis, localRange_ext.volume);
+  // Device copies:
+  struct gkyl_array *rho_ho, *phi_ho;
+  if (use_gpu) {
+    rho_ho = mkarr(false, rho->ncomp, rho->size);
+    phi_ho = mkarr(false, phi->ncomp, phi->size);
+  } else {
+    rho_ho = gkyl_array_acquire(rho);
+    phi_ho = gkyl_array_acquire(phi);
+  }
+
+  // Project RHS charge density on basis.
+  gkyl_proj_on_basis_advance(projob, 0.0, &localRange, rho_ho);
+  gkyl_array_copy(rho, rho_ho);
+
+  // Project the permittivity onto the basis.
+  double dg0norm = pow(sqrt(2.), dim);
+  gkyl_array_shiftc(eps, epsilon_0 * dg0norm, 0 * basis.num_basis);
+
+  // Project kSq onto the basis.
+  gkyl_array_shiftc(kSqFld, kSq * dg0norm, 0);
+
+  // Project the analytic solution.
+  gkyl_proj_on_basis_advance(projob_sol, 0.0, &localRange, phisol_ho);
+
+  // FEM Helmholtz solver.
+  struct gkyl_fem_poisson_perp *poisson = gkyl_fem_poisson_perp_new(&localRange, &grid, basis,
+    &bcs, eps, kSqFld, use_gpu);
+
+  // Set the RHS source.
+  gkyl_fem_poisson_perp_set_rhs(poisson, rho);
+
+  // Solve the problem.
+  gkyl_fem_poisson_perp_solve(poisson, phi);
+  gkyl_array_copy(phi_ho, phi);
+
+#ifdef GKYL_HAVE_CUDA
+  if (use_gpu) cudaDeviceSynchronize();
+#endif
+
+  // Write data to text file for visualization (Python notebook can read this)
+  FILE *fp = fopen("helmholtz_2x_results.txt", "w");
+  if (fp) {
+    fprintf(fp, "# x z phi_numerical phi_analytical\n");
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &localRange);
+    while (gkyl_range_iter_next(&iter)) {
+      double xc[2];
+      gkyl_rect_grid_cell_center(&grid, iter.idx, xc);
+      long loc = gkyl_range_idx(&localRange, iter.idx);
+      const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+      const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+      // Write cell center coordinates and the 0th basis coefficient (cell average)
+      fprintf(fp, "%.16e %.16e %.16e %.16e\n", xc[0], xc[1], phi_p[0]/dg0norm, phisol_p[0]/dg0norm);
+    }
+    fclose(fp);
+  }
+
+  // Write parameters file for visualization.
+  fp = fopen("helmholtz_2x_params.txt", "w");
+  if (fp) {
+    fprintf(fp, "lower: %.16e %.16e\n", lower[0], lower[1]);
+    fprintf(fp, "upper: %.16e %.16e\n", upper[0], upper[1]);
+    fprintf(fp, "cells: %d %d\n", cells[0], cells[1]);
+    fprintf(fp, "poly_order: %d\n", poly_order);
+    fprintf(fp, "kSq: %.16e\n", kSq);
+    fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
+    fclose(fp);
+  }
+
+  // Write parameters file for visualization.
+  fp = fopen("helmholtz_2x_params.txt", "w");
+  if (fp) {
+    fprintf(fp, "lower: %.16e %.16e\n", lower[0], lower[1]);
+    fprintf(fp, "upper: %.16e %.16e\n", upper[0], upper[1]);
+    fprintf(fp, "cells: %d %d\n", cells[0], cells[1]);
+    fprintf(fp, "poly_order: %d\n", poly_order);
+    fprintf(fp, "kSq: %.16e\n", kSq);
+    fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
+    fclose(fp);
+  }
+
+  double errL2 = error_L2norm(grid, localRange, basis, phi_ho, phisol_ho);
+  printf("\nerror L2 norm = %g\n",errL2);
+
+  // Compare solution to analytic result.
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &localRange);
+  while (gkyl_range_iter_next(&iter)) {
+    long loc = gkyl_range_idx(&localRange, iter.idx);
+    const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+    const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+    for (int m = 0; m < basis.num_basis; m++) {
+      // TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
+      // TEST_MSG("Expected: %.13e in cell (%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1]);
+      // TEST_MSG("Produced: %.13e", phi_p[m]);
+    }
+  }
+
+  gkyl_fem_poisson_perp_release(poisson);
+  gkyl_proj_on_basis_release(projob);
+  gkyl_proj_on_basis_release(projob_sol);
+  gkyl_array_release(rho);
+  gkyl_array_release(eps);
+  gkyl_array_release(kSqFld);
+  gkyl_array_release(phi);
+  gkyl_array_release(phisol_ho);
+  gkyl_array_release(rho_ho);
+  gkyl_array_release(phi_ho);
+}
+
+void
+test_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisson_bc bcs, bool use_gpu)
+{
+  double epsilon_0 = 1.0;
+  double kSq = ksquare();  // Helmholtz wave number squared.
+
+  double lower[] = {0.0, 0.0, -M_PI}, upper[] = {1.0, 1.0, M_PI};
+  int dim = sizeof(lower)/sizeof(lower[0]);
+  int dim_perp = dim - 1;
+
+  // Grids.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, dim, lower, upper, cells);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, dim, poly_order);
+
+  int ghost[] = { 1, 1, 1 };
+  struct gkyl_range localRange, localRange_ext; // local, local-ext ranges.
+  gkyl_create_grid_ranges(&grid, ghost, &localRange_ext, &localRange);
+
+  // Projection updater for DG field.
+  gkyl_proj_on_basis *projob = NULL, *projob_sol = NULL, *projob_kSq = NULL;
+  if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
+      (bcs.lo_type[1] == GKYL_POISSON_DIRICHLET && bcs.up_type[1] == GKYL_POISSON_DIRICHLET)) {
+    projob = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_rhs_dirichletx_dirichlety_3x, NULL);
+    projob_sol = gkyl_proj_on_basis_new(&grid, &basis,
+      2 * (poly_order + 1), 1, evalFunc_sol_dirichletx_dirichlety_3x, NULL);
+  } else if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
+             (bcs.lo_type[1] == GKYL_POISSON_PERIODIC && bcs.up_type[1] == GKYL_POISSON_PERIODIC)) {
+    projob = gkyl_proj_on_basis_new(&grid, &basis,
+      poly_order + 1, 1, evalFunc_rhs_dirichletx_periodicy_3x, NULL);
+    projob_sol = gkyl_proj_on_basis_new(&grid, &basis,
+      2 * (poly_order + 1), 1, evalFunc_sol_dirichletx_periodicy_3x, NULL);
+  }
+  projob_kSq = gkyl_proj_on_basis_new(&grid, &basis, 
+    2 * (poly_order + 1), 1, evalFunc_ksquare, NULL);
+
+  // Create DG field we wish to make continuous.
+  struct gkyl_array *rho = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Create array holding continuous field we'll compute.
+  struct gkyl_array *phi = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Create DG field for permittivity tensor.
+  int epsnum = dim_perp + (int)ceil((pow(3., dim_perp - 1) - dim_perp) / 2);
+  struct gkyl_array *eps = mkarr(use_gpu, epsnum * basis.num_basis, localRange_ext.volume);
+  // Create DG field for kSq.
+  struct gkyl_array *kSqFld = mkarr(use_gpu, basis.num_basis, localRange_ext.volume);
+  // Analytic solution.
+  struct gkyl_array *phisol_ho = mkarr(false, basis.num_basis, localRange_ext.volume);
+  // Device copies:
+  struct gkyl_array *rho_ho, *phi_ho;
+  if (use_gpu) {
+    rho_ho = mkarr(false, rho->ncomp, rho->size);
+    phi_ho = mkarr(false, phi->ncomp, phi->size);
+  } else {
+    rho_ho = gkyl_array_acquire(rho);
+    phi_ho = gkyl_array_acquire(phi);
+  }
+
+  // Project RHS charge density on basis.
+  gkyl_proj_on_basis_advance(projob, 0.0, &localRange, rho_ho);
+  gkyl_array_copy(rho, rho_ho);
+
+  // Project the permittivity onto the basis.
+  double dg0norm = pow(sqrt(2.), dim);
+  gkyl_array_shiftc(eps, epsilon_0 * dg0norm, 0 * basis.num_basis);
+  gkyl_array_shiftc(eps, 0.0 * dg0norm, 1 * basis.num_basis);           // gxy = 0
+  gkyl_array_shiftc(eps, epsilon_0 * dg0norm, 2 * basis.num_basis);
+
+  // Project kSq onto the basis.
+  // gkyl_array_shiftc(kSqFld, kSq * dg0norm, 0);
+  gkyl_proj_on_basis_advance(projob_kSq, 0.0, &localRange, kSqFld);
+
+  // Project the analytic solution.
+  gkyl_proj_on_basis_advance(projob_sol, 0.0, &localRange, phisol_ho);
+
+  // FEM Helmholtz solver.
+  struct gkyl_fem_poisson_perp *poisson = gkyl_fem_poisson_perp_new(&localRange, &grid, basis,
+    &bcs, eps, kSqFld, use_gpu);
+
+  // Set the RHS source.
+  gkyl_fem_poisson_perp_set_rhs(poisson, rho);
+
+  // Solve the problem.
+  gkyl_fem_poisson_perp_solve(poisson, phi);
+  gkyl_array_copy(phi_ho, phi);
+
+#ifdef GKYL_HAVE_CUDA
+  if (use_gpu) cudaDeviceSynchronize();
+#endif
+
+  // Write data to text file for visualization (Python notebook can read this)
+  FILE *fp = fopen("helmholtz_3x_results.txt", "w");
+  if (fp) {
+    fprintf(fp, "# x y z phi_numerical phi_analytical\n");
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &localRange);
+    while (gkyl_range_iter_next(&iter)) {
+      double xc[3];
+      gkyl_rect_grid_cell_center(&grid, iter.idx, xc);
+      long loc = gkyl_range_idx(&localRange, iter.idx);
+      const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+      const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+      // Write cell center coordinates and the 0th basis coefficient (cell average)
+      fprintf(fp, "%.16e %.16e %.16e %.16e %.16e\n", xc[0], xc[1], xc[2], phi_p[0]/dg0norm, phisol_p[0]/dg0norm);
+    }
+    fclose(fp);
+  }
+
+  // Write parameters file for visualization.
+  fp = fopen("helmholtz_3x_params.txt", "w");
+  if (fp) {
+    fprintf(fp, "lower: %.16e %.16e %.16e\n", lower[0], lower[1], lower[2]);
+    fprintf(fp, "upper: %.16e %.16e %.16e\n", upper[0], upper[1], upper[2]);
+    fprintf(fp, "cells: %d %d %d\n", cells[0], cells[1], cells[2]);
+    fprintf(fp, "poly_order: %d\n", poly_order);
+    fprintf(fp, "kSq: %.16e\n", kSq);
+    fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
+    fclose(fp);
+  }
+
+  double errL2 = error_L2norm(grid, localRange, basis, phi_ho, phisol_ho);
+  printf("\nerror L2 norm = %g\n",errL2);
+
+  // Compare solution to analytic result.
+  if (poly_order == 1) {
+    if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
+        (bcs.lo_type[1] == GKYL_POISSON_DIRICHLET && bcs.up_type[1] == GKYL_POISSON_DIRICHLET)) {
+      struct gkyl_range_iter iter;
+      gkyl_range_iter_init(&iter, &localRange);
+      while (gkyl_range_iter_next(&iter)) {
+        long loc = gkyl_range_idx(&localRange, iter.idx);
+        const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+        const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+        for (int m = 0; m < basis.num_basis; m++) {
+          TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
+          TEST_MSG("Expected: %.13e in cell (%d,%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1], iter.idx[2]);
+          TEST_MSG("Produced: %.13e", phi_p[m]);
+        }
+      }
+    } else if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
+               (bcs.lo_type[1] == GKYL_POISSON_PERIODIC && bcs.up_type[1] == GKYL_POISSON_PERIODIC)) {
+      struct gkyl_range_iter iter;
+      gkyl_range_iter_init(&iter, &localRange);
+      while (gkyl_range_iter_next(&iter)) {
+        long loc = gkyl_range_idx(&localRange, iter.idx);
+        const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+        const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+        for (int m = 0; m < basis.num_basis; m++) {
+          TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
+          TEST_MSG("Expected: %.13e in cell (%d,%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1], iter.idx[2]);
+          TEST_MSG("Produced: %.13e", phi_p[m]);
+        }
+      }
+    } else {
+      TEST_CHECK( gkyl_compare(1., 2., 1e-10) );
+      TEST_MSG("This BC combination is not available");
+    }
+  } else {
+    TEST_CHECK( gkyl_compare(1., 2., 1e-10) );
+    TEST_MSG("This poly_order is not available");
+  }
+
+  gkyl_fem_poisson_perp_release(poisson);
+  gkyl_proj_on_basis_release(projob);
+  gkyl_proj_on_basis_release(projob_sol);
+  gkyl_proj_on_basis_release(projob_kSq);
+  gkyl_array_release(rho);
+  gkyl_array_release(eps);
+  gkyl_array_release(kSqFld);
+  gkyl_array_release(phi);
+  gkyl_array_release(phisol_ho);
+  gkyl_array_release(rho_ho);
+  gkyl_array_release(phi_ho);
+}
+
+// 2x test wrappers
+void test_2x_p1_dirichletx() {
+  // Read grid resolution from environment variables, or use defaults
+  int nx = 32, nz = 48;
+  char *env_nx = getenv("TEST_NX");
+  char *env_nz = getenv("TEST_NZ");
+  if (env_nx) nx = atoi(env_nx);
+  if (env_nz) nz = atoi(env_nz);
+  
+  int cells[] = {nx, nz};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = x_dirichletbc_lo();
+  bc_tv.up_value[0].v[0] = x_dirichletbc_up();
+  test_fem_helmholtz_perp_2x(1, cells, bc_tv, false);
+}
+
+void test_2x_p1_periodicx() {
+  // Read grid resolution from environment variables, or use defaults
+  int nx = 32, nz = 48;
+  char *env_nx = getenv("TEST_NX");
+  char *env_nz = getenv("TEST_NZ");
+  if (env_nx) nx = atoi(env_nx);
+  if (env_nz) nz = atoi(env_nz);
+  
+  int cells[] = {nx, nz};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_PERIODIC;
+  bc_tv.up_type[0] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.;
+  bc_tv.up_value[0].v[0] = 0.;
+  test_fem_helmholtz_perp_2x(1, cells, bc_tv, false);
+}
+
+
+// 3x test wrappers
+void test_3x_p1_dirichletx_dirichlety() {
+  // Read grid resolution from environment variables, or use defaults
+  int nx = 32, ny = 16, nz = 2;
+  char *env_nx = getenv("TEST_NX");
+  char *env_ny = getenv("TEST_NY");
+  char *env_nz = getenv("TEST_NZ");
+  if (env_nx) nx = atoi(env_nx);
+  if (env_ny) ny = atoi(env_ny);
+  if (env_nz) nz = atoi(env_nz);
+  
+  int cells[] = {nx, ny, nz};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[1] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = 0.0;
+  bc_tv.up_value[0].v[0] = 0.0;
+  bc_tv.lo_value[1].v[0] = 0.0;
+  bc_tv.up_value[1].v[0] = 0.0;
+  test_fem_helmholtz_perp_3x(1, cells, bc_tv, false);
+}
+
+void test_3x_p1_dirichletx_periodicy() {
+  // Read grid resolution from environment variables, or use defaults
+  int nx = 32, ny = 16, nz = 2;
+  char *env_nx = getenv("TEST_NX");
+  char *env_ny = getenv("TEST_NY");
+  char *env_nz = getenv("TEST_NZ");
+  if (env_nx) nx = atoi(env_nx);
+  if (env_ny) ny = atoi(env_ny);
+  if (env_nz) nz = atoi(env_nz);
+  
+  int cells[] = {nx, ny, nz};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_PERIODIC;
+  bc_tv.up_type[1] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.0;
+  bc_tv.up_value[0].v[0] = 0.0;
+  bc_tv.lo_value[1].v[0] = 0.;
+  bc_tv.up_value[1].v[0] = 0.;
+  test_fem_helmholtz_perp_3x(1, cells, bc_tv, false);
+}
+
+#ifdef GKYL_HAVE_CUDA
+void gpu_test_2x_p1_dirichletx() {
+  int cells[] = {8, 8};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = 0.;
+  bc_tv.up_value[0].v[0] = 0.;
+  test_fem_helmholtz_perp_2x(1, cells, bc_tv, true);
+}
+
+void gpu_test_2x_p1_periodicx() {
+  int cells[] = {8, 8};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_PERIODIC;
+  bc_tv.up_type[0] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.;
+  bc_tv.up_value[0].v[0] = 0.;
+  test_fem_helmholtz_perp_2x(1, cells, bc_tv, true);
+}
+
+void gpu_test_3x_p1_dirichletx_dirichlety() {
+  int cells[] = {4, 4, 4};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[1] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = 0.;
+  bc_tv.up_value[0].v[0] = 0.;
+  bc_tv.lo_value[1].v[0] = 0.;
+  bc_tv.up_value[1].v[0] = 0.;
+  test_fem_helmholtz_perp_3x(1, cells, bc_tv, true);
+}
+
+void gpu_test_3x_p1_dirichletx_periodicy() {
+  int cells[] = {4, 4, 4};
+  struct gkyl_poisson_bc bc_tv;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_PERIODIC;
+  bc_tv.up_type[1] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.;
+  bc_tv.up_value[0].v[0] = 0.;
+  test_fem_helmholtz_perp_3x(1, cells, bc_tv, true);
+}
+#endif
+
+TEST_LIST = {
+  // 2x tests
+  { "test_2x_p1_dirichletx", test_2x_p1_dirichletx },
+  { "test_2x_p1_periodicx", test_2x_p1_periodicx },
+
+  // 3x tests
+  { "test_3x_p1_dirichletx_dirichlety", test_3x_p1_dirichletx_dirichlety },
+  { "test_3x_p1_dirichletx_periodicy", test_3x_p1_dirichletx_periodicy },
+
+#ifdef GKYL_HAVE_CUDA
+  { "gpu_test_2x_p1_dirichletx", gpu_test_2x_p1_dirichletx },
+  { "gpu_test_2x_p1_periodicx", gpu_test_2x_p1_periodicx },
+  { "gpu_test_3x_p1_dirichletx_dirichlety", gpu_test_3x_p1_dirichletx_dirichlety },
+  { "gpu_test_3x_p1_dirichletx_periodicy", gpu_test_3x_p1_dirichletx_periodicy },
+#endif
+  { NULL, NULL },
+};

From 29e0ae41ce75281f41eefd03d42a0b2914c14197 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 2 Mar 2026 05:58:34 -0800
Subject: [PATCH 112/181] manual fix to the previous merge with main, this
 branch compiles

---
 gyrokinetic/apps/gk_species.c               | 8 ++++----
 gyrokinetic/apps/gk_species_collisionless.c | 2 +-
 gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c  | 2 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h | 2 +-
 4 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index b8c318f55b..ea7e8b6531 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -2040,9 +2040,9 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *gks
     gkyl_deflated_fem_poisson_release(gks->flr_op);
   }
 
-  gkyl_array_release(s->gyro_apar);
-  gkyl_array_release(s->gyro_apardot);
-  gk_species_moment_release(app, &s->m1);
+  gkyl_array_release(gks->gyro_apar);
+  gkyl_array_release(gks->gyro_apardot);
+  gk_species_moment_release(app, &gks->m1);
 
-  s->release_func(app, s);
+  gks->release_func(app, gks);
 }
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index b0cfbcf44b..a90773e655 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -206,7 +206,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
         app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
       gkcls->slvr_em_star = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
         &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gks->info.skip_cell_threshold, gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
+        gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
         &aux_inp, app->use_gpu);
       // Methods chosen at runtime.
       gkcls->flux_func_star = gk_species_collisionless_flux_star_enabled; // ES + Apar.
diff --git a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
index 6eeeefe4cb..2e35daa53d 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
@@ -400,7 +400,7 @@ int main(int argc, char **argv)
     .basis_type = app_args.basis_type,
 
     .geometry = {
-      .geometry_id = GKYL_MAPC2P,
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
       .mapc2p = mapc2p, // mapping of computational to physical space
       .c2p_ctx = &ctx,
       .bfield_func = bfield_func, // magnetic field
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 7fca3cc97f..39ceb764fa 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -389,7 +389,7 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
  */
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
-  const double charge, const double mass, double skip_if_smaller_than, enum gkyl_gk_collisionless_type collless_type,
+  const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
   const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**

From 8f5118ee27fb1f66ffb9a1f8e72b5e4c3e3b0a57 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 2 Mar 2026 06:47:08 -0800
Subject: [PATCH 113/181] adapt the em regression test with the new mac2p enum

---
 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c | 2 +-
 gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
index 74e5e59bbe..7893e230c4 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
@@ -405,7 +405,7 @@ int main(int argc, char **argv)
     .basis_type = app_args.basis_type,
 
     .geometry = {
-      .geometry_id = GKYL_MAPC2P,
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
       .world = {0., 0.},
       .mapc2p = mapc2p, // mapping of computational to physical space
       .c2p_ctx = &ctx,
diff --git a/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
index 4f6ac2d389..b22a61c190 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
@@ -410,7 +410,7 @@ int main(int argc, char **argv)
     .basis_type = app_args.basis_type,
 
     .geometry = {
-      .geometry_id = GKYL_MAPC2P,
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
       .mapc2p = mapc2p, // mapping of computational to physical space
       .c2p_ctx = &ctx,
       .bfield_func = bfield_func, // magnetic field

From 69c49b33fee272e731ae02dca9dac50bf61da6e3 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 2 Mar 2026 06:47:30 -0800
Subject: [PATCH 114/181] add a KBM regression test, the branch works fine with
 the latest main + new makefile merge

---
 gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c | 572 +++++++++++++++++++++++++++
 1 file changed, 572 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c b/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c
new file mode 100644
index 0000000000..f77f672128
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c
@@ -0,0 +1,572 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  double mu0;
+
+  // Geometry and magnetic field.
+  double R; // Major radius of the simulation box [m].
+  double a; // Minor radius at outboard midplane [m].
+  double r; // Minor radius of the simulation box [m].
+  double B; // Magnetic field magnitude in the simulation box [T].
+
+  double kperp;  // Perpendicular wavenumber.
+  double beta_hat; // Plasma beta parameter.
+
+  // Plasma parameters.
+  double me;  double qe;
+  double mi;  double qi;
+  double n0;  double Te0;  double Ti0; 
+
+  // Initial profile parameters.
+  double r0, wTi, wTe, wN, kTi, kTe, kN;
+  double L_n, L_Te, L_Ti;
+
+  // Grid parameters.
+  int Nx, Ny, Nz, Nvpar, Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double x_min, y_min, z_min;
+  double x_max, y_max, z_max;
+  double vpar_max_elc, mu_max_elc;
+  double vpar_max_ion, mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Ion initial conditions.
+void density_init_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xn[0];
+  double y = xn[1];
+  double z = xn[2];
+
+  double kN = app->kN;
+  double wN = app->wN;
+  double a = app->a;
+  double Lref = app->R;
+  double r0 = app->r0;
+
+  fout[0] = app->n0;// * exp(-kN * wN * a/Lref * tanh((x-r0)/(wN * a)));
+}
+void upar_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_ion(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xn[0];
+  double y = xn[1];
+  double z = xn[2];
+
+  double kTi = app->kTi;
+  double wTi = app->wTi;
+  double a = app->a;
+  double Lref = app->R;
+  double r0 = app->r0;
+
+  fout[0] = app->Ti0 ;//* exp(-kTi * wTi * a/Lref * tanh((x-r0)/(wTi * a)));
+}
+
+// Electron initial conditions.
+void density_init_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xn[0];
+  double y = xn[1];
+  double z = xn[2];
+
+  double kN = app->kN;
+  double wN = app->wN;
+  double a = app->a;
+  double Lref = app->R;
+  double r0 = app->r0;
+
+  fout[0] = app->n0;// * exp(-kN * wN * a/Lref * tanh((x-r0)/(wN * a)));
+}
+void upar_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 0.0;
+}
+void temp_elc(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xn[0];
+  double y = xn[1];
+  double z = xn[2];
+
+  double kTe = app->kTe;
+  double wTe = app->wTe;
+  double a = app->a;
+  double Lref = app->R;
+  double r0 = app->r0;
+
+  fout[0] = app->Te0;// * exp(-kTe * wTe * a/Lref * tanh((x-r0)/(wTe * a)));
+}
+
+// Slab magnetic equilibrium.
+static inline void
+mapc2p(double t, const double* xc, double* GKYL_RESTRICT xp, void* ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xc[0], y = xc[1], z = xc[2];
+  xp[0] = x; xp[1] = y; xp[2] = z;
+}
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double x = xc[0], y = xc[1], z = xc[2];
+  fout[0] = 0.0;
+  fout[1] = 0.0;
+  fout[2] = app->B*app->R/(app->R + x);
+}
+
+void mapc2p_vel_elc(double t, const double *vc, double* GKYL_RESTRICT vp, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double vpar_max_elc = app->vpar_max_elc;
+  double mu_max_elc = app->mu_max_elc;
+
+  double cvpar = vc[0], cmu = vc[1];
+  // Linear map up to vpar_max/2, then quadratic.
+  if (fabs(cvpar) <= 0.5)
+    vp[0] = vpar_max_elc*cvpar;
+  else if (cvpar < -0.5)
+    vp[0] = -vpar_max_elc*2.0*pow(cvpar,2);
+  else
+    vp[0] =  vpar_max_elc*2.0*pow(cvpar,2);
+
+  // Quadratic map in mu.
+  vp[1] = mu_max_elc*pow(cmu,2);
+}
+
+void mapc2p_vel_ion(double t, const double *vc, double* GKYL_RESTRICT vp, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double vpar_max_ion = app->vpar_max_ion;
+  double mu_max_ion = app->mu_max_ion;
+
+  double cvpar = vc[0], cmu = vc[1];
+  // Linear map up to vpar_max/2, then quadratic.
+  if (fabs(cvpar) <= 0.5)
+    vp[0] = vpar_max_ion*cvpar;
+  else if (cvpar < -0.5)
+    vp[0] = -vpar_max_ion*2.0*pow(cvpar,2);
+  else
+    vp[0] =  vpar_max_ion*2.0*pow(cvpar,2);
+
+  // Quadratic map in mu.
+  vp[1] = mu_max_ion*pow(cmu,2);
+}
+
+
+void
+write_ctx_to_json(const struct gk_app_ctx *ctx)
+{
+  FILE *fp = fopen("ctx.json", "w");
+  if (!fp) {
+    perror("Error opening file for writing context");
+    return;
+  }
+
+  fprintf(fp, "{\n");
+  fprintf(fp, "  \"cdim\": %d,\n", ctx->cdim);
+  fprintf(fp, "  \"vdim\": %d,\n", ctx->vdim);
+  fprintf(fp, "  \"mu0\": %e,\n", ctx->mu0);
+  fprintf(fp, "  \"R\": %e,\n", ctx->R);
+  fprintf(fp, "  \"a\": %e,\n", ctx->a);
+  fprintf(fp, "  \"r\": %e,\n", ctx->r);
+  fprintf(fp, "  \"B\": %e,\n", ctx->B);
+  fprintf(fp, "  \"x_min\": %e,\n", ctx->x_min);
+  fprintf(fp, "  \"x_max\": %e,\n", ctx->x_max);
+  fprintf(fp, "  \"y_min\": %e,\n", ctx->y_min);
+  fprintf(fp, "  \"y_max\": %e,\n", ctx->y_max);
+  fprintf(fp, "  \"z_min\": %e,\n", ctx->z_min);
+  fprintf(fp, "  \"z_max\": %e,\n", ctx->z_max);
+  fprintf(fp, "  \"kperp\": %e,\n", ctx->kperp);
+  fprintf(fp, "  \"beta_hat\": %e,\n", ctx->beta_hat);
+  fprintf(fp, "  \"me\": %e,\n", ctx->me);
+  fprintf(fp, "  \"qe\": %e,\n", ctx->qe);
+  fprintf(fp, "  \"mi\": %e,\n", ctx->mi);
+  fprintf(fp, "  \"qi\": %e,\n", ctx->qi);
+  fprintf(fp, "  \"n0\": %e,\n", ctx->n0);
+  fprintf(fp, "  \"Te0\": %e,\n", ctx->Te0);
+  fprintf(fp, "  \"Ti0\": %e,\n", ctx->Ti0);
+  fprintf(fp, "  \"r0\": %e,\n", ctx->r0);
+  fprintf(fp, "  \"wTi\": %e,\n", ctx->wTi);
+  fprintf(fp, "  \"wTe\": %e,\n", ctx->wTe);
+  fprintf(fp, "  \"wN\": %e,\n", ctx->wN);
+  fprintf(fp, "  \"kTi\": %e,\n", ctx->kTi);
+  fprintf(fp, "  \"kTe\": %e,\n", ctx->kTe);
+  fprintf(fp, "  \"kN\": %e,\n", ctx->kN);
+  fprintf(fp, "  \"L_n\": %e,\n", ctx->L_n);
+  fprintf(fp, "  \"L_Te\": %e,\n", ctx->L_Te);
+  fprintf(fp, "  \"L_Ti\": %e,\n", ctx->L_Ti);
+  fprintf(fp, "  \"Nx\": %d,\n", ctx->Nx);
+  fprintf(fp, "  \"Ny\": %d,\n", ctx->Ny);
+  fprintf(fp, "  \"Nz\": %d,\n", ctx->Nz);
+  fprintf(fp, "  \"Nvpar\": %d,\n", ctx->Nvpar);
+  fprintf(fp, "  \"Nmu\": %d,\n", ctx->Nmu);
+  fprintf(fp, "  \"poly_order\": %d,\n", ctx->poly_order);
+  fprintf(fp, "  \"vpar_max_elc\": %e,\n", ctx->vpar_max_elc);
+  fprintf(fp, "  \"mu_max_elc\": %e,\n", ctx->mu_max_elc);
+  fprintf(fp, "  \"vpar_max_ion\": %e,\n", ctx->vpar_max_ion);
+  fprintf(fp, "  \"mu_max_ion\": %e,\n", ctx->mu_max_ion);
+  fprintf(fp, "  \"t_end\": %e,\n", ctx->t_end);
+  fprintf(fp, "  \"num_frames\": %d,\n", ctx->num_frames);
+  fprintf(fp, "  \"write_phase_freq\": %e,\n", ctx->write_phase_freq);
+  fprintf(fp, "  \"int_diag_calc_num\": %d,\n", ctx->int_diag_calc_num);
+  fprintf(fp, "  \"dt_failure_tol\": %e,\n", ctx->dt_failure_tol);
+  fprintf(fp, "  \"num_failures_max\": %d\n", ctx->num_failures_max);
+  fprintf(fp, "}\n");
+
+  fclose(fp);
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 3, vdim = 2; // Dimensionality.
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+  double me = GKYL_ELECTRON_MASS;
+  double mi = 2*GKYL_PROTON_MASS;
+  double mu0 = GKYL_MU0;
+  // Geometry, magnetic field and gradients.
+  double R0 = 1.313; // Major radius of the simulation box [m].
+  double a = 0.4701; // Minor radius at outboard midplane [m].
+  double B0 = 1.91; // Magnetic field magnitude in the simulation box [T].
+  double Ti0 = 1000*eV;
+  double eps_n = 0.2; // aspect ratio (= normalized density gradient length).
+  double eta_e = 2.0; // Normalized electron temperature gradient.
+  double eta_i = 2.5; // Normalized ion temperature gradient.
+  double ky_rhoi = 0.5; // Normalized perpendicular wavenumber.
+  double kz_Ln = 0.1; // Normalized parallel wavenumber.
+  double beta_i = 0.0045; // Ion beta.
+  double tau = 1.0; // Temperature ratio Ti/Te.
+
+  // Derived paramters.
+  double r0 = 0.5*a; // Minor radius of the simulation box [m].
+  double R = R0 + r0; // Major radius at center of simulation box [m].
+  double B = B0 * R0/R; // Magnetic field at center of simulation box [T].
+  double Te0 = Ti0/tau; // Electron temperature [J].
+  double n0 = beta_i*B*B/(2*mu0*Ti0); // Density [m^-3].
+  double vte = sqrt(Te0/me); // Electron thermal speed [m/s].
+  double vti = sqrt(Ti0/mi); // Ion thermal speed [m/s].
+  double c_s = sqrt(Te0/mi); // Sound speed [m/s].
+  double omega_ci = fabs(qi*B/mi); // Ion cyclotron frequency [rad/s].
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius [m]
+  double rho_e = vte/omega_ci; // Electron thermal gyroradius [m].
+  double rho_i = vti/omega_ci; // Ion thermal gyroradius [m].
+  double ky_min = ky_rhoi / rho_i; // Minimum ky.
+  double dr = 2*M_PI/ky_min; // Cell size in x-direction [m].
+  double L_n = R * eps_n;
+  double L_Te = L_n/eta_e;
+  double L_Ti = L_n/eta_i;
+  double kz_min = kz_Ln / L_n;
+  double L_parallel = 2*M_PI/kz_min;
+
+  double kTi = R0/L_Ti;
+  double kTe = R0/L_Te;
+  double kN = R0/L_n;
+  double wTi = 0.3;
+  double wTe = 0.3;
+  double wN = 0.3;
+
+  // Grid parameters
+  int Nx = 16;
+  int Ny = 8;
+  int Nz = 8;
+  int Nvpar = 16;
+  int Nmu = 8;
+
+  double x_min = r0;
+  double x_max = r0 * (1+2*wN);
+  double y_min = -dr/2;
+  double y_max = dr/2;
+  double z_min = -L_parallel/2;  // Min z-coordinate [m].
+  double z_max = L_parallel/2;   // Max z-coordinate [m].
+  double vpar_max_elc = 4.0*vte; // Max electron parallel velocity [m/s].
+  double vpar_min_elc = -vpar_max_elc; // Min electron parallel velocity [m/s].
+  double vpar_max_ion = 4.0*vti; // Max ion parallel velocity [m/s].
+  double vpar_min_ion = -vpar_max_ion; // Min ion parallel
+  double mu_max_elc = me*pow(4*vte,2)/(2*B); // Max electron mu [J/T].
+  double mu_max_ion = mi*pow(4*vti,2)/(2*B); // Max ion mu [J/T].
+
+  int poly_order = 1;
+
+  double t_end = 0.01*L_n/vti; // End time [s].
+  int num_frames = 100;
+  double write_phase_freq = 0.1; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*1000;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 50; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .mu0 = mu0,
+    .R = R,
+    .B = B,
+    .me = me,  .qe = qe,
+    .mi = mi,  .qi = qi,
+    .n0 = n0,  .Te0 = Te0,  .Ti0 = Ti0,
+
+    .kN = kN,  .kTi = kTi,  .kTe = kTe,
+    .wN = wN,  .wTi = wTi,  .wTe = wTe,
+    .r0 = r0,  .L_n = L_n,  .L_Te = L_Te,  .L_Ti = L_Ti,
+    .a = a,
+
+    .Nx = Nx,
+    .Ny = Ny,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .x_min = x_min,
+    .x_max = x_max,
+    .y_min = y_min,
+    .y_max = y_max,
+    .z_min = z_min,
+    .z_max = z_max,
+    .vpar_max_elc = vpar_max_elc,  .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion,  .mu_max_ion = mu_max_ion,
+    .cells = {Nx, Ny, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+
+    .t_end = t_end,  .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+int main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // Electrons.
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_elc, 0.0},
+    .upper = {  ctx.vpar_max_elc, ctx.mu_max_elc}, 
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    // .mapc2p = {
+    //   .mapping = mapc2p_vel_elc,
+    //   .ctx = &ctx,
+    // },
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init_elc,
+      .upar= upar_elc,
+      .temp = temp_elc,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ABSORB },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Ions.
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = {  ctx.vpar_max_ion, ctx.mu_max_ion}, 
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    // .mapc2p = {
+    //   .mapping = mapc2p_vel_ion,
+    //   .ctx = &ctx,
+    // },
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM, 
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init_ion,
+      .upar= upar_ion,
+      .temp = temp_ion,      
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 7,
+    .diag_moments = { GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP },
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    .time_rate_diagnostics = true,
+
+    .boundary_flux_diagnostics = {
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+//      .time_integrated = true,
+    },
+  };
+
+  // Field.
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
+    },
+    .mu0 = ctx.mu0,
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .name = "wk/kbm",
+    .cfl_frac = 1.0,
+    .cfl_frac_omegaH = 1.0,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.y_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.y_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1], cells_x[2] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx
+    },
+
+    .num_periodic_dir = 1,
+    .periodic_dirs = {1},
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .comm = comm,
+      .cuts = { app_args.cuts[0], app_args.cuts[1], app_args.cuts[2] },
+    },
+  };
+
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+    .print_verbosity = {
+      .enabled = true,
+      .frequency = 0.1,
+    }
+  };
+
+  write_ctx_to_json(&ctx);
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+  return 0;
+}

From 3da6a279f774eee4126a18686577bee91f5e0e19 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 2 Mar 2026 11:45:17 -0500
Subject: [PATCH 115/181] small logic bug fix

---
 gyrokinetic/apps/gyrokinetic.c | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 3cf530efff..231e87a117 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -902,7 +902,7 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
       }
     }
 
-    if (app->field->info.init_from_file.type == 0 && app->field->info.init_field_profile == 0)
+    if (app->field->info.init_from_file.type == 0 && app->field->info.init_field_profile == 0) {
       // Compute the field.
       // MF 2024/09/27/: Need the cast here for consistency. Fixing
       // this may require removing 'const' from a lot of places.
@@ -919,7 +919,8 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
         }
         gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
       }
-    else {
+
+    } else {
       if (app->field->info.init_field_profile == 0)
         // Read the field.
         gk_field_file_import_init(app, app->field->info.init_from_file);
@@ -927,7 +928,6 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
         // Project the field.
         gk_field_project_init(app);
     }
-
   }
 
   // Compute the phase-space advection speeds and boundary fluxes as t=0

From ee68ddb47231b14b4b1d22561f116666edbbc69a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 30 Mar 2026 08:48:21 -0700
Subject: [PATCH 116/181] fix a bug rising from merge

---
 gyrokinetic/apps/gk_field_2x3x.c | 14 ++------------
 1 file changed, 2 insertions(+), 12 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 642806b12a..c3932ca874 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -138,16 +138,6 @@ gk_field_twistshift_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *f
   // Do nothing
 }
 
-static void 
-gk_field_twistshift_enabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
-  gkyl_bc_twistshift_advance(up, fdo, ftar);
-}
-
-static void
-gk_field_twistshift_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
-  // Do nothing
-}
-
 static void
 gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
 {
@@ -159,7 +149,7 @@ gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_
     num_periodic_dir, periodic_dirs, finout); 
   
   // Update the lower z ghosts with twist-and-shift if we are in 3x2v
-   field->twistshift_func(field->bc_T_LU_lo, finout, finout);
+   field->twistshift_func(field->bc_ts_lo, finout, finout);
 
   // Sync ghost cells between MPI processes.
   gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);
@@ -179,7 +169,7 @@ gk_field_enforce_parallel_bc_em_enabled(const struct gkyl_gyrokinetic_app *app,
     num_periodic_dir, periodic_dirs, finout); 
   
   // Update the lower z ghosts with twist-and-shift if we are in 3x2v
-  field->twistshift_func(field->bc_T_LU_lo, finout, finout);
+  field->twistshift_func(field->bc_ts_lo, finout, finout);
 
   // Sync ghost cells between MPI processes.
   gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);

From 80c4918e9e1a8343b4f2869954eb67500ca18da1 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 30 Mar 2026 08:55:28 -0700
Subject: [PATCH 117/181] Add the helical geometry SOL regression test (see
 Section 6 of Mandell et al. J. Plasma Phys. (2020), vol. 86, 905860109)

---
 .../creg/rt_gk_em_helical_sol_3x2v_p1.c       | 586 ++++++++++++++++++
 1 file changed, 586 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
new file mode 100644
index 0000000000..56c5429f5f
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
@@ -0,0 +1,586 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  
+  // Geometry and magnetic field.
+  double B_axis;
+  double R0;
+  double a0;
+  double Rc;
+  double B0;
+  double Lp; // Poloidal length (used to get the field line pitch).
+  double Lt; // Toroidal length (used to get the field line pitch).
+
+  // Plasma parameters.
+  double me; double qe;
+  double mi; double qi;
+  double n0; double Te0; double Ti0; 
+
+  // Collisions.
+  double nu_frac;
+
+  // Source parameters.
+  double P_SOL;
+  double S0;
+  double xSource;
+  double lambdaSource;
+
+  // Grid parameters.
+  double Lx; // Domain size in radial direction.
+  double Ly; // Domain size in binormal direction.
+  double Lz; // Domain size along magnetic field.
+  double x_min; double x_max;
+  double y_min; double y_max;
+  double z_min; double z_max;
+  int Nx;
+  int Ny;
+  int Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc; double mu_max_elc;
+  double vpar_max_ion; double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+double random0to1()
+{
+  return (double)rand() / (double)RAND_MAX;
+}
+
+// Common source density profiles.
+double sourceDensity(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[2];
+  double sourceFloor = 0.1;
+
+  struct gk_app_ctx *app = ctx;
+  double S0 = app->S0;
+  double lambdaSource = app->lambdaSource;
+  double xSource = app->xSource;
+  double Lz = app->Lz;
+
+  if (x < xSource) {
+    sourceFloor = 0.5;
+  }
+  if (fabs(z) < Lz/4) {
+    return 0.90625*S0*fmax(exp(-0.5*pow((x-xSource)/lambdaSource,2)),sourceFloor);
+  } else {
+    return 1e-10;
+  }
+}
+
+// Common source temperature profile.
+double sourceTemperature(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3 * lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 30*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial density.
+double densityInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double Ls = app->Lz/4;
+  double xSource[3] = {x, y, 0};
+  double effectiveSource = sourceDensity(t, xSource, ctx);
+  double c_ss = sqrt(5/3*sourceTemperature(t, xSource, ctx)/app->mi);
+  double nPeak = 4*sqrt(5)/3/c_ss*Ls*effectiveSource/2;
+  double perturb = 1e-3*(random0to1() - 0.5)*2.0;
+  if (fabs(z) <= Ls) {
+    return nPeak * (1 + sqrt(1-pow(z/Ls,2)))/2 * (1+perturb);
+  } else {
+    return nPeak/2 * (1+perturb);
+  }
+}
+
+// Initial temperature.
+double temperatureInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3*lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 20*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial ion drift speed.
+double driftSpeed(const double * GKYL_RESTRICT xn, void *ctx){
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  double Lz = app->Lz;
+  double mi = app->mi;
+  double Te;
+  if (x < xSource + 3*lambdaSource) {
+    Te = 50*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    Te = 20*GKYL_ELEMENTARY_CHARGE;
+  }
+  double Ls = Lz/4;
+  if (fabs(z) <= Ls) {
+    return z/Ls*sqrt(Te/mi);
+  } else {
+    return (z > 0 ? 1.0 : -1.0)*sqrt(Te/mi);
+  }
+}
+
+// Magnetic field strength.
+double bmag(const double *xc, void *ctx)
+{
+  double x = xc[0];
+  struct gk_app_ctx *app = ctx;
+  double B0 = app->B0;
+  double Rc = app->Rc;
+  return B0*Rc/x;
+}
+
+// Interface function calls.
+void source_density(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceDensity(t, xn, ctx); }
+void source_temperature(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceTemperature(t, xn, ctx); }
+void density_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = densityInit(t, xn, ctx); }
+void temp_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = temperatureInit(t, xn, ctx); }
+void upar_ion_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = driftSpeed(xn, ctx); }
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = bmag(xc, ctx); }
+void zero_func(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = 0.0; }
+
+// Geometry evaluation functions for the gk app
+void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+
+  struct gk_app_ctx *app = ctx;
+  double Rc = app->Rc;
+  double Lp = app->Lp;
+  double Lt = app->Lt;
+
+  double theta = asin(Lp/Lt);
+
+  // Map to cylindrical (R, Z, phi) coordinates.
+  double R   = x;
+  double Z   = z*sin(theta);
+  double phi = (y/sin(theta) + z*cos(theta)/Rc);
+  // Map to Cartesian (X, Y, Z) coordinates.
+  double X = R*cos(phi);
+  double Y = R*sin(phi);
+
+  xp[0] = X; xp[1] = Y; xp[2] = Z;
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 3, vdim = 2; // Dimensionality.
+
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double mp = GKYL_PROTON_MASS, me = GKYL_ELECTRON_MASS;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+
+  // Plasma parameters. Chosen based on the value of a cubic sline
+  // between the last TS data inside the LCFS and the probe data in
+  // in the far SOL, near R=0.475 m.
+  double AMU = 2.01410177811;
+  double mi = mp*AMU; // Deuterium ions.
+  double Te0 = 40*eV;
+  double Ti0 = 40*eV;
+  double n0 = 7e18*10; // [1/m^3]
+
+  // Geometry and magnetic field.
+  double B_axis = 0.5;
+  double R0 = 0.85;
+  double a0 = 0.5;
+  double Lp = 2.4; // Poloidal length (used to get the field line pitch).
+  double Lt = 8.0; // Toroidal length (used to get the field line pitch).
+  double Rc = R0 + a0;
+  double B0 = B_axis*R0/Rc;
+
+  // Source parameters.
+  double P_SOL = 8.1e5;
+  double S0 = 5.7691e23*10;
+  double xSource = Rc - 0.05;
+  double lambdaSource = 0.005;
+
+  // Collisions;
+  double nuFrac = 0.1;
+
+  // Derived parameters.
+  double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
+  double c_s = sqrt(Te0/mi); // Sound speed.
+  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius.
+
+  // Box size.
+  double Lx = 50*rho_s;
+  double Ly = 100*rho_s;
+  double Lz = Lt; // [m]
+
+  double x_min = Rc - Lx/2;
+  double x_max = Rc + Lx/2;
+  double y_min = -Ly/2;
+  double y_max = Ly/2;
+  double z_min = -Lz/2;
+  double z_max = Lz/2;
+
+  // Grid parameters
+  int Nx = 4;
+  int Ny = 4;
+  int Nz = 4;
+  int Nvpar = 4;
+  int Nmu = 4;
+  int poly_order = 1;
+
+  double vpar_max_elc = 4.*vte;
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
+  double vpar_max_ion = 4.*vti;
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
+
+  double t_end = 1.e-6; // End time, should terminate in 43 steps.
+  int num_frames = 1;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*100;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 20; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .B_axis = B_axis,
+    .R0 = R0,
+    .a0 = a0,
+    .Lp = Lp,
+    .Lt = Lt,
+    .Rc = Rc,
+    .B0 = B0,
+    .Lx = Lx,
+    .Ly = Ly,
+    .Lz = Lz,
+    .x_min = x_min, .x_max = x_max,
+    .y_min = y_min, .y_max = y_max,
+    .z_min = z_min, .z_max = z_max,
+
+    .me = me, .qe = qe,
+    .mi = mi, .qi = qi,
+    .n0 = n0, .Te0 = Te0, .Ti0 = Ti0,
+  
+    .nu_frac = nuFrac,
+    
+    .P_SOL = P_SOL,
+    .S0 = S0,
+    .xSource = xSource,
+    .lambdaSource = lambdaSource,
+  
+    .Nx = Nx,
+    .Ny = Ny,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .cells = {Nx, Ny, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+    .vpar_max_elc = vpar_max_elc, .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion, .mu_max_ion = mu_max_ion,
+
+    .t_end = t_end, .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+
+int 
+main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // electrons
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = {-ctx.vpar_max_elc, 0.0},
+    .upper = { ctx.vpar_max_elc, ctx.mu_max_elc},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = zero_func,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "elc" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Te0,
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+    
+    .time_rate_diagnostics = true,
+  };
+
+  // ions
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = { ctx.vpar_max_ion, ctx.mu_max_ion},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = upar_ion_init,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "ion" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Ti0, 
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+  };
+
+  // field
+  struct gkyl_gyrokinetic_field field = {
+    .gkfield_id = GKYL_GK_FIELD_EM,
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .mu0 = GKYL_MU0,
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+    .cfl_frac_omegaH = 1.0,
+    .cfl_frac = 0.9,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.y_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.y_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1], cells_x[2] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx,
+    },
+
+    .num_periodic_dir = 1,
+    .periodic_dirs = { 1 },
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .comm = comm,
+      .cuts = { app_args.cuts[0], app_args.cuts[1], app_args.cuts[2] },
+    }
+  };
+
+  // Set app output name from the executable name (argv[0]).
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+  
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+
+  return 0;
+}

From 2098654befebb7c467e2af4c80dec77e9c621ecc Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 30 Mar 2026 08:55:57 -0700
Subject: [PATCH 118/181] Add citation to Mandel 2020

---
 gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
index 56c5429f5f..43969a0c90 100644
--- a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
@@ -12,6 +12,9 @@
 
 #include <rt_arg_parse.h>
 
+// This regression test is directly inspired from the helical SOL demonstration
+// in Section 6 of Mandell et al. J. Plasma Phys. (2020), vol. 86, 905860109.
+
 // Define the context of the simulation. This is basically all the globals
 struct gk_app_ctx {
   int cdim, vdim; // Dimensionality.

From 7d607e9318c03e9669c234489ee97c2e2a726a4a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 30 Mar 2026 09:05:50 -0700
Subject: [PATCH 119/181] add Apar solve in the timing metrics

---
 gyrokinetic/apps/gyrokinetic.c | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 231e87a117..44bc1bebf6 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -2061,7 +2061,8 @@ gkyl_gyrokinetic_app_stat(gkyl_gyrokinetic_app* app)
     + stat->species_omega_cfl_tm + stat->species_src_tm + stat->species_heat_tm
     + stat->neut_species_collisionless_tm + stat->neut_species_coll_tm + stat->neut_species_react_tm
     + stat->neut_species_omega_cfl_tm + stat->neut_species_src_tm + stat->dfdt_dt_reduce_tm + stat->fwd_euler_step_f_tm;
-  stat->field_sum_tm = stat->field_phi_rhs_tm  + stat->field_phi_solve_tm;
+  stat->field_sum_tm = stat->field_phi_rhs_tm  + stat->field_phi_solve_tm
+    + stat->field_apar_rhs_tm + stat->field_apar_solve_tm;
   stat->bc_sum_tm = stat->species_bc_tm + stat->neut_species_bc_tm;
   stat->time_rate_diags_sum_tm = stat->fdot_tm + stat->phidot_tm;
   stat->pos_shift_sum_tm = stat->species_pos_shift_tm + stat->neut_species_pos_shift_tm + stat->pos_shift_quasineut_tm;
@@ -2122,6 +2123,8 @@ gkyl_gyrokinetic_app_print_timings(gkyl_gyrokinetic_app* app, FILE *iostream)
   gkyl_gyrokinetic_app_cout(app, iostream, "    * Field solves:                    %.4e sec. / %4.2f %%.\n", stat->field_tm, ratio_to_percent(stat->field_tm,stat->time_loop_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Phi eqn RHS:                   %.4e sec. / %4.2f %%.\n", stat->field_phi_rhs_tm  , ratio_to_percent(stat->field_phi_rhs_tm  ,stat->field_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Phi eqn solve:                 %.4e sec. / %4.2f %%.\n", stat->field_phi_solve_tm, ratio_to_percent(stat->field_phi_solve_tm,stat->field_tm, 0.0));
+  gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Apar eqn RHS:                  %.4e sec. / %4.2f %%.\n", stat->field_apar_rhs_tm, ratio_to_percent(stat->field_apar_rhs_tm,stat->field_tm, 0.0));
+  gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Apar eqn solve:                %.4e sec. / %4.2f %%.\n", stat->field_apar_solve_tm, ratio_to_percent(stat->field_apar_solve_tm,stat->field_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Accounted for:                 %4.2f %%.\n", ratio_to_percent(stat->field_sum_tm, stat->field_tm, 100.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "    * Boundary conditions::            %.4e sec. / %4.2f %%.\n", stat->bc_tm, ratio_to_percent(stat->bc_tm,stat->time_loop_tm, 0.0));
   gkyl_gyrokinetic_app_cout(app, iostream, "      ^ Species (charged):             %.4e sec. / %4.2f %%.\n", stat->species_bc_tm     , ratio_to_percent(stat->species_bc_tm     ,stat->bc_tm, 0.0));

From 6fdeef481052e339eb513e0926a8cad7faa6b9df Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 31 Mar 2026 16:39:26 -0400
Subject: [PATCH 120/181] refactor some names to be clear about what is axis
 and what is center values

---
 .../creg/rt_gk_em_helical_sol_3x2v_p1.c       | 54 +++++++++----------
 1 file changed, 26 insertions(+), 28 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
index 43969a0c90..884967d33b 100644
--- a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
@@ -12,19 +12,16 @@
 
 #include <rt_arg_parse.h>
 
-// This regression test is directly inspired from the helical SOL demonstration
-// in Section 6 of Mandell et al. J. Plasma Phys. (2020), vol. 86, 905860109.
-
 // Define the context of the simulation. This is basically all the globals
 struct gk_app_ctx {
   int cdim, vdim; // Dimensionality.
   
   // Geometry and magnetic field.
   double B_axis;
-  double R0;
-  double a0;
-  double Rc;
-  double B0;
+  double R_axis;
+  double a_center;
+  double R_center;
+  double B_center;
   double Lp; // Poloidal length (used to get the field line pitch).
   double Lt; // Toroidal length (used to get the field line pitch).
 
@@ -167,9 +164,9 @@ double bmag(const double *xc, void *ctx)
 {
   double x = xc[0];
   struct gk_app_ctx *app = ctx;
-  double B0 = app->B0;
-  double Rc = app->Rc;
-  return B0*Rc/x;
+  double B_axis = app->B_axis;
+  double R_axis = app->R_axis;
+  return B_axis * R_axis/x;
 }
 
 // Interface function calls.
@@ -194,7 +191,7 @@ void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
   double x = xc[0], y = xc[1], z = xc[2];
 
   struct gk_app_ctx *app = ctx;
-  double Rc = app->Rc;
+  double R_center = app->R_center;
   double Lp = app->Lp;
   double Lt = app->Lt;
 
@@ -203,7 +200,8 @@ void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
   // Map to cylindrical (R, Z, phi) coordinates.
   double R   = x;
   double Z   = z*sin(theta);
-  double phi = (y/sin(theta) + z*cos(theta)/Rc);
+  double phi = (y/sin(theta) + z*cos(theta))/R_center;
+
   // Map to Cartesian (X, Y, Z) coordinates.
   double X = R*cos(phi);
   double Y = R*sin(phi);
@@ -233,17 +231,17 @@ create_ctx(void)
 
   // Geometry and magnetic field.
   double B_axis = 0.5;
-  double R0 = 0.85;
-  double a0 = 0.5;
+  double R_axis = 0.85;
+  double a_center = 0.5; // Minor radius of the center of the domain.
+  double R_center = R_axis + a_center; // Major radius of the center of the domain.
+  double B_center = B_axis*R_axis/R_center; // Magnetic field strength at the center of the domain.
   double Lp = 2.4; // Poloidal length (used to get the field line pitch).
   double Lt = 8.0; // Toroidal length (used to get the field line pitch).
-  double Rc = R0 + a0;
-  double B0 = B_axis*R0/Rc;
 
   // Source parameters.
   double P_SOL = 8.1e5;
   double S0 = 5.7691e23*10;
-  double xSource = Rc - 0.05;
+  double xSource = R_center - 0.05;
   double lambdaSource = 0.005;
 
   // Collisions;
@@ -252,7 +250,7 @@ create_ctx(void)
   // Derived parameters.
   double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
   double c_s = sqrt(Te0/mi); // Sound speed.
-  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
+  double omega_ci = fabs(qi*B_center/mi); // Ion cyclotron frequency.
   double rho_s = c_s/omega_ci; // Ion sound gyroradius.
 
   // Box size.
@@ -260,25 +258,25 @@ create_ctx(void)
   double Ly = 100*rho_s;
   double Lz = Lt; // [m]
 
-  double x_min = Rc - Lx/2;
-  double x_max = Rc + Lx/2;
+  double x_min = R_center - Lx/2;
+  double x_max = R_center + Lx/2;
   double y_min = -Ly/2;
   double y_max = Ly/2;
   double z_min = -Lz/2;
   double z_max = Lz/2;
 
   // Grid parameters
-  int Nx = 4;
-  int Ny = 4;
+  int Nx = 2;
+  int Ny = 2;
   int Nz = 4;
   int Nvpar = 4;
   int Nmu = 4;
   int poly_order = 1;
 
   double vpar_max_elc = 4.*vte;
-  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B_center);
   double vpar_max_ion = 4.*vti;
-  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B_center);
 
   double t_end = 1.e-6; // End time, should terminate in 43 steps.
   int num_frames = 1;
@@ -291,12 +289,12 @@ create_ctx(void)
     .cdim = cdim,
     .vdim = vdim,
     .B_axis = B_axis,
-    .R0 = R0,
-    .a0 = a0,
+    .R_axis = R_axis,
+    .a_center = a_center,
     .Lp = Lp,
     .Lt = Lt,
-    .Rc = Rc,
-    .B0 = B0,
+    .R_center = R_center,
+    .B_center = B_center,
     .Lx = Lx,
     .Ly = Ly,
     .Lz = Lz,

From 4f1333e6e6c3cca914093e67cec32cfd26ca6c19 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 3 Apr 2026 13:16:41 -0400
Subject: [PATCH 121/181] add an option in the gk field table to have a static
 Apar, this means that we solve only Apar at t=0 and do not compute Apardot.
 It is equivalent to a electrostatic simulation with a constant fluctuation to
 the magnetic field.

---
 gyrokinetic/apps/gk_field.c              | 2 +-
 gyrokinetic/apps/gk_field_1x.c           | 2 +-
 gyrokinetic/apps/gk_field_2x3x.c         | 8 ++++++--
 gyrokinetic/apps/gkyl_gyrokinetic.h      | 1 +
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 1 +
 5 files changed, 10 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 73e387cf21..4a38818e6e 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -393,7 +393,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
-    f->step_apar = gk_field_step_apar_enabled;
+    f->step_apar = f->info.is_apar_static ? gk_field_step_apar_disabled : gk_field_step_apar_enabled;
     f->em_combine_func = gk_field_combine_enabled;
     f->em_copy_func = gk_field_copy_range_enabled;
   } else {
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 0f67e5327e..640e9cbcf5 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -171,7 +171,7 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Set function pointers.
   f->rhs_phi_func = gk_field_rhs_phi_1x;
   if (f->is_em) {
-    f->em_rhs_func = gk_field_em_rhs_enabled;
+    f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
     f->ampere_solve = gk_field_ampere_solve_1x_enabled;
   } else {
     f->em_rhs_func = gk_field_em_rhs_none;
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index c3932ca874..9d8d3c1b51 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -234,7 +234,7 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
   gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
 
-  // gkyl_array_clear_range(field->apardot, 0.0, &app->local_ext);
+  field->invert_flr(app, field, field->apardot);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -242,8 +242,12 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
 static void 
 gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
+
   gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
   gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
+
+  field->invert_flr(app, field, field->apar);
+
   field->enforce_parallel_bc_em_func(app, field, field->apar);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -550,7 +554,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
 
     f->ampere_solve = gk_field_ampere_solve_enabled;
-    f->em_rhs_func = gk_field_em_rhs_enabled;
+    f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
   }
 
   gkyl_array_set(f->es_energy_fac, 0.5, f->epsilon);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 0a38db7ef7..cc6450d59a 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -476,6 +476,7 @@ struct gkyl_gyrokinetic_neut_species {
 struct gkyl_gyrokinetic_field {
   enum gkyl_gkfield_id gkfield_id;
   bool is_static; // =true field does not change in time.
+  bool is_apar_static; // =true Apar at initial time is used for all time steps.
   bool zero_init_field; // =true doesn't compute the initial field.
 
   double polarization_bmag; 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e3f6545d66..8514ba4141 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1221,6 +1221,7 @@ struct gk_field {
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
   bool is_em; // Whether we solve the EM field equations.
+  bool freeze_apar; // Whether we set Apardot=0. 
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density

From 86d1b106293dbeaa234cd9b59edcf0154c10d13d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 3 Apr 2026 17:31:35 -0400
Subject: [PATCH 122/181] fix the is_apar_static option

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 4a38818e6e..73e387cf21 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -393,7 +393,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
-    f->step_apar = f->info.is_apar_static ? gk_field_step_apar_disabled : gk_field_step_apar_enabled;
+    f->step_apar = gk_field_step_apar_enabled;
     f->em_combine_func = gk_field_combine_enabled;
     f->em_copy_func = gk_field_copy_range_enabled;
   } else {

From 826c982e5e2cdf3e301ab4106df66629705fd8f1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 6 Apr 2026 13:26:59 -0400
Subject: [PATCH 123/181] remove unused variables

---
 .../dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c    | 2 --
 .../dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c    | 2 --
 2 files changed, 4 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
index 889648f0c1..2c9e566d31 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
@@ -21,8 +21,6 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   double rdx2 = 2.0/dxv[0];
   double rdvpar2 = 2.0/dxv[1];
 
-  double rdvpar2Sq = rdvpar2*rdvpar2;
-  double dvparSq = dxv[1]*dxv[1];
 
   const double *b_x = &b_i[0];
   const double *b_y = &b_i[2];
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
index 491eab8b83..0cf6e8271f 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
@@ -22,8 +22,6 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   double rdvpar2 = 2.0/dxv[1];
   double rdmu2 = 2.0/dxv[2];
 
-  double rdvpar2Sq = rdvpar2*rdvpar2;
-  double dvparSq = dxv[1]*dxv[1];
 
   const double *b_x = &b_i[0];
   const double *b_y = &b_i[2];

From fe27709e00c4d018b321cdb887f549f69eff2c98 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 6 Apr 2026 10:33:14 -0700
Subject: [PATCH 124/181] leave apar stepping even if apar is static since it
 is already forcing dApar/dt = 0

---
 gyrokinetic/apps/gk_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 4a38818e6e..73e387cf21 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -393,7 +393,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   }
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
-    f->step_apar = f->info.is_apar_static ? gk_field_step_apar_disabled : gk_field_step_apar_enabled;
+    f->step_apar = gk_field_step_apar_enabled;
     f->em_combine_func = gk_field_combine_enabled;
     f->em_copy_func = gk_field_copy_range_enabled;
   } else {

From 267e8eda24d4d509f6ddb1ff55e75781b2b2377c Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 6 Apr 2026 13:34:09 -0400
Subject: [PATCH 125/181] rerunning the maaxima scripts changes the kernel for
 unknown reason, maybe it is equivalent. let's check...

---
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c | 50 +++++++++----------
 1 file changed, 24 insertions(+), 26 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index 0b083c62b0..bc8238da1c 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -23,8 +23,6 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   double rdvpar2 = 2.0/dxv[2];
   double rdmu2 = 2.0/dxv[3];
 
-  double rdvpar2Sq = rdvpar2*rdvpar2;
-  double dvparSq = dxv[2]*dxv[2];
 
   const double *b_x = &b_i[0];
   const double *b_y = &b_i[4];
@@ -57,14 +55,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -81,14 +79,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = ((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/(vmap[1]*m_); 
-  alphaz[1] = ((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/(vmap[1]*m_); 
-  alphaz[2] = ((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/(vmap[1]*m_); 
-  alphaz[3] = ((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdz2)/(vmap[1]*m_); 
-  alphaz[5] = ((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/(vmap[1]*m_); 
-  alphaz[6] = ((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdz2)/(vmap[1]*m_); 
-  alphaz[7] = ((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdz2)/(vmap[1]*m_); 
-  alphaz[11] = ((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdz2)/(vmap[1]*m_); 
+  alphaz[0] = (((0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_y[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[3]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_y[3]*hamil[16]+1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -105,14 +103,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_x[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_z[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_z[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_z[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_z[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 

From 06c3289efae8fb089eee7bf83a2cd0ff2c1dd523 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 6 Apr 2026 15:42:10 -0400
Subject: [PATCH 126/181] this seems more correct fomr the gkylcas pov but I
 don't see any difference in the test simulation

---
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c |  48 +++----
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c | 128 +++++++++---------
 2 files changed, 88 insertions(+), 88 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index bc8238da1c..a5bad6c840 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -79,14 +79,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = (((0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_y[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[3]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_y[3]*hamil[16]+1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = (((0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_y[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[3]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_y[3]*hamil[16]+1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -103,14 +103,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_z[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_z[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_z[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_z[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_x[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
index d2f445577a..898842baeb 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -60,22 +60,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -104,22 +104,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
 
 
   out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -148,22 +148,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
 
 
   out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -192,22 +192,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_z[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_z[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_z[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_x[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_z[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_x[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_z[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_z[3]*apar[4])*rdx2)/vmap[1])/m_; 
-  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[4])*rdx2)/vmap[1])/m_; 
+  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
 
 
   out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 

From 561c01bdce9d570e025766978382829c8ef679d2 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 7 Apr 2026 13:22:45 -0400
Subject: [PATCH 127/181] the electrostatic contribution is not written in one
 line anymore, this allows to simplify the maxima code.

---
 ...nless_flux_em_no_by_surfvpar_2x2v_ser_p1.c |  16 +-
 ...nless_flux_em_no_by_surfvpar_3x2v_ser_p1.c |  32 ++--
 ..._flux_em_star_no_by_surfvpar_2x2v_ser_p1.c |  16 +-
 ..._flux_em_star_no_by_surfvpar_3x2v_ser_p1.c |  32 ++--
 ...onless_flux_em_star_surfvpar_1x1v_ser_p1.c |   6 +-
 ...onless_flux_em_star_surfvpar_1x2v_ser_p1.c |  12 +-
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c |  32 +++-
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c | 164 +++++++++++-------
 ...llisionless_flux_em_surfvpar_1x1v_ser_p1.c |   6 +-
 ...llisionless_flux_em_surfvpar_1x2v_ser_p1.c |  12 +-
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  32 +++-
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c | 164 +++++++++++-------
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |  16 +-
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |  32 ++--
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |   6 +-
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |  12 +-
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  32 +++-
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  80 +++++++--
 18 files changed, 456 insertions(+), 246 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
index 9960f87ece..0a5d9c3bdd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
@@ -70,7 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -134,7 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -144,7 +144,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -166,7 +166,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -176,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
index f17e7210c7..83850b2dcb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
@@ -75,7 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -85,7 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -107,7 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -117,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -171,7 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -181,7 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -213,7 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -235,7 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -245,7 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -267,7 +267,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -277,7 +277,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -299,7 +299,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -309,7 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
index aa09067e70..d17d941b99 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
@@ -70,7 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -100,7 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -130,7 +130,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
index 7c16b44bc7..d34e10d738 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
@@ -75,7 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -84,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -114,7 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -135,7 +135,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -144,7 +144,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -165,7 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -195,7 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -204,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -225,7 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -234,7 +234,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -255,7 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -264,7 +264,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -285,7 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -294,7 +294,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
index 3f7f1533e1..e0c6aa029e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
@@ -63,7 +63,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
index ca427e16b1..8fb9185a77 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
@@ -65,7 +65,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -75,7 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -107,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index 4ae855d703..e916a91757 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -70,7 +70,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -83,7 +85,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -108,7 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -121,7 +127,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -146,7 +154,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -159,7 +169,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -184,7 +196,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -197,7 +211,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index c9f2ca2ad9..a1315546c2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -75,7 +75,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
@@ -90,7 +93,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
@@ -117,10 +123,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -132,10 +141,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -159,10 +171,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -174,10 +189,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -201,10 +219,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -216,10 +237,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -243,10 +267,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -258,10 +285,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -285,10 +315,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -300,10 +333,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -327,10 +363,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -342,10 +381,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -369,10 +411,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -384,10 +429,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
index 2989bfd7d0..8c97527add 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
@@ -63,7 +63,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
@@ -86,7 +87,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
index d248598c35..384ab7c242 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
@@ -65,7 +65,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
@@ -76,7 +77,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
@@ -99,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index 626389a2ec..96d0890885 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -70,7 +70,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -84,7 +86,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -110,7 +114,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -124,7 +130,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
@@ -150,7 +158,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -164,7 +174,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -190,7 +202,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
@@ -204,7 +218,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index 3dd040864b..8749770574 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -75,7 +75,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[0].g_33; 
   mag_e_3 = gkdgv[0].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
@@ -91,7 +94,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
@@ -119,10 +125,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[1].g_33; 
   mag_e_3 = gkdgv[1].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -135,10 +144,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -163,10 +175,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[2].g_33; 
   mag_e_3 = gkdgv[2].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -179,10 +194,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -207,10 +225,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[3].g_33; 
   mag_e_3 = gkdgv[3].mag_e_3; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -223,10 +244,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -251,10 +275,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[4].g_33; 
   mag_e_3 = gkdgv[4].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -267,10 +294,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -295,10 +325,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[5].g_33; 
   mag_e_3 = gkdgv[5].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -311,10 +344,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -339,10 +375,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[6].g_33; 
   mag_e_3 = gkdgv[6].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -355,10 +394,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -383,10 +425,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   g_33 = gkdgv[7].g_33; 
   mag_e_3 = gkdgv[7].mag_e_3; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
@@ -399,10 +444,13 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index e9cd2a02a3..dac0eb306d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -59,7 +59,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -84,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -134,7 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -143,7 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 80f1415fb5..bc4e135bb5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -64,7 +64,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -73,7 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -114,7 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -164,7 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -223,7 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -239,7 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad ;
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index d7d9e3ffbc..786ebf6bcc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -52,7 +52,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
@@ -68,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]);
+  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 2605f00d88..7417d4164d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -54,7 +54,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -63,7 +64,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -79,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -88,7 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]);
+  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 40b8d09f56..7ff1b44199 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -59,7 +59,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -68,7 +70,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -84,7 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -93,7 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -109,7 +117,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -118,7 +128,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -134,7 +146,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -143,7 +157,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1])-((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]);
+  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 515d1b1f98..0ceca0c8cf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -64,7 +64,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -73,7 +76,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -89,7 +95,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -98,7 +107,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -114,7 +126,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -123,7 +138,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -139,7 +157,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -148,7 +169,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -164,7 +188,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -173,7 +200,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -189,7 +219,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -198,7 +231,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -214,7 +250,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -223,7 +262,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -239,7 +281,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
 
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -248,7 +293,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1])-((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]);
+  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];

From 5f3b878c832006e44a2996d0ccf22fb47705a97f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 7 Apr 2026 13:37:48 -0400
Subject: [PATCH 128/181] standardize the space at the end of the line.

---
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c | 24 +++++++++----------
 12 files changed, 144 insertions(+), 144 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 54f701c4de..504b0aaf8f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 457ae57c6e..4bea67af76 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +91,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +167,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +200,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 035985c9ac..ebc7824711 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +116,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +127,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index c789feeaab..a974c432a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +116,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +127,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index 166f58b19f..af712a1116 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +91,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +167,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +200,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 9742dac181..370c1eb0ea 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +116,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +127,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index 72d8bee3db..3844cc89a9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +116,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +127,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index 5e84833bd1..3bbde6882b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +91,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +167,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +200,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index f23c376835..d133d7f659 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +91,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +167,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +200,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 3b707055bf..81c771ad0c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +147,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -165,7 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index b7c585f799..684a1e4eb1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +147,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +156,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index 528b7070de..7d546cb447 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad;
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 

From eeacdd17e7f49f5708827cc2ed2e153ac1351f55 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 7 Apr 2026 13:51:45 -0400
Subject: [PATCH 129/181] split the electrostatic contributions between
 parallel streaming and curvature drift. This simplidies the maxima logic.

---
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c | 36 ++++++----
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c | 36 ++++++----
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c | 36 ++++++----
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c | 36 ++++++----
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 60 files changed, 2304 insertions(+), 1152 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index b42929a7c1..d20a55e66f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 6ffcb3b181..7069dfdc76 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 504b0aaf8f..cf53960b2a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 1fb10c7e31..c427818757 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -92,7 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,7 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,7 +144,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -147,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -156,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -211,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -220,7 +234,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -229,7 +244,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -247,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -266,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -275,7 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -284,7 +304,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -293,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -302,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 07e496557a..b7cc942d31 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index 543122e6e1..ad46012cfb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index 21cd3f2031..adb507ce54 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 4bea67af76..3d73195136 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index 0fe90bc65a..f6f7c93c63 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -96,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -107,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -129,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -150,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -172,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -248,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -259,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -270,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -281,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -302,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -324,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -335,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -346,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index 7a83ba0f4b..292aa63c7f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 34004a4621..25d1ab21a7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index e78f7c7f70..aabe9ae468 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index ebc7824711..610fbfba30 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 2c43901ca5..e1e17cc518 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -122,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -133,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -144,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -155,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -176,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -187,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -198,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -209,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -220,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -252,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +276,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -274,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -285,7 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -296,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -307,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -328,7 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -339,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -350,7 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -361,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -372,7 +394,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +406,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 563eb0d645..d52061210b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index f1e0ed2e6f..fa42cf3f03 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index a08bcb0502..46c6a90ffd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index a974c432a3..eccf2b6485 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index 312892cec8..38e9eeebe9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -122,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -133,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -144,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -155,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -176,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -187,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -198,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -209,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -220,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -252,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +276,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -274,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -285,7 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -296,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -307,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -328,7 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -339,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -350,7 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -361,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -372,7 +394,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +406,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index 0fe30219a5..f63c017e5e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
index 82c9d44359..c6b13686fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index 644327770f..f868b98cbb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index af712a1116..19995f12b5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 70fa8792a5..2c5db771cf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -96,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -107,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -129,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -150,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -172,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -248,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -259,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -270,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -281,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -302,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -324,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -335,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -346,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index dde338cae6..7d5e8bf199 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 3e7ca37c52..0140cc770c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
index aaa1f5f526..00585ff530 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 370c1eb0ea..9158dd797a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
index cd9733339a..366d2a07f4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -122,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -133,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -144,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -155,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -176,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -187,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -198,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -209,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -220,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -252,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +276,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -274,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -285,7 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -296,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -307,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -328,7 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -339,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -350,7 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -361,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -372,7 +394,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +406,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 7e945d1213..403ccec69a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
index 0d08c4712f..d99d73413e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
index 91ce1d5dc3..6df1b38376 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index 3844cc89a9..cb3ae87781 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -116,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -127,7 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -138,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -159,7 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -170,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -192,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
index 19a1a165f5..efc88d3c2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -122,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -133,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -144,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -155,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -176,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -187,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -198,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -209,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -220,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -252,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +276,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -274,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -285,7 +300,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -296,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -307,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -328,7 +346,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -339,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -350,7 +370,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -361,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -372,7 +394,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +406,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
index 14e533ab79..3710e3c8a9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -120,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -142,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -153,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -174,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -185,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -196,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -207,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -218,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -250,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -272,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -283,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -294,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -305,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -326,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -337,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -348,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -359,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -370,7 +392,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
index 92557904d8..c062fe363d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index d2112db809..f76429fba5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index 3bbde6882b..5c87e72750 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index 9b5f6282d9..3873b6555f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -96,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -107,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -129,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -150,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -172,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -248,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -259,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -270,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -281,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -302,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -324,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -335,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -346,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 80deed09d6..258ead1235 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index dbf9971dc9..c5526e3b1d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index b1570cade8..5e0e6cc600 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index d133d7f659..9ac3cb97e8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -91,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -102,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -124,7 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -167,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -189,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index 11bfc03e8e..3364005980 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -96,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -107,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -129,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -150,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -172,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +216,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -248,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -259,7 +274,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -270,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -281,7 +298,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -302,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -324,7 +344,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -335,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -346,7 +368,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +380,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index d95b14e1e5..c3318c6cd3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -116,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -127,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -148,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -170,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -192,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -224,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -257,7 +272,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -268,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -279,7 +296,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -300,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -322,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -333,7 +354,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -344,7 +366,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index ecd3ba844a..8668e498be 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index da7d97aeb6..fc3b8f246b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 81c771ad0c..a81ff09dbb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 5ca2d688a4..a7104a5c12 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,7 +130,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -136,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +150,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,7 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -209,7 +220,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -255,7 +270,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -273,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -292,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -301,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -310,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -319,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -328,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -337,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 9ae1961330..9e1a55b957 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index c1cc0f5020..75cbb22062 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 5c61b1f8a9..59cd8de219 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index 684a1e4eb1..facf9ca8fd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index e8bf6132d6..acb8705944 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -100,7 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -118,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -127,7 +130,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -136,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -145,7 +150,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -164,7 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -173,7 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -182,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -209,7 +220,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -228,7 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -237,7 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -246,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -255,7 +270,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -264,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -273,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -292,7 +310,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -301,7 +320,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -310,7 +330,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -319,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -328,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -337,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index da17447f50..f359b6db31 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index dba5b7cb2d..83887770c7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 00d228fa69..d8da1e4e90 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index 7d546cb447..8abd60acea 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 359e2550e7..6defc24114 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -74,7 +74,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -92,7 +94,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,7 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,7 +124,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,7 +144,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -147,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -156,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,7 +214,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -211,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -220,7 +234,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -229,7 +244,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -247,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -266,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -275,7 +294,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -284,7 +304,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -293,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -302,7 +324,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = 0.0; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 192ec8bdf9..dcafa9d0e3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad) + mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad) + mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad) + mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 

From a16ea9b7e38e144d33a22aa2767e7659cfb4263f Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 7 Apr 2026 13:59:21 -0400
Subject: [PATCH 130/181] another logic simplification of the kernels
 generation.

---
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |  3 +
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfx_1x1v_ser_p1.c |  3 +
 ...isionless_flux_em_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |  3 +
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfx_1x1v_ser_p1.c |  3 +
 ...lux_em_multib_boundary_surfx_1x2v_ser_p1.c |  6 ++
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c |  3 +
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c |  3 +
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c |  3 +
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c |  6 ++
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c |  3 +
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c |  6 ++
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfx_1x1v_ser_p1.c |  3 +
 ..._collisionless_flux_em_surfx_1x2v_ser_p1.c |  6 ++
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c | 36 ++++++----
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c | 36 ++++++----
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |  3 +
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |  6 ++
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |  3 +
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |  6 ++
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c | 36 ++++++----
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c | 36 ++++++----
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |  3 +
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |  6 ++
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c | 36 ++++++----
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c | 36 ++++++----
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c | 72 ++++++++++++-------
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c | 72 ++++++++++++-------
 84 files changed, 2412 insertions(+), 1152 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index 21395c014a..d9d8c6878c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 39e7d6f8f4..c0745ed517 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index d20a55e66f..fb02cca785 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -100,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -120,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -140,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -150,7 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -160,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -180,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -190,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 7069dfdc76..31eb3a8913 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -103,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -123,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -223,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -233,7 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -243,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -253,7 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -263,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -293,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -303,7 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -313,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -323,7 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -333,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index cf53960b2a..80ee615386 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -100,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -120,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -140,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -150,7 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -180,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -190,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index c427818757..79e47bfc3d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -95,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -115,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,7 +130,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -185,7 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -195,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,7 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -225,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -255,7 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -265,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -295,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -305,7 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -315,7 +336,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -325,7 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index b7cc942d31..a2942eb6ce 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -93,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -103,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -123,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -223,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -233,7 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -243,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -263,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -283,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -293,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -303,7 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -313,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -323,7 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -333,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
index c523120459..88113df453 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
index 5b1a91cf59..07f6bcbb11 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index ad46012cfb..6bea230e76 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index adb507ce54..87876dda64 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 3d73195136..e35d4bb68a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index f6f7c93c63..0ea29b024c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -87,7 +88,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -99,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -123,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -135,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -157,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -169,7 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -193,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -217,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -275,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -287,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -299,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -321,7 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -333,7 +352,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -345,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -369,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index 292aa63c7f..c47a56acf3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 3d0b9f5171..e457920881 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 38f15344ea..3b74a2c7a5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 25d1ab21a7..c913ee4e71 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index aabe9ae468..3887a7303c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 610fbfba30..93e466c316 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index e1e17cc518..97423aa883 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -113,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -125,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -137,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -149,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -195,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -207,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -219,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -243,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -265,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -277,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -289,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -301,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -325,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -347,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -359,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -371,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -395,7 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -407,7 +430,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index d52061210b..2bf533f3ae 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
index 0d6428a5b3..394243a7fc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
index 1d4dd33bbf..c242961c7c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index fa42cf3f03..69262b1929 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index 46c6a90ffd..7bff59a4d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index eccf2b6485..0ac778da02 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index 38e9eeebe9..59b6370741 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -113,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -125,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -137,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -149,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -195,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -207,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -219,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -243,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -265,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -277,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -289,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -301,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -325,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -347,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -359,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -371,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -395,7 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -407,7 +430,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index f63c017e5e..4b1424f41d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
index 78f68add35..0c5c7a448b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
index 43bae49e46..52c4f4f6f8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
index c6b13686fb..6b167e952a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index f868b98cbb..c347ea7f74 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index 19995f12b5..1b6fdf8c43 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 2c5db771cf..2a34878e80 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -87,7 +88,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -99,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -123,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -135,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -157,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -169,7 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -193,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -217,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -275,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -287,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -299,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -321,7 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -333,7 +352,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -345,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -369,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index 7d5e8bf199..92d2b8ce0c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
index ba2f277224..f9d4c206bc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 6c6e3762ce..be7a260df0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 0140cc770c..2f8a663411 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 00585ff530..d44dc93e16 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 9158dd797a..ef85969448 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 366d2a07f4..d5c9062374 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -113,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -125,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -137,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -149,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -195,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -207,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -219,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -243,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -265,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -277,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -289,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -301,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -325,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -347,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -359,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -371,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -395,7 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -407,7 +430,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 403ccec69a..161d07ec52 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
index f605e8c5e5..5f086bd889 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
index 00ac69d1b9..8c9b645369 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
index d99d73413e..bf9609b67b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
index 6df1b38376..090f74bb16 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index cb3ae87781..c907452ecf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -96,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -108,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -132,7 +136,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -144,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -166,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -178,7 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -190,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -202,7 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -214,7 +224,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -226,7 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
index efc88d3c2c..d09c4976ba 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -113,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -125,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -137,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -149,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -161,7 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -183,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -195,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -207,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -219,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -231,7 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -243,7 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -265,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -277,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -289,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -301,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -313,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -325,7 +342,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -347,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -359,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -371,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -383,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -395,7 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -407,7 +430,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
index 3710e3c8a9..c322f5a43b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -123,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -135,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -147,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -181,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -193,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -205,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -217,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -229,7 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -241,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -263,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -275,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -287,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -299,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -311,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -323,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -345,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -357,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -369,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -381,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -393,7 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -405,7 +428,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
index 49283bbf91..aa81e8a0c7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
index 1aae86a624..6175abb89d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
index c062fe363d..65b0026fda 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index f76429fba5..561d69a340 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index 5c87e72750..36871adf9d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index 3873b6555f..9f6bd795ee 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -87,7 +88,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -99,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -123,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -135,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -157,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -169,7 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -193,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -217,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -275,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -287,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -299,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -321,7 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -333,7 +352,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -345,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -369,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 258ead1235..2c389eeda4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
index 850f927129..a10b295fa8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
index ea0b519c46..c17b5a4efc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index c5526e3b1d..1cb70ea3bb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index 5e0e6cc600..0461eeb076 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index 9ac3cb97e8..179cb57944 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -82,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -94,7 +96,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -106,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -118,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -130,7 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -152,7 +158,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -176,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -188,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -200,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
@@ -212,7 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index 3364005980..b5fd7e463d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -87,7 +88,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -99,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -111,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -123,7 +127,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -135,7 +140,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -157,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -169,7 +176,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -181,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -193,7 +202,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -205,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -217,7 +228,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -263,7 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -275,7 +290,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -287,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -299,7 +316,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
 
@@ -321,7 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -333,7 +352,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -345,7 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -357,7 +378,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -369,7 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
@@ -381,7 +404,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index c3318c6cd3..339799d820 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -97,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -109,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -121,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -133,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -155,7 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -167,7 +174,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -179,7 +187,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -191,7 +200,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -203,7 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -215,7 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
 
@@ -237,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -273,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -285,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -297,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -319,7 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -331,7 +350,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -343,7 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -355,7 +376,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -367,7 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
@@ -379,7 +402,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index b5fadd95ca..7797b17ed9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index ec1c2e82f7..acd8abf567 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 8668e498be..f4b9b6e769 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -104,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -124,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -154,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -174,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -204,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index fc3b8f246b..b6dad316fa 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,7 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -129,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -149,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -169,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,7 +186,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -209,7 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -259,7 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -269,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -279,7 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -289,7 +306,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -319,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -329,7 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -339,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -349,7 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -359,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index a81ff09dbb..41fc7daa92 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -104,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -124,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -134,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -154,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -184,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -204,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index a7104a5c12..a8ac6090d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -121,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -141,7 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -151,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -191,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -211,7 +221,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -221,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -241,7 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -281,7 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -291,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -321,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -331,7 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -341,7 +362,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -351,7 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -361,7 +384,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 9e1a55b957..bf32c2f574 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -119,7 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -129,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -139,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -149,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -169,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -179,7 +186,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -209,7 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -259,7 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -269,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -279,7 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -289,7 +306,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -309,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -319,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -329,7 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -339,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -349,7 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -359,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 048bd3237b..0d48ffc867 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -68,6 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,6 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -86,6 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 5f4580602c..ff5cba37d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -69,6 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,6 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,6 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -96,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -105,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -114,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 75cbb22062..4b71d59261 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -104,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -114,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -124,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -134,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -154,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -204,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 59cd8de219..fc95ee388b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -119,7 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -129,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -139,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -149,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -169,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -179,7 +186,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -209,7 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -219,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -259,7 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -269,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -279,7 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -289,7 +306,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -309,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -319,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -329,7 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -339,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -349,7 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -359,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index facf9ca8fd..c4d9853f8d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -84,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -94,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -104,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -114,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -124,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -134,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -154,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -164,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -194,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -204,7 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index acb8705944..5d8d7ca8c7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,7 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -111,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -121,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -131,7 +134,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -141,7 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -151,7 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -171,7 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -181,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -191,7 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -201,7 +210,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -211,7 +221,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -221,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -241,7 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -251,7 +264,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -261,7 +275,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +286,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -281,7 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -291,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -311,7 +329,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -321,7 +340,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -331,7 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -341,7 +362,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -351,7 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -361,7 +384,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index f359b6db31..f6a72aee5e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -99,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -109,7 +110,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -119,7 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -129,7 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -139,7 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -149,7 +154,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -169,7 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -179,7 +186,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -209,7 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -219,7 +230,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -239,7 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -249,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -259,7 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -269,7 +284,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -279,7 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -289,7 +306,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -309,7 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -319,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -329,7 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -339,7 +360,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -349,7 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -359,7 +382,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 21823e2e6d..8952f57d1b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -66,6 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,6 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -84,6 +86,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index eb9c4c7812..3558d069dd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -67,6 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -85,6 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -94,6 +97,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -103,6 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -112,6 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index 83887770c7..b22ff9a1f8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -100,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -120,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -140,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -150,7 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -160,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -180,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -190,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index d8da1e4e90..8753a3a796 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -103,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -123,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -223,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -233,7 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -243,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -253,7 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -263,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -293,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -303,7 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -313,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -323,7 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -333,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index 8abd60acea..ace5865d75 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -70,7 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -100,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -120,7 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -140,7 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -150,7 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -180,7 +190,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -190,7 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * -bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 6defc24114..6bc7a680fc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -75,7 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -85,7 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -95,7 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -105,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -115,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,7 +130,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,7 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -185,7 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -195,7 +206,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,7 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -225,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +249,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +260,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -255,7 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -265,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,7 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -295,7 +314,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -305,7 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -315,7 +336,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -325,7 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index dcafa9d0e3..fc837435b4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -73,7 +73,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -83,7 +84,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -93,7 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -103,7 +106,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -113,7 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -123,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,7 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,7 +204,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,7 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -223,7 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -233,7 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -243,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -263,7 +280,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -283,7 +301,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -293,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -303,7 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -313,7 +334,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -323,7 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -333,7 +356,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += (mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_) + 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)))*area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 

From d20f703f6186738d0246e5e19ab8d71cc810d2e7 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 7 Apr 2026 14:49:23 -0400
Subject: [PATCH 131/181] Found a missing factor in conf surf flux kernel for
 Apar, it seems that 1/area_elem_quad and the area_elem_quad/Jc_quad factor
 was missing in the gradA times b term. Also combine the
 area_elem_quad/Jc_quad factor at the end of the building of alpha_quad to
 avoid repeating this operation.

---
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |  60 +++--
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c | 120 ++++++----
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |  84 ++++---
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c | 120 ++++++----
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c | 168 ++++++++------
 ...isionless_flux_em_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...isionless_flux_em_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c |  84 ++++---
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c | 108 +++++----
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c |  84 ++++---
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c | 108 +++++----
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...lux_em_multib_boundary_surfx_1x1v_ser_p1.c |  15 +-
 ...lux_em_multib_boundary_surfx_1x2v_ser_p1.c |  30 ++-
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c |  84 ++++---
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c | 108 +++++----
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...ess_flux_em_no_by_edge_surfx_2x2v_ser_p1.c |  12 +
 ...ess_flux_em_no_by_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...ess_flux_em_no_by_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...ess_flux_em_no_by_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...ess_flux_em_no_by_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  12 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  12 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  36 ++-
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  72 ++++--
 ...sionless_flux_em_no_by_surfx_2x2v_ser_p1.c |  12 +
 ...sionless_flux_em_no_by_surfx_3x2v_ser_p1.c |  24 ++
 ...sionless_flux_em_no_by_surfy_2x2v_ser_p1.c |  36 ++-
 ...sionless_flux_em_no_by_surfy_3x2v_ser_p1.c |  24 ++
 ...sionless_flux_em_no_by_surfz_3x2v_ser_p1.c |  72 ++++--
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c |  84 ++++---
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c | 108 +++++----
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c |  84 ++++---
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c | 108 +++++----
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c |  15 +-
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c |  30 ++-
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c |  84 ++++---
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c | 108 +++++----
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...lux_em_star_no_by_edge_surfx_2x2v_ser_p1.c |  12 +
 ...lux_em_star_no_by_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...lux_em_star_no_by_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...lux_em_star_no_by_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...lux_em_star_no_by_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  12 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  12 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  36 ++-
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  72 ++++--
 ...ess_flux_em_star_no_by_surfx_2x2v_ser_p1.c |  12 +
 ...ess_flux_em_star_no_by_surfx_3x2v_ser_p1.c |  24 ++
 ...ess_flux_em_star_no_by_surfy_2x2v_ser_p1.c |  36 ++-
 ...ess_flux_em_star_no_by_surfy_3x2v_ser_p1.c |  24 ++
 ...ess_flux_em_star_no_by_surfz_3x2v_ser_p1.c |  72 ++++--
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c |  15 +-
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c |  30 ++-
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c |  84 ++++---
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c | 108 +++++----
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ..._collisionless_flux_em_surfx_1x1v_ser_p1.c |  15 +-
 ..._collisionless_flux_em_surfx_1x2v_ser_p1.c |  30 ++-
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c |  84 ++++---
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 168 ++++++++------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c | 108 +++++----
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 168 ++++++++------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 216 ++++++++++--------
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |  15 +-
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |  30 ++-
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |  60 +++--
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c | 120 ++++++----
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |  84 ++++---
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c | 120 ++++++----
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c | 168 ++++++++------
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |  15 +-
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |  30 ++-
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |  60 +++--
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c | 120 ++++++----
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |  84 ++++---
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c | 120 ++++++----
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c | 168 ++++++++------
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |  12 +
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  12 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  36 ++-
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  24 ++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  72 ++++--
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  12 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  36 ++-
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  24 ++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  72 ++++--
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |  12 +
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |  24 ++
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |  36 ++-
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |  24 ++
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |  72 ++++--
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |  15 +-
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |  30 ++-
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c |  60 +++--
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c | 120 ++++++----
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c |  84 ++++---
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c | 120 ++++++----
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c | 168 ++++++++------
 144 files changed, 6564 insertions(+), 4152 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index d9d8c6878c..a266ef3c3e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index c0745ed517..965fe74fae 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index fb02cca785..36ba1fea10 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -70,8 +70,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -81,8 +82,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -92,8 +94,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -103,8 +106,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -114,8 +118,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -125,8 +130,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -146,8 +152,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -157,8 +164,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -168,8 +176,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,8 +188,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -190,8 +200,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -201,8 +212,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 31eb3a8913..e489640137 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -73,8 +73,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,8 +85,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -95,8 +97,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -106,8 +109,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -128,8 +133,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -149,8 +155,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -160,8 +167,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,8 +179,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,8 +191,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,8 +203,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -204,8 +215,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,8 +237,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,8 +249,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -247,8 +261,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -258,8 +273,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -269,8 +285,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -280,8 +297,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,8 +319,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -312,8 +331,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -323,8 +343,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -334,8 +355,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -345,8 +367,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -356,8 +379,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index 80ee615386..c1f4cc7d70 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -69,9 +69,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -80,9 +81,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -91,9 +93,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -102,9 +105,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -113,9 +117,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -124,9 +129,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -145,9 +151,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,9 +163,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -167,9 +175,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,9 +187,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -189,9 +199,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -200,9 +211,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 79e47bfc3d..4abf974c5e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -75,8 +75,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -97,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,8 +111,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -130,8 +135,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -151,8 +157,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -162,8 +169,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,8 +181,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,8 +193,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -195,8 +205,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -206,8 +217,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,8 +239,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,8 +251,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -249,8 +263,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -260,8 +275,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,8 +287,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -282,8 +299,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,8 +321,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -314,8 +333,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -325,8 +345,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,8 +357,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -347,8 +369,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -358,8 +381,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index a2942eb6ce..64470288c2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -72,9 +72,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -83,9 +84,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -94,9 +96,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -105,9 +108,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,9 +120,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -127,9 +132,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -148,9 +154,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -159,9 +166,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,9 +178,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,9 +190,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -192,9 +202,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,9 +214,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -224,9 +236,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,9 +248,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -246,9 +260,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -257,9 +272,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -268,9 +284,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -279,9 +296,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,9 +318,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -311,9 +330,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -322,9 +342,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -333,9 +354,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -344,9 +366,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -355,9 +378,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
index 88113df453..2fe98f6682 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
index 07f6bcbb11..e3225f86b7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index 6bea230e76..9d319506ed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -70,10 +70,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -83,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -109,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -122,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -135,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,10 +164,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -171,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -197,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -210,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -223,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index 87876dda64..00a7dea761 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -73,10 +73,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,10 +87,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,10 +167,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,10 +181,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -249,10 +261,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,10 +275,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -337,10 +355,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -350,10 +369,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index e35d4bb68a..54b88039ef 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -69,11 +69,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -82,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -95,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -108,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -121,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -134,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -157,11 +163,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -196,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -209,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -222,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index 0ea29b024c..04aa78d07c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -75,10 +75,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,10 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,10 +103,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +117,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +131,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +145,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -176,10 +183,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +197,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +211,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +225,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +239,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,10 +277,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -277,10 +291,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +305,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +319,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +333,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -352,10 +371,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +385,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +399,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +413,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +427,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index c47a56acf3..a14470b3b9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -72,11 +72,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -85,11 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -98,11 +100,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +114,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +128,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +142,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -160,11 +166,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,11 +180,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -186,11 +194,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +208,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +222,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +236,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -248,11 +260,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,11 +274,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,11 +288,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +302,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +316,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +330,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,11 +354,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -349,11 +368,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -362,11 +382,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +396,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +410,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +424,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
index e457920881..92b51ca333 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 3b74a2c7a5..21bdc8e646 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index c913ee4e71..0637f96946 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -110,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -123,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -136,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -149,10 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -172,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -185,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -198,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -211,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -224,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -237,10 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 3887a7303c..9f40259cff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,10 +99,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +113,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +127,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +141,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -151,10 +155,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +193,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +207,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +221,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +235,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -239,10 +249,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -252,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +287,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +301,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +315,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +329,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,10 +343,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -340,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +381,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +395,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +409,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +423,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -415,10 +437,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -428,10 +451,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 93e466c316..c3c0b6acec 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -109,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -122,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -135,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -148,11 +153,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -171,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -184,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -197,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -210,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -223,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -236,11 +247,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 97423aa883..0f44d08528 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,10 +157,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,10 +171,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -241,10 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -254,10 +265,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -277,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,10 +345,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -342,10 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -417,10 +439,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -430,10 +453,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 2bf533f3ae..83e09311df 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,11 +98,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +112,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +126,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +140,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -150,11 +154,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -163,11 +168,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -186,11 +192,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +206,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +220,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +234,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -238,11 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,11 +262,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,11 +286,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +300,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +314,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +328,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -326,11 +342,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,11 +356,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -362,11 +380,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +394,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +408,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +422,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -414,11 +436,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -427,11 +450,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
index 394243a7fc..f805246ea4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
index c242961c7c..c1c25d1dd4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index 69262b1929..519637e5b7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -97,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -110,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -123,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -136,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -149,10 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -172,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -185,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -198,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -211,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -224,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -237,10 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index 7bff59a4d4..7b07cf337b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,10 +99,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -112,10 +113,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,10 +127,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -138,10 +141,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -151,10 +155,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -164,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -187,10 +193,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -200,10 +207,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -213,10 +221,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,10 +235,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -239,10 +249,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -252,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -275,10 +287,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -288,10 +301,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -301,10 +315,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -314,10 +329,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -327,10 +343,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -340,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -363,10 +381,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -376,10 +395,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -389,10 +409,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -402,10 +423,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -415,10 +437,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -428,10 +451,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index 0ac778da02..c5eba93f40 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -96,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -109,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -122,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -135,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -148,11 +153,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -171,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -197,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -210,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -223,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -236,11 +247,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index 59b6370741..9c47c715a0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -114,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -127,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -140,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -153,10 +157,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -166,10 +171,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -189,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -202,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -215,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -228,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -241,10 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -254,10 +265,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -277,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -303,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -316,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -329,10 +345,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -342,10 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -365,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -378,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -391,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -404,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -417,10 +439,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -430,10 +453,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index 4b1424f41d..8c6726dd8d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,11 +98,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -111,11 +112,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -124,11 +126,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -137,11 +140,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -150,11 +154,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -163,11 +168,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -186,11 +192,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,11 +206,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -212,11 +220,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -225,11 +234,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -238,11 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -251,11 +262,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -274,11 +286,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -287,11 +300,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -300,11 +314,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -313,11 +328,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -326,11 +342,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -339,11 +356,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -362,11 +380,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -375,11 +394,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -388,11 +408,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -401,11 +422,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -414,11 +436,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -427,11 +450,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
index 922a2d2a11..962754d863 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
index 84adee49a6..07cf133c7d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
index 3e5463c316..b6d94852fd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
index a6fd2411df..16ae6e6457 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
index 594123ddf8..3edfb2bec4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 16d1b0bd97..3d9224a449 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 982a3c1806..bb102d731a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index a8a7840a32..6db6d85773 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index bda9e10f3c..64ad80ab51 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 221bf629fb..d9c1650115 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 9def8c690a..1898589ca4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 20ad12619b..fd4cdafb4e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 40266505b0..7e6c977977 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index bb62460cf2..f33afe2ec5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index a9227a6401..1d010f61ff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
index 37fe20dca7..bcd43f34a8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
index 4eafcb85af..9a3ed84042 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
index 25e5751268..e682671edd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
index f7b24b2131..682135df7a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
index 61bfba4e75..363a5d4584 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
index 0c5c7a448b..2a8bf51834 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
index 52c4f4f6f8..40311e9356 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
index 6b167e952a..e59fc9b049 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -70,10 +70,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -83,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -109,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -122,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -135,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,10 +164,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -171,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -197,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -210,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -223,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index c347ea7f74..03670ee55a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -73,10 +73,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,10 +87,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,10 +167,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,10 +181,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -249,10 +261,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,10 +275,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -337,10 +355,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -350,10 +369,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index 1b6fdf8c43..bc24a62da2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -69,11 +69,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -82,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -95,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -108,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -121,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -134,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -157,11 +163,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -196,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -209,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -222,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 2a34878e80..23c1a2a136 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -75,10 +75,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,10 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,10 +103,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +117,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +131,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +145,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -176,10 +183,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +197,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +211,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +225,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +239,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,10 +277,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -277,10 +291,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +305,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +319,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +333,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -352,10 +371,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +385,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +399,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +413,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +427,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index 92d2b8ce0c..e952951819 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -72,11 +72,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -85,11 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -98,11 +100,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +114,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +128,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +142,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -160,11 +166,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,11 +180,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -186,11 +194,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +208,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +222,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +236,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -248,11 +260,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,11 +274,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,11 +288,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +302,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +316,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +330,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,11 +354,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -349,11 +368,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -362,11 +382,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +396,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +410,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +424,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
index f9d4c206bc..4c93412b8b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
index be7a260df0..3cc4606e24 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 2f8a663411..4b950af060 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -110,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -123,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -136,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -149,10 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -172,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -185,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -198,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -211,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -224,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -237,10 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
index d44dc93e16..d268ffdc29 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,10 +99,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +113,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +127,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +141,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -151,10 +155,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +193,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +207,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +221,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +235,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -239,10 +249,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -252,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +287,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +301,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +315,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +329,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,10 +343,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -340,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +381,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +395,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +409,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +423,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -415,10 +437,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -428,10 +451,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index ef85969448..12a268c27a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -109,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -122,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -135,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -148,11 +153,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -171,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -184,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -197,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -210,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -223,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -236,11 +247,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
index d5c9062374..1633321359 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -153,10 +157,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,10 +171,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -241,10 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -254,10 +265,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -277,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,10 +345,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -342,10 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -417,10 +439,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -430,10 +453,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 161d07ec52..b29ef01f9e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,11 +98,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +112,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +126,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +140,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -150,11 +154,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -163,11 +168,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -186,11 +192,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +206,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +220,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +234,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -238,11 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,11 +262,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,11 +286,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +300,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +314,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +328,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -326,11 +342,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,11 +356,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -362,11 +380,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +394,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +408,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +422,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -414,11 +436,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -427,11 +450,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
index 5f086bd889..33549ad913 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
index 8c9b645369..b8c9fbbc7e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
index bf9609b67b..b22f64932c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -97,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -110,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -123,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -136,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -149,10 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -172,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -185,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -198,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -211,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -224,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -237,10 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
index 090f74bb16..434bec1437 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,10 +99,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -112,10 +113,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,10 +127,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -138,10 +141,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -151,10 +155,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -164,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -187,10 +193,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -200,10 +207,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -213,10 +221,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,10 +235,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -239,10 +249,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -252,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -275,10 +287,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -288,10 +301,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -301,10 +315,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -314,10 +329,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -327,10 +343,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -340,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -363,10 +381,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -376,10 +395,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -389,10 +409,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -402,10 +423,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -415,10 +437,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -428,10 +451,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index c907452ecf..b64e8dbaec 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -96,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -109,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -122,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -135,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -148,11 +153,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -171,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -197,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -210,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -223,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -236,11 +247,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
index d09c4976ba..fea9f5a7b0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -114,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -127,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -140,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -153,10 +157,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -166,10 +171,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -189,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -202,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -215,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -228,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -241,10 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -254,10 +265,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -277,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -303,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -316,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -329,10 +345,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -342,10 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -365,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -378,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -391,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -404,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -417,10 +439,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -430,10 +453,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
index c322f5a43b..e32362aca0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,11 +98,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -111,11 +112,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -124,11 +126,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -137,11 +140,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -150,11 +154,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -163,11 +168,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -186,11 +192,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,11 +206,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -212,11 +220,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -225,11 +234,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -238,11 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -251,11 +262,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -274,11 +286,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -287,11 +300,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -300,11 +314,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -313,11 +328,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -326,11 +342,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -339,11 +356,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -362,11 +380,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -375,11 +394,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -388,11 +408,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -401,11 +422,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -414,11 +436,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -427,11 +450,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
index 59f6d3cadc..3a6ed49216 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
index 0a0a8600a3..b36f735aa9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
index 2cc04c4882..31b515c00b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
index 3b47a467d8..54a68c611a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
index d7c0ae209c..88c5f19992 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 0ddae0edea..4d3f035e60 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 8aa9ab8802..c480062590 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index cebf6859ea..c25e95d46a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index b4b1e0d722..8f63f2b2d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index f9f93ebcf3..505f4c1c0f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 0be6a0fa4e..25a4f401b1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index bbb398d1f5..6ce1635f91 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 25dc5aa761..cc40492811 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 2f56cf6794..13b104a97f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 3f88a65d7c..fa420703d2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
index 4c11b54983..4947a0b9c3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
index 37c9f0661e..9553614b91 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
index facf04d3db..9738cec169 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
index 8392c9d227..5f50fe8ef2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
index 735a25a7e4..9e954c6beb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
index aa81e8a0c7..c777f47565 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
index 6175abb89d..b5d6ffc73b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
index 65b0026fda..99a6714615 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -70,10 +70,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -83,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -109,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -122,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -135,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,10 +164,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -171,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -197,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -210,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -223,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index 561d69a340..e0b82123a7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -73,10 +73,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,10 +87,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,10 +167,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,10 +181,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -249,10 +261,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,10 +275,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -337,10 +355,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -350,10 +369,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index 36871adf9d..c97c693445 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -69,11 +69,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -82,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -95,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -108,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -121,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -134,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -157,11 +163,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -196,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -209,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -222,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index 9f6bd795ee..fbc62eeb89 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -75,10 +75,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,10 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,10 +103,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +117,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +131,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +145,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -176,10 +183,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +197,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +211,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +225,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +239,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,10 +277,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -277,10 +291,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +305,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +319,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +333,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -352,10 +371,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +385,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +399,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +413,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +427,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 2c389eeda4..342bd01612 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -72,11 +72,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -85,11 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -98,11 +100,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +114,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +128,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +142,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -160,11 +166,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,11 +180,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -186,11 +194,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +208,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +222,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +236,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -248,11 +260,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,11 +274,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,11 +288,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +302,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +316,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +330,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,11 +354,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -349,11 +368,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -362,11 +382,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +396,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +410,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +424,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
index a10b295fa8..53c6f1492b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
index c17b5a4efc..a822ec8120 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index 1cb70ea3bb..d3c6c99e8c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -70,10 +70,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -83,10 +84,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -96,10 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -109,10 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -122,10 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -135,10 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -158,10 +164,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -171,10 +178,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,10 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -197,10 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -210,10 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -223,10 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index 0461eeb076..90b48246d7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -73,10 +73,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,10 +87,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -99,10 +101,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,10 +115,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -125,10 +129,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -138,10 +143,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -161,10 +167,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,10 +181,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -187,10 +195,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,10 +209,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -213,10 +223,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,10 +237,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -249,10 +261,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,10 +275,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -275,10 +289,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -288,10 +303,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,10 +317,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -314,10 +331,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -337,10 +355,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -350,10 +369,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -363,10 +383,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -376,10 +397,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -389,10 +411,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -402,10 +425,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index 179cb57944..0cb5a8675e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -69,11 +69,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -82,11 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -95,11 +97,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -108,11 +111,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -121,11 +125,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -134,11 +139,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -157,11 +163,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,11 +177,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,11 +191,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -196,11 +205,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -209,11 +219,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -222,11 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index b5fd7e463d..fad227e7b6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -75,10 +75,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -88,10 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -101,10 +103,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -114,10 +117,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -127,10 +131,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -140,10 +145,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,10 +169,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -176,10 +183,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,10 +197,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -202,10 +211,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -215,10 +225,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,10 +239,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,10 +263,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,10 +277,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -277,10 +291,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,10 +305,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,10 +319,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -316,10 +333,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -339,10 +357,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -352,10 +371,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -365,10 +385,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -378,10 +399,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -391,10 +413,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -404,10 +427,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index 339799d820..018239315a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -72,11 +72,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -85,11 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -98,11 +100,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -111,11 +114,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -124,11 +128,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -137,11 +142,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -160,11 +166,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,11 +180,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -186,11 +194,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,11 +208,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -212,11 +222,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,11 +236,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -248,11 +260,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,11 +274,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,11 +288,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -287,11 +302,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,11 +316,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -313,11 +330,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,11 +354,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -349,11 +368,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -362,11 +382,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -375,11 +396,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -388,11 +410,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -401,11 +424,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 7797b17ed9..e0d595d3fd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index acd8abf567..a0183d2fea 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index f4b9b6e769..7aec7c1174 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,8 +84,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -95,8 +96,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,8 +108,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -117,8 +120,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -128,8 +132,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -139,8 +144,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -160,8 +166,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -171,8 +178,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -182,8 +190,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -193,8 +202,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -204,8 +214,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -215,8 +226,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index b6dad316fa..ca40ecf294 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,8 +111,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -121,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -132,8 +135,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -143,8 +147,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,8 +159,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,8 +181,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -186,8 +193,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -197,8 +205,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -208,8 +217,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,8 +229,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -230,8 +241,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -251,8 +263,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -262,8 +275,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -273,8 +287,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -284,8 +299,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -295,8 +311,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -306,8 +323,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,8 +345,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -338,8 +357,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -349,8 +369,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -360,8 +381,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -371,8 +393,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -382,8 +405,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 41fc7daa92..7ea596b97a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,9 +83,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -94,9 +95,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,9 +107,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -116,9 +119,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -127,9 +131,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -138,9 +143,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -159,9 +165,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -170,9 +177,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -181,9 +189,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,9 +201,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -203,9 +213,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -214,9 +225,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index a8ac6090d4..7cdf6e59e6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -112,8 +113,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -123,8 +125,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -134,8 +137,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,8 +149,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -156,8 +161,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -177,8 +183,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -188,8 +195,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,8 +207,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,8 +219,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -221,8 +231,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -232,8 +243,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -253,8 +265,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,8 +277,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -275,8 +289,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -286,8 +301,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -297,8 +313,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -308,8 +325,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,8 +347,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -340,8 +359,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -351,8 +371,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -362,8 +383,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -373,8 +395,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -384,8 +407,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index bf32c2f574..00ba9ae584 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,9 +98,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -109,9 +110,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -120,9 +122,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -131,9 +134,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -142,9 +146,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -153,9 +158,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -174,9 +180,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -185,9 +192,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -196,9 +204,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,9 +216,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -218,9 +228,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -229,9 +240,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -250,9 +262,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -261,9 +274,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -272,9 +286,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -283,9 +298,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,9 +310,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -305,9 +322,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -326,9 +344,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -337,9 +356,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -348,9 +368,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -359,9 +380,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -370,9 +392,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -381,9 +404,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 0d48ffc867..9619be16fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -67,8 +67,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -77,8 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -87,8 +89,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index ff5cba37d6..af23cd30e1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -68,8 +68,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -78,8 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -88,8 +90,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -98,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -108,8 +112,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
@@ -118,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 4b71d59261..e3da94ba96 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,8 +84,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -95,8 +96,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -106,8 +108,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -117,8 +120,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,8 +132,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -139,8 +144,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -160,8 +166,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -171,8 +178,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -182,8 +190,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -193,8 +202,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -204,8 +214,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -215,8 +226,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index fc95ee388b..000b03b922 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -110,8 +111,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -121,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -132,8 +135,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,8 +147,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -154,8 +159,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -175,8 +181,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -186,8 +193,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -197,8 +205,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -208,8 +217,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -219,8 +229,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -230,8 +241,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -251,8 +263,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,8 +275,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -273,8 +287,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -284,8 +299,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -295,8 +311,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -306,8 +323,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -327,8 +345,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -338,8 +357,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -349,8 +369,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -360,8 +381,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -371,8 +393,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -382,8 +405,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index c4d9853f8d..f17b4abda2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,9 +83,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -94,9 +95,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -105,9 +107,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -116,9 +119,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -127,9 +131,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -138,9 +143,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -159,9 +165,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -170,9 +177,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -181,9 +189,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -192,9 +201,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -203,9 +213,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -214,9 +225,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index 5d8d7ca8c7..d84c7f993c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,8 +101,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -112,8 +113,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -123,8 +125,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,8 +137,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -145,8 +149,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -156,8 +161,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -177,8 +183,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -188,8 +195,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,8 +207,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -210,8 +219,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -221,8 +231,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -232,8 +243,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -253,8 +265,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -264,8 +277,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -275,8 +289,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -286,8 +301,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -297,8 +313,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -308,8 +325,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -329,8 +347,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -340,8 +359,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -351,8 +371,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -362,8 +383,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -373,8 +395,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -384,8 +407,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index f6a72aee5e..e202b69597 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,9 +98,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -109,9 +110,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -120,9 +122,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -131,9 +134,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -142,9 +146,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -153,9 +158,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -174,9 +180,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -185,9 +192,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -196,9 +204,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,9 +216,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -218,9 +228,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -229,9 +240,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -250,9 +262,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -261,9 +274,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -272,9 +286,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -283,9 +298,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -294,9 +310,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -305,9 +322,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -326,9 +344,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -337,9 +356,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -348,9 +368,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -359,9 +380,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -370,9 +392,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -381,9 +404,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 221b5d1423..47dd50e920 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index 443f043456..9b0e361df1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index 82e53feddc..c5d012f06a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index 369c86f08b..4da146f811 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index fcaca72bb8..1c3d1b577b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index f994230a51..dcec602bad 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index cbc6b5b929..ac1f4606ed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index e45ee49e08..a693a8d3d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 4d7217100b..7a2c577e54 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 80d5ed0ce3..9c84941d6f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 63e9a1f60e..6de9b89901 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -84,6 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -93,6 +94,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -102,6 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -111,6 +114,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -120,6 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -129,6 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -148,6 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -157,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -166,6 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -175,6 +184,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -184,6 +194,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -193,6 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 0c955575e9..2626cd24da 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -99,6 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -108,6 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -117,6 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -126,6 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -135,6 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -144,6 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -163,6 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -172,6 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -181,6 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -190,6 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -199,6 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -208,6 +219,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -227,6 +239,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -236,6 +249,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -245,6 +259,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -254,6 +269,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -263,6 +279,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -272,6 +289,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -291,6 +309,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -300,6 +319,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -309,6 +329,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -318,6 +339,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -327,6 +349,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -336,6 +359,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index ea60efd4fd..2253e195ed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -83,7 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -92,7 +93,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
@@ -101,7 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -110,7 +113,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -119,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -128,7 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
@@ -147,7 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -156,7 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -165,7 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -174,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
@@ -183,7 +193,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
@@ -192,7 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 7381fcb251..83f1f49c29 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -101,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -110,6 +111,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -119,6 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -128,6 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -137,6 +141,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -146,6 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -165,6 +171,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -174,6 +181,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -183,6 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -192,6 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -201,6 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -210,6 +221,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -229,6 +241,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -238,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -247,6 +261,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -256,6 +271,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -265,6 +281,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -274,6 +291,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -293,6 +311,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -302,6 +321,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -311,6 +331,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -320,6 +341,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -329,6 +351,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -338,6 +361,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index cefe23f089..00805d7452 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -98,7 +98,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -107,7 +108,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -116,7 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -125,7 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -134,7 +138,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -143,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
@@ -162,7 +168,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -171,7 +178,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -180,7 +188,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -189,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -198,7 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -207,7 +218,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
@@ -226,7 +238,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -235,7 +248,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -244,7 +258,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -253,7 +268,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -262,7 +278,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -271,7 +288,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
@@ -290,7 +308,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -299,7 +318,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -308,7 +328,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -317,7 +338,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -326,7 +348,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
@@ -335,7 +358,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index 6a5dd6206d..f4775e4ff2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -70,6 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -79,6 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -88,6 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -97,6 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -106,6 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -115,6 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -134,6 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -143,6 +150,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -152,6 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -161,6 +170,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -170,6 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,6 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index b9284c26fd..007b8c717a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -73,6 +73,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -82,6 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -91,6 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -100,6 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -109,6 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -118,6 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -137,6 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -146,6 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -155,6 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -164,6 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,6 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -201,6 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -210,6 +223,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -219,6 +233,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -228,6 +243,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -237,6 +253,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -246,6 +263,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -265,6 +283,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -274,6 +293,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -283,6 +303,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -292,6 +313,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,6 +323,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -310,6 +333,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index 355ac1a61b..08ce32d959 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -69,7 +69,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -78,7 +79,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -87,7 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -96,7 +99,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -105,7 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -114,7 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -133,7 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -142,7 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -151,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -160,7 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -169,7 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index e82df8b127..44312bc9a4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -75,6 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,6 +85,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -93,6 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -102,6 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -111,6 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -120,6 +125,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -139,6 +145,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -148,6 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -157,6 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -166,6 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -175,6 +185,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,6 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,6 +215,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -212,6 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -221,6 +235,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -230,6 +245,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -239,6 +255,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -248,6 +265,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -267,6 +285,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -276,6 +295,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -285,6 +305,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -294,6 +315,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,6 +325,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -312,6 +335,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index c32a86f42e..d6ad3632c6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -72,7 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -90,7 +92,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -99,7 +102,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -108,7 +112,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -117,7 +122,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -136,7 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -145,7 +152,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -154,7 +162,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -163,7 +172,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -172,7 +182,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,7 +192,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -200,7 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -209,7 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -218,7 +232,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -227,7 +242,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -236,7 +252,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -245,7 +262,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -264,7 +282,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -273,7 +292,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -282,7 +302,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -291,7 +312,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -300,7 +322,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -309,7 +332,8 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 8952f57d1b..9a63687952 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -65,8 +65,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -75,8 +76,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
@@ -85,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index 3558d069dd..3665094082 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -66,8 +66,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -76,8 +77,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -86,8 +88,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -96,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -106,8 +110,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
@@ -116,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index b22ff9a1f8..2ead917c5f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -70,8 +70,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -81,8 +82,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -92,8 +94,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -103,8 +106,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -114,8 +118,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -125,8 +130,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -146,8 +152,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -157,8 +164,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -168,8 +176,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -179,8 +188,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -190,8 +200,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
@@ -201,8 +212,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 8753a3a796..8e83ab7d4b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -73,8 +73,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -84,8 +85,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -95,8 +97,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -106,8 +109,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -117,8 +121,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -128,8 +133,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -149,8 +155,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -160,8 +167,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -171,8 +179,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -182,8 +191,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -193,8 +203,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -204,8 +215,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -225,8 +237,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -236,8 +249,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -247,8 +261,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -258,8 +273,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -269,8 +285,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -280,8 +297,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -301,8 +319,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -312,8 +331,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -323,8 +343,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -334,8 +355,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -345,8 +367,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -356,8 +379,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index ace5865d75..2d6b0df100 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -69,9 +69,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -80,9 +81,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -91,9 +93,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -102,9 +105,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -113,9 +117,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -124,9 +129,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
@@ -145,9 +151,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -156,9 +163,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -167,9 +175,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -178,9 +187,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -189,9 +199,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
@@ -200,9 +211,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 6bc7a680fc..f45d49c8ab 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -75,8 +75,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -86,8 +87,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -97,8 +99,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -108,8 +111,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -119,8 +123,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -130,8 +135,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -151,8 +157,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -162,8 +169,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -173,8 +181,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -184,8 +193,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -195,8 +205,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -206,8 +217,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -227,8 +239,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -238,8 +251,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -249,8 +263,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -260,8 +275,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -271,8 +287,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -282,8 +299,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -303,8 +321,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -314,8 +333,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -325,8 +345,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -336,8 +357,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -347,8 +369,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -358,8 +381,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
   alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)) * area_elem_quad/Jc_quad; 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index fc837435b4..eb9fbe0b7a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -72,9 +72,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -83,9 +84,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -94,9 +96,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -105,9 +108,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -116,9 +120,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -127,9 +132,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
@@ -148,9 +154,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -159,9 +166,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -170,9 +178,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -181,9 +190,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -192,9 +202,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -203,9 +214,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
@@ -224,9 +236,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -235,9 +248,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -246,9 +260,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -257,9 +272,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -268,9 +284,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -279,9 +296,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
@@ -300,9 +318,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -311,9 +330,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -322,9 +342,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -333,9 +354,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -344,9 +366,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
@@ -355,9 +378,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad))*area_elem_quad/Jc_quad; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_)*area_elem_quad/Jc_quad; 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)) * area_elem_quad/Jc_quad; 
+  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
+  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
   JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 

From 59fa6508c6fc1b948bc37d9093fe68bafeb58a7d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 8 Apr 2026 10:10:31 -0400
Subject: [PATCH 132/181] =?UTF-8?q?try=20a=20reformulation=20of=20the=20vp?=
 =?UTF-8?q?ar=20surf=20flux=20kernel=20using=20=E2=88=87Apar=20x=20b=20.?=
 =?UTF-8?q?=20=E2=88=87H=20=3D=20=E2=88=87H=20x=20=E2=88=87Apar=20.=20b?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c | 24 ++---
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c | 96 +++++++++----------
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c | 24 ++---
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c | 96 +++++++++----------
 4 files changed, 112 insertions(+), 128 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index e916a91757..b9c0556e80 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -75,8 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -90,8 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -117,8 +115,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -132,8 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -159,8 +155,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -174,8 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -201,8 +195,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -216,8 +209,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index a1315546c2..e2ef670d8d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -80,11 +80,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -98,11 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -128,11 +128,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -146,11 +146,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -176,11 +176,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -194,11 +194,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -224,11 +224,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -242,11 +242,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -272,11 +272,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -290,11 +290,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -320,11 +320,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -338,11 +338,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -368,11 +368,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -386,11 +386,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -416,11 +416,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -434,11 +434,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index 96d0890885..a332f9b5f6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -75,8 +75,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -91,8 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -119,8 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -135,8 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -163,8 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -179,8 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -207,8 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -223,8 +216,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (-g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*rdz2)); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * ( g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*rdx2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index 8749770574..e3e0d57a11 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -80,11 +80,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -99,11 +99,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -130,11 +130,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -149,11 +149,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -180,11 +180,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -199,11 +199,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -230,11 +230,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -249,11 +249,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -280,11 +280,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -299,11 +299,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -330,11 +330,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -349,11 +349,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -380,11 +380,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -399,11 +399,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -430,11 +430,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -449,11 +449,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2) - g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*rdz2) - g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * 1/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*rdx2) - g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*rdy2)); 
+  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;

From c91b27eda87e5e2caa3c7becc60257dccdd5655e Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 8 Apr 2026 11:05:55 -0400
Subject: [PATCH 133/181] use bioverJB instead of the e_3_mag and metric tensor
 component

---
 ...nless_flux_em_no_by_surfvpar_2x2v_ser_p1.c |  44 +--
 ...nless_flux_em_no_by_surfvpar_3x2v_ser_p1.c |  80 ++----
 ..._flux_em_star_no_by_surfvpar_2x2v_ser_p1.c |  44 +--
 ..._flux_em_star_no_by_surfvpar_3x2v_ser_p1.c |  80 ++----
 ...onless_flux_em_star_surfvpar_1x1v_ser_p1.c |  30 +-
 ...onless_flux_em_star_surfvpar_1x2v_ser_p1.c |  34 +--
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c |  92 +++---
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c | 272 ++++++++----------
 ...llisionless_flux_em_surfvpar_1x1v_ser_p1.c |  30 +-
 ...llisionless_flux_em_surfvpar_1x2v_ser_p1.c |  34 +--
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  92 +++---
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c | 272 ++++++++----------
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |   5 -
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |   9 -
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |   3 -
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |   3 -
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |   5 -
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |   9 -
 gyrokinetic/zero/gk_dg_geom.c                 |   6 +
 gyrokinetic/zero/gkyl_gk_dg_geom.h            |   1 +
 20 files changed, 439 insertions(+), 706 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
index 0a5d9c3bdd..5a7695a864 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
@@ -44,31 +44,22 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
@@ -92,15 +83,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
@@ -124,15 +112,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
@@ -156,15 +141,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
index 83850b2dcb..7de5131f8b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
@@ -49,31 +49,22 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -97,15 +88,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -129,15 +117,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -161,15 +146,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -193,15 +175,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -225,15 +204,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -257,15 +233,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
@@ -289,15 +262,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
index d17d941b99..a4d4852316 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
@@ -44,31 +44,22 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -90,15 +81,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -120,15 +108,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -150,15 +135,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
index d34e10d738..9db01b0ddb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
@@ -49,31 +49,22 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -95,15 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -125,15 +113,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -155,15 +140,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -185,15 +167,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -215,15 +194,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -245,15 +221,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
@@ -275,15 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
index e0c6aa029e..81863bd899 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
@@ -37,35 +37,26 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
@@ -76,19 +67,16 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
index 8fb9185a77..d86d28cdd8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
@@ -39,35 +39,26 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -78,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -89,19 +80,16 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -112,7 +100,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index b9c0556e80..468c7ebeeb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -44,38 +44,29 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -87,9 +78,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -100,22 +91,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -127,9 +115,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -140,22 +128,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -167,9 +152,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -180,22 +165,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -207,9 +189,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index e2ef670d8d..0df2c1103b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -49,42 +49,33 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -97,12 +88,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -113,26 +104,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -145,12 +133,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -161,26 +149,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -193,12 +178,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -209,26 +194,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -241,12 +223,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -257,26 +239,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -289,12 +268,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -305,26 +284,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -337,12 +313,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -353,26 +329,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -385,12 +358,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -401,26 +374,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -433,12 +403,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
index 8c97527add..cc407711b2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
@@ -37,35 +37,26 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -77,19 +68,16 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
index 384ab7c242..23fb41943f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
@@ -39,35 +39,26 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -79,7 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -91,19 +82,16 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -115,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*m_bmag_inv * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index a332f9b5f6..e22733ed54 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -44,38 +44,29 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -88,9 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -102,22 +93,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -130,9 +118,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -144,22 +132,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -172,9 +157,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -186,22 +171,19 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -214,9 +196,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*m_bmag_inv * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2)); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index e3e0d57a11..e69f21d77b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -49,42 +49,33 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double m_bmag_inv = 0.0; 
-  double mvpar_over_q = 0.0; 
-  double  g_13 = 0.0; 
-  double  g_23 = 0.0; 
-  double  g_33 = 0.0; 
-  double  mag_e_3 = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[0].g_13; 
-  g_23 = gkdgv[0].g_23; 
-  g_33 = gkdgv[0].g_33; 
-  mag_e_3 = gkdgv[0].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -98,12 +89,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -115,26 +106,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[1].g_13; 
-  g_23 = gkdgv[1].g_23; 
-  g_33 = gkdgv[1].g_33; 
-  mag_e_3 = gkdgv[1].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -148,12 +136,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -165,26 +153,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[2].g_13; 
-  g_23 = gkdgv[2].g_23; 
-  g_33 = gkdgv[2].g_33; 
-  mag_e_3 = gkdgv[2].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -198,12 +183,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -215,26 +200,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[3].g_13; 
-  g_23 = gkdgv[3].g_23; 
-  g_33 = gkdgv[3].g_33; 
-  mag_e_3 = gkdgv[3].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -248,12 +230,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -265,26 +247,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[4].g_13; 
-  g_23 = gkdgv[4].g_23; 
-  g_33 = gkdgv[4].g_33; 
-  mag_e_3 = gkdgv[4].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -298,12 +277,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -315,26 +294,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[5].g_13; 
-  g_23 = gkdgv[5].g_23; 
-  g_33 = gkdgv[5].g_33; 
-  mag_e_3 = gkdgv[5].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -348,12 +324,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -365,26 +341,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[6].g_13; 
-  g_23 = gkdgv[6].g_23; 
-  g_33 = gkdgv[6].g_33; 
-  mag_e_3 = gkdgv[6].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -398,12 +371,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -415,26 +388,23 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  m_bmag_inv = 1.0/(m_*bmag_quad); 
-  g_13 = gkdgv[7].g_13; 
-  g_23 = gkdgv[7].g_23; 
-  g_33 = gkdgv[7].g_33; 
-  mag_e_3 = gkdgv[7].mag_e_3; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -448,12 +418,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_13 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_23 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2)); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*m_bmag_inv * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -1/m_/bmag_quad/mag_e_3/Jc_quad * (g_33 * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2)); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index dac0eb306d..d87bbae7cc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -44,7 +44,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -54,7 +53,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -79,7 +77,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
@@ -104,7 +101,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
@@ -129,7 +125,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index bc4e135bb5..2a02044eb8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -49,7 +49,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -59,7 +58,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -84,7 +82,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
@@ -109,7 +106,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
@@ -134,7 +130,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
@@ -159,7 +154,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
@@ -184,7 +178,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
@@ -209,7 +202,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
@@ -234,7 +226,6 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index 786ebf6bcc..f15895d3c4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -37,7 +37,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -47,7 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -64,7 +62,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 7417d4164d..3039e2e84a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -39,7 +39,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -49,7 +48,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -76,7 +74,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 7ff1b44199..1b6b303679 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -44,7 +44,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -54,7 +53,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -83,7 +81,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
@@ -112,7 +109,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
@@ -141,7 +137,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 0ceca0c8cf..f328a124fe 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -49,7 +49,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
   double B3_quad = 0.0; 
-  double Jc_quad = 0.0; 
   double dualcurlbhat_quad[3] = {0.0}; 
   double alpha_quad = 0.0; 
   double JfL_quad = 0.0; 
@@ -59,7 +58,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
-  Jc_quad = dgv[0].Jc; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
@@ -90,7 +88,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[1].bmag; 
   B3_quad = gkdgv[1].B3; 
-  Jc_quad = dgv[1].Jc; 
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
@@ -121,7 +118,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[2].bmag; 
   B3_quad = gkdgv[2].B3; 
-  Jc_quad = dgv[2].Jc; 
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
@@ -152,7 +148,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[3].bmag; 
   B3_quad = gkdgv[3].B3; 
-  Jc_quad = dgv[3].Jc; 
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
@@ -183,7 +178,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[4].bmag; 
   B3_quad = gkdgv[4].B3; 
-  Jc_quad = dgv[4].Jc; 
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
@@ -214,7 +208,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[5].bmag; 
   B3_quad = gkdgv[5].B3; 
-  Jc_quad = dgv[5].Jc; 
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
@@ -245,7 +238,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[6].bmag; 
   B3_quad = gkdgv[6].B3; 
-  Jc_quad = dgv[6].Jc; 
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
@@ -276,7 +268,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
 
   bmag_quad = gkdgv[7].bmag; 
   B3_quad = gkdgv[7].B3; 
-  Jc_quad = dgv[7].Jc; 
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
diff --git a/gyrokinetic/zero/gk_dg_geom.c b/gyrokinetic/zero/gk_dg_geom.c
index be48188840..6348a9ef12 100644
--- a/gyrokinetic/zero/gk_dg_geom.c
+++ b/gyrokinetic/zero/gk_dg_geom.c
@@ -169,6 +169,12 @@ gkyl_gk_dg_geom_populate_vol(struct gkyl_dg_geom *dg_geom, struct gkyl_gk_dg_geo
 
       // set magnitude of e_3
       gkdgv[qvloc].mag_e_3 = sqrt(gkdgv[qvloc].g_33); // |e_3|
+
+      // set b_i/J_c/B
+      global_val = gkyl_array_cfetch(gk_geom->geo_int.bioverJB_nodal, global_loc);
+      gkdgv[qvloc].bioverJB.x[0] = global_val[0];
+      gkdgv[qvloc].bioverJB.x[1] = global_val[1];
+      gkdgv[qvloc].bioverJB.x[2] = global_val[2];
     }
   }
 }
diff --git a/gyrokinetic/zero/gkyl_gk_dg_geom.h b/gyrokinetic/zero/gkyl_gk_dg_geom.h
index 4cfb0768f8..2ce47525bb 100644
--- a/gyrokinetic/zero/gkyl_gk_dg_geom.h
+++ b/gyrokinetic/zero/gkyl_gk_dg_geom.h
@@ -28,6 +28,7 @@ struct gkyl_gk_dg_vol_geom {
   double g_23; // metric tensor component g_{23} = e_2 . e_3
   double g_33; // metric tensor component g_{33} = e_3 . e_3
   double mag_e_3; // magnitude of e_3
+  struct gkyl_vec3 bioverJB; // b_i/J_c/B
 };
 
 

From 72a597a8d218ad375cbb21ae545c89dc712c56bb Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 9 Apr 2026 14:21:06 -0400
Subject: [PATCH 134/181] =?UTF-8?q?the=20sign=20of=20the=20v=20parallel=20?=
 =?UTF-8?q?surface=20flux=20=E2=88=87A=20x=20b=20.=20=E2=88=87H=20term=20w?=
 =?UTF-8?q?as=20wrong,=20thanks=20@akashukla?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c |  13 --
 .../dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c |  22 ---
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c |  48 +++----
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c | 128 +++++++++---------
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c |  16 +--
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c |  96 ++++++-------
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  16 +--
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  96 ++++++-------
 8 files changed, 200 insertions(+), 235 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
index 2c9e566d31..f29ff1cb68 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
@@ -47,25 +47,12 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   hamil2[1] = hamil[4]*hamil[4]; 
 
   double alphax[6] = {0.}; 
-  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
-  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
-  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+1.5811388300841895*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdx2)/(vmap[1]*m_); 
-  alphax[3] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+1.5811388300841895*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdx2)/(vmap[1]*m_); 
 
 
-  out[1] += 0.8660254037844386*(alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
-  out[3] += 0.7745966692414834*alphax[3]*fin[5]+0.7745966692414833*alphax[2]*fin[4]+0.8660254037844386*(alphax[1]*fin[3]+fin[1]*alphax[3]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
-  out[5] += 0.8660254037844386*alphax[1]*fin[5]+0.8660254037844387*alphax[0]*fin[4]+0.7745966692414834*(alphax[3]*fin[3]+alphax[2]*fin[2]); 
 
   double alphavpar[6] = {0.}; 
-  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
-  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
 
 
-  out[2] += 0.8660254037844386*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[3] += 0.8660254037844386*(alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[4] += 1.9364916731037085*(alphavpar[1]*fin[3]+alphavpar[0]*fin[2]); 
-  out[5] += 1.9364916731037085*(alphavpar[0]*fin[3]+alphavpar[1]*fin[2]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
index 0cf6e8271f..7867f153e4 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
@@ -50,34 +50,12 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[8]*hamil[8]; 
 
   double alphax[12] = {0.}; 
-  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
-  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
-  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]+1.5811388300841895*apar[0]*dualcurlbhatoverB_z[0]*hamil[8])*rdx2)/(vmap[1]*m_); 
-  alphax[4] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]+1.5811388300841895*dualcurlbhatoverB_z[0]*apar[1]*hamil[8])*rdx2)/(vmap[1]*m_); 
 
 
-  out[1] += 0.6123724356957944*(alphax[4]*fin[4]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
-  out[4] += 0.5477225575051661*(alphax[4]*fin[9]+alphax[2]*fin[8])+0.6123724356957944*(alphax[1]*fin[4]+fin[1]*alphax[4]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
-  out[5] += 0.6123724356957944*(alphax[4]*fin[7]+alphax[2]*fin[6]+alphax[1]*fin[5]+alphax[0]*fin[3]); 
-  out[7] += 0.5477225575051661*(alphax[4]*fin[11]+alphax[2]*fin[10])+0.6123724356957944*(alphax[1]*fin[7]+alphax[0]*fin[6]+alphax[4]*fin[5]+alphax[2]*fin[3]); 
-  out[9] += 0.6123724356957944*(alphax[1]*fin[9]+alphax[0]*fin[8])+0.5477225575051661*(alphax[4]*fin[4]+alphax[2]*fin[2]); 
-  out[11] += 0.6123724356957944*(alphax[1]*fin[11]+alphax[0]*fin[10])+0.5477225575051661*(alphax[4]*fin[7]+alphax[2]*fin[6]); 
 
   double alphavpar[12] = {0.}; 
-  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
-  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
-  alphavpar[3] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_z[1]*hamil[5])-0.7071067811865475*apar[0]*dualcurlbhatoverB_z[0]*hamil[5])*rdx2)/(vmap[1]*m_); 
-  alphavpar[5] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_z[1]*hamil[5])-0.7071067811865475*dualcurlbhatoverB_z[0]*apar[1]*hamil[5])*rdx2)/(vmap[1]*m_); 
 
 
-  out[2] += 0.6123724356957944*(alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
-  out[4] += 0.6123724356957944*(alphavpar[3]*fin[5]+fin[3]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
-  out[6] += 0.6123724356957944*(alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
-  out[7] += 0.6123724356957944*(alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
-  out[8] += 1.369306393762915*(alphavpar[5]*fin[7]+alphavpar[3]*fin[6]+alphavpar[1]*fin[4]+alphavpar[0]*fin[2]); 
-  out[9] += 1.369306393762915*(alphavpar[3]*fin[7]+alphavpar[5]*fin[6]+alphavpar[0]*fin[4]+alphavpar[1]*fin[2]); 
-  out[10] += 1.369306393762915*(alphavpar[1]*fin[7]+alphavpar[0]*fin[6]+fin[4]*alphavpar[5]+fin[2]*alphavpar[3]); 
-  out[11] += 1.369306393762915*(alphavpar[0]*fin[7]+alphavpar[1]*fin[6]+fin[2]*alphavpar[5]+alphavpar[3]*fin[4]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index a5bad6c840..57e728ad3b 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = (((-(0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[0]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[3])-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_y[3]*hamil[16])-1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_x[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_x[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[0] = ((-(0.6123724356957944*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]-0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[1] = ((-(1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*apar[2]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]-0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[2] = ((-(0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[3] = ((-(1.369306393762915*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[5] = ((-(0.5511351921262146*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.5511351921262146*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[2]*hamil[3]*jacobtot_inv[3]-1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[6] = ((-(2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.232375754386623*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]-1.369306393762915*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]-1.232375754386623*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[7] = ((-(0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16])-0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[11] = ((-(1.232375754386623*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.232375754386623*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[16]-2.4647515087732463*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -79,14 +79,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = (((0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((1.369306393762915*bioverJB_y[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_y[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[0]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[3]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_y[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((1.369306393762915*bioverJB_y[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_y[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_y[3]*hamil[16]+1.369306393762915*bioverJB_y[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_z[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_z[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = ((0.6123724356957944*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[1] = ((0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[2] = ((1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[3] = ((1.369306393762915*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[5] = ((0.5511351921262146*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[6] = ((0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[7] = ((2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+1.232375754386623*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+1.232375754386623*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[11] = ((1.232375754386623*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.232375754386623*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+2.4647515087732463*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]+0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -103,14 +103,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[5]-0.6123724356957944*bioverJB_y[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_z[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[5]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_y[3]+0.6123724356957944*bioverJB_y[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[2]+0.6123724356957944*bioverJB_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_x[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_x[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[5])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[12]-0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[5])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_y[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_y[3]-0.6123724356957944*bioverJB_y[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_y[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_z[3]-0.3535533905932737*dualcurlbhatoverB_z[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.3535533905932737*dualcurlbhatoverB_x[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_x[2]-0.3535533905932737*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[1]*hamil[9]+0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_z[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[12])+0.6123724356957944*bioverJB_y[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_y[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_y[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_x[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_y[2]*hamil[12])+0.6123724356957944*bioverJB_y[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_y[3]*hamil[9]-0.6123724356957944*bioverJB_y[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_y[3]*hamil[8]+0.6123724356957944*bioverJB_y[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_z[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_z[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_z[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_z[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_z[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_x[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_x[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_x[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_x[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[5])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[5]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[5]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[5]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[5]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3]-0.6123724356957944*b_y[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*b_y[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*jacobtot_inv[2]*apar[3]*b_y[3]-0.6123724356957944*jacobtot_inv[1]*hamil[2]*apar[3]*b_y[3]-0.3061862178478971*apar[0]*hamil[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[0]*apar[2]*hamil[2]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]-0.3061862178478971*b_y[0]*hamil[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*hamil[2]*apar[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[2]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[2]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[2]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[2]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[2]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[5])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[5]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[5]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[5]+1.1022703842524295*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*hamil[2]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*hamil[2]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*hamil[2]*apar[3]*b_y[3]-0.6123724356957944*apar[1]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.6123724356957944*hamil[1]*apar[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[1]*apar[2]*hamil[2]*b_y[3]+0.5511351921262146*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]-0.6123724356957944*b_y[1]*hamil[2]*jacobtot_inv[2]*apar[3]+0.6123724356957944*hamil[1]*b_y[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*hamil[2]*apar[3]+0.5511351921262146*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[2]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[2]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[2]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[2] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[5]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[5]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[5]-1.1022703842524295*hamil[2]*apar[3]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3]-0.5511351921262146*apar[2]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.6123724356957944*apar[1]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[2]*b_y[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3]-0.5511351921262146*b_y[2]*hamil[2]*jacobtot_inv[2]*apar[3]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[2]*apar[3]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*b_y[2]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[2]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[2]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[4] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[12])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[12]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[12]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[12]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[12]-0.6123724356957944*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[9]+0.6123724356957944*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[5] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[5]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[5]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[5]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[5]-0.5511351921262146*apar[2]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.5511351921262146*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]-0.5511351921262146*b_y[2]*hamil[2]*apar[3]*jacobtot_inv[3]+0.5511351921262146*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[3]-1.1022703842524295*hamil[2]*jacobtot_inv[2]*apar[3]*b_y[3]+1.1022703842524295*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.6123724356957944*jacobtot_inv[0]*apar[1]*hamil[2]*b_y[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*hamil[2]*apar[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*b_y[2]*apar[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[2]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[2]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[8] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[12]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[12]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[12]-0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[9]+1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[8]+0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[8]+0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[9] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[12]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[12]-1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[9]-0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[9]+0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[12] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[12]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[12]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[9]-1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[9]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[9]+0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[8]+1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
index 898842baeb..2cbc2e69ad 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -60,22 +60,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7]+0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[6]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5])-0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5]+0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[4] = (((-(0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[0]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_x[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_y[5])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7])-0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[9] = (((-(0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[10] = (((-(0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[16] = (((-(0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_x[5]+0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
-  alphax[17] = (((-(0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_y[5]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_z[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_z[5]*hamil[32]+0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_x[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[19] = (((-(0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[3]*hamil[32])*rdx2)/vmap[1])/m_; 
-  alphax[26] = (((-(0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_y[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_x[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_x[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_x[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.21650635094610965*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]-0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]+0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*apar[3]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_z[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]+0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[2] = ((-(0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]-0.21650635094610965*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[3] = (((-(0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.4841229182759271*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[6] = ((-(0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7])-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[7] = (((-(0.19485571585149863*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.19485571585149863*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[3]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]+0.19485571585149863*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[2]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[8] = ((-(0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[9] = (((-(0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.43571062644833425*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]+0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[10] = ((-(0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]-0.4841229182759271*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[11] = (((-(0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]+0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[16] = ((-(0.19485571585149863*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[17] = ((-(0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[18] = (((-(0.43571062644833425*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.7842791276070014*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]+0.43571062644833425*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphax[19] = ((-(0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[26] = ((-(0.43571062644833425*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -104,22 +104,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[1] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_z[5])-0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[2] = (((0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_x[5]+0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[4] = (((0.6846531968814573*bioverJB_x[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[0]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[6] = (((0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_z[5]*apar[7])-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_y[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_x[5]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_z[5])-0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7]+0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[9] = (((0.6846531968814573*bioverJB_x[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_z[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[10] = (((0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_x[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_z[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[16] = (((0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_y[5]+0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
-  alphay[17] = (((0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_x[5]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_z[5]*hamil[32])-0.6846531968814573*bioverJB_z[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_y[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[19] = (((0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[3]*hamil[32])*rdy2)/vmap[1])/m_; 
-  alphay[26] = (((0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_z[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_z[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_y[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_y[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_y[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[0] = (((0.21650635094610965*apar[3]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*b_x[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[5]+0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[4]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*apar[1]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*b_z[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.38971143170299727*hamil[4]*apar[5]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*apar[3]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_x[5]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[0]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.10825317547305482*b_z[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_z[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]+0.21650635094610965*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.10825317547305482*apar[0]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*apar[5]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*apar[1]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_z[5]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.4841229182759271*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.38971143170299727*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.19485571585149863*apar[1]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[3]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[3]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.19485571585149863*b_z[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*apar[1]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[5]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]-0.21650635094610965*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.8714212528966685*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.43571062644833425*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]+0.4841229182759271*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.24206145913796356*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[32]-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.8714212528966685*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.43571062644833425*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]-0.4841229182759271*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]-0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
 
 
   out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -148,22 +148,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[7])-0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((-(0.3061862178478971*bioverJB_x[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_y[5]+0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.3061862178478971*bioverJB_y[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((-(0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_x[5]-0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[4] = (((-(0.6846531968814573*bioverJB_x[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[0]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_z[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((-(0.3061862178478971*bioverJB_x[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_x[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_x[5]-0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[8] = (((0.3061862178478971*bioverJB_y[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[9] = (((-(0.6846531968814573*bioverJB_x[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_x[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_y[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[10] = (((0.6846531968814573*bioverJB_y[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((-(0.6846531968814573*bioverJB_x[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_x[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_y[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[16] = (((0.3061862178478971*bioverJB_y[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_z[5]+0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
-  alphaz[17] = (((0.6846531968814573*bioverJB_y[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[18] = (((-(0.6846531968814573*bioverJB_x[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_x[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_x[5]*hamil[32]-0.6846531968814573*bioverJB_x[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_y[5]*hamil[32]+0.6846531968814573*bioverJB_y[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_z[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[19] = (((0.6846531968814573*bioverJB_y[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[3]*hamil[32])*rdz2)/vmap[1])/m_; 
-  alphaz[26] = (((0.6846531968814573*bioverJB_y[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_y[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_z[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_z[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_z[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = (((-(0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[4]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.21650635094610965*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[2] = ((0.21650635094610965*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[3] = (((-(0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.4841229182759271*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[6] = ((0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[7] = (((-(0.35074028853269745*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]-0.19485571585149863*b_x[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*apar[2]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*apar[1]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[8] = ((0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]+0.21650635094610965*b_y[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[9] = (((-(0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]-0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[10] = ((0.4841229182759271*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[11] = (((-(0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]-0.43571062644833425*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[16] = ((0.19485571585149863*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_y[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[17] = ((0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[18] = (((-(0.7842791276070014*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]-0.43571062644833425*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.43571062644833425*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
+  alphaz[19] = ((0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]+0.4841229182759271*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[26] = ((0.43571062644833425*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]+0.43571062644833425*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -192,22 +192,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[16])-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_x[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[7]+0.3061862178478971*bioverJB_y[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[8]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_z[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[5]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[8]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_x[5]*apar[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_y[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_y[5]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[3]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[7]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[7]+0.3061862178478971*bioverJB_z[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_z[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_z[5]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[2]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_y[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_x[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[7]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[3] = (((-(0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[7]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_x[5]*hamil[6]-0.3061862178478971*bioverJB_x[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_x[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_x[5]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[7]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_z[5]*hamil[6]+0.3061862178478971*bioverJB_z[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[21]-0.3061862178478971*bioverJB_z[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[6] = (((0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_x[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_x[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_x[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[8]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_y[5]*apar[7]+0.3061862178478971*bioverJB_y[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_y[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_z[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[16]+0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_z[5]*apar[7]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[7] = (((-(0.5511351921262146*bioverJB_x[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_x[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_x[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_x[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[7]+0.3061862178478971*bioverJB_x[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_x[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_x[3]*hamil[6]+0.3061862178478971*bioverJB_x[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_x[5]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[5]+0.3061862178478971*bioverJB_x[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[7]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_y[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_y[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_y[5]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_z[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_z[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_z[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_z[1]*hamil[8]-0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_z[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_z[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_z[3]*hamil[6]-0.3061862178478971*bioverJB_z[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_z[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_z[5]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_y[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_y[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_y[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_y[3]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_x[5]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_x[3]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[16]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[8]-0.3061862178478971*bioverJB_x[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[7]-0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[16])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[8]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[7]-0.3061862178478971*bioverJB_y[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[6]-0.3061862178478971*bioverJB_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_z[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_z[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_y[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[3])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((0.5511351921262146*bioverJB_x[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_x[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[1]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_z[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[13] = (((0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[14] = (((0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[21]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_x[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_x[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[21])+0.3061862178478971*bioverJB_y[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_y[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_z[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_x[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[8]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_x[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_x[3]*apar[7]-0.3061862178478971*bioverJB_x[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_x[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[16])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[8]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_y[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_y[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[6]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_y[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_y[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_z[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_z[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_z[5]-0.1767766952966368*dualcurlbhatoverB_z[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_z[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_z[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_z[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_z[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_y[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_y[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_y[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_y[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_y[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_y[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_y[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_y[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_y[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_y[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_x[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_x[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_x[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_x[3]*apar[4])*rdx2)/vmap[1])/m_; 
-  alphavpar[20] = (((0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[21] = (((0.5511351921262146*bioverJB_x[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_x[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_x[3]*hamil[21]+0.3061862178478971*bioverJB_x[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_x[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_x[5]*hamil[14]+0.3061862178478971*bioverJB_x[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_y[3]*hamil[21])+0.3061862178478971*bioverJB_y[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_y[5]*hamil[14]-0.3061862178478971*bioverJB_y[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_y[5]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_z[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_z[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_z[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_z[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_z[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_z[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_z[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_z[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_z[5]*hamil[12]-0.3061862178478971*bioverJB_z[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_x[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_x[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[22] = (((0.3061862178478971*bioverJB_y[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[21]-0.3061862178478971*bioverJB_y[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_y[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[3]*hamil[12])*rdx2)/vmap[1])/m_; 
-  alphavpar[27] = (((0.3061862178478971*bioverJB_y[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_y[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_y[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_y[5]*hamil[14]+0.3061862178478971*bioverJB_y[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_y[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_z[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_z[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_z[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_z[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_z[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_x[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_x[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_x[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_x[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_x[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((-(0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[7]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[6]+0.10825317547305482*apar[2]*hamil[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*b_x[3]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[5]*b_x[5]+0.10825317547305482*hamil[3]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[4]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[3]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[3]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[3]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[8]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[6]*apar[7]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[6]-0.21650635094610965*apar[1]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*b_y[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*apar[5]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*hamil[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[3]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[16]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.38971143170299727*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.21650635094610965*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[8]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[7]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[7]+0.10825317547305482*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[6]+0.21650635094610965*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[6]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[6]+0.21650635094610965*apar[1]*hamil[2]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[5]*jacobtot_inv[5]+0.21650635094610965*b_z[1]*hamil[2]*apar[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[5]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[3]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[4]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[3]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[3]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[2]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[2]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[16]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[7]+0.19485571585149863*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[6]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[6]-0.38971143170299727*hamil[2]*apar[5]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*hamil[3]*apar[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_x[5]-0.21650635094610965*hamil[2]*apar[3]*jacobtot_inv[3]*b_x[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[5]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[5]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[5]+0.10825317547305482*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[4]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[3]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[16]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]-0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[7]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[6]*apar[7]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[6]+0.38971143170299727*hamil[1]*apar[5]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[5]*b_y[5]-0.21650635094610965*apar[1]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.21650635094610965*hamil[1]*apar[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[3]*b_y[5]+0.19485571585149863*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[5]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[16]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[7]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[6]-0.19485571585149863*hamil[1]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_z[5]+0.21650635094610965*apar[1]*hamil[2]*jacobtot_inv[3]*b_z[5]-0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*apar[3]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[4]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[2]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[2]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[16])-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[8]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*hamil[6]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[6]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[7]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.21650635094610965*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[6]-0.21650635094610965*hamil[3]*apar[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_y[5]-0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[4]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[16]+0.38971143170299727*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[8]+0.21650635094610965*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[2]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[4]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[16]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[16]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[7]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[6]-0.10825317547305482*apar[0]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[1]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[16]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[16]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[8]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[7]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[6]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[6]-0.38971143170299727*hamil[3]*apar[5]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[5]*jacobtot_inv[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[5]*b_y[5]-0.19485571585149863*apar[3]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[3]*b_y[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[5]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[5]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[5]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[16]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[8]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[7]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[7]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[6]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[6]+0.38971143170299727*hamil[2]*apar[5]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[4]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_z[5]+0.19485571585149863*hamil[2]*apar[3]*jacobtot_inv[3]*b_z[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[5]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[5]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[5]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[3]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[3]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[3]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[21]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[14]+0.10825317547305482*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[21]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[14]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[21]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[12]-0.10825317547305482*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[6] = (((-(0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[16])-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[3]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*hamil[6]*apar[7]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*hamil[6]*apar[7]-0.38971143170299727*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[6]-0.19485571585149863*jacobtot_inv[1]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[8]-0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[7]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[7]+0.38971143170299727*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[6]-0.10825317547305482*apar[2]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[3]*jacobtot_inv[3]*apar[4]*b_y[5]+0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[4]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[16]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[8]+0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[8]+0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*apar[2]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*hamil[2]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[4]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.7014805770653949*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.7014805770653949*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.7014805770653949*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[16]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[16]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[8]+0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[7]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[7]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[7]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[7]+0.35074028853269745*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[7]-0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[6]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[6]-0.19485571585149863*apar[1]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.19485571585149863*b_x[1]*hamil[2]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*apar[5]*b_x[5]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[16]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[8]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[8]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[8]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[7]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[7]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.19485571585149863*apar[3]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*apar[1]*hamil[1]*b_y[5]*jacobtot_inv[5]-0.19485571585149863*b_y[3]*hamil[3]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_y[1]*hamil[1]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[5]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*apar[5]*b_y[5]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[3]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[16]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[16]+0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[8]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[8]-0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[7]-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[7]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[7]-0.35074028853269745*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[6]+0.19485571585149863*hamil[2]*apar[3]*b_z[5]*jacobtot_inv[5]+0.19485571585149863*hamil[2]*b_z[3]*apar[5]*jacobtot_inv[5]-0.19485571585149863*b_z[1]*hamil[1]*apar[4]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[5]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*apar[5]*b_z[5]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[4]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[3]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[3]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[8] = (((-(0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[16])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[6]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[6]-0.10825317547305482*apar[2]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*b_x[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[16]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[7]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[7]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[7]-0.38971143170299727*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[7]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[6]+0.10825317547305482*hamil[1]*apar[2]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*b_y[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[4]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[8]+0.38971143170299727*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[6]*apar[7]+0.38971143170299727*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[6]+0.21650635094610965*b_z[1]*hamil[2]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[4]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[3])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[14]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[14]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[21])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[21]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[14]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[12]-0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[12]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[13] = ((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[14]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[14]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[12]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[14] = (((0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[14]+0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[21]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[21]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[14]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[21]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[12]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[16] = (((-(0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[16])-0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[0]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[0]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[7]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[6]-0.19485571585149863*hamil[2]*apar[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_x[5]-0.10825317547305482*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[16]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[7]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[7]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[6]-0.19485571585149863*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[6]+0.19485571585149863*hamil[1]*apar[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[4]*b_y[5]+0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[16]+0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[16]+0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.35074028853269745*b_z[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[5]*apar[7]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[6]+0.10825317547305482*b_z[0]*hamil[2]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[4])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[20] = ((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[21]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[12]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[21] = (((0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[21]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[21]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[14]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[21]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[21]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[21]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[14]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[21])-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[21]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[21]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[12]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
+  alphavpar[22] = ((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[21]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[21]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[14]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[14]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[12]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[27] = ((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[21]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[14]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[14]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[14]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[12]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
 
 
   out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index 468c7ebeeb..99f17bec3e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -117,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -140,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -154,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -177,7 +177,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -191,7 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index 0df2c1103b..d758236228 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -71,11 +71,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -89,11 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -116,11 +116,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -134,11 +134,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -161,11 +161,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -179,11 +179,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -224,11 +224,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -251,11 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -269,11 +269,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -296,11 +296,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -341,11 +341,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -359,11 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -386,11 +386,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -404,11 +404,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index e22733ed54..ef3f8fd71a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -81,7 +81,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -120,7 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -144,7 +144,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index e69f21d77b..4c0363ace2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -71,11 +71,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -90,11 +90,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -118,11 +118,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -137,11 +137,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -165,11 +165,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -184,11 +184,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -212,11 +212,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -231,11 +231,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -259,11 +259,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -278,11 +278,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -306,11 +306,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -325,11 +325,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -353,11 +353,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -372,11 +372,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -400,11 +400,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -419,11 +419,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;

From 119c3c7dd04e3c80caae057fff98fe22ef08c8cb Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 10 Apr 2026 20:54:31 -0400
Subject: [PATCH 135/181] this is a refactor version of the kernel, rewritten
 to match equations as much as possible and reviewed

---
 .../dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c |  31 ++-
 .../dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c |  40 +++-
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c |  66 +++----
 .../dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c | 146 +++++++-------
 .../dg_gyrokinetic_no_by_vol_2x2v_ser_p1.c    |  12 +-
 .../dg_gyrokinetic_no_by_vol_3x2v_ser_p1.c    |  12 +-
 .../dg_gyrokinetic_vol_1x1v_ser_p1.c          |  32 ++--
 .../dg_gyrokinetic_vol_1x2v_ser_p1.c          |  40 ++--
 .../dg_gyrokinetic_vol_2x2v_ser_p1.c          | 108 +++++------
 .../dg_gyrokinetic_vol_3x2v_ser_p1.c          | 180 +++++++++---------
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ...isionless_flux_em_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...isionless_flux_em_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c |  62 +++---
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 110 +++++------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 110 +++++------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c |  62 +++---
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 110 +++++------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 110 +++++------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...lux_em_multib_boundary_surfx_1x1v_ser_p1.c |  20 +-
 ...lux_em_multib_boundary_surfx_1x2v_ser_p1.c |  26 +--
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c |  62 +++---
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 110 +++++------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 110 +++++------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...ess_flux_em_no_by_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...ess_flux_em_no_by_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...ess_flux_em_no_by_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...ess_flux_em_no_by_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...ess_flux_em_no_by_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  38 ++--
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  62 +++---
 ...sionless_flux_em_no_by_surfx_2x2v_ser_p1.c |  14 +-
 ...sionless_flux_em_no_by_surfx_3x2v_ser_p1.c |  14 +-
 ...sionless_flux_em_no_by_surfy_2x2v_ser_p1.c |  38 ++--
 ...sionless_flux_em_no_by_surfy_3x2v_ser_p1.c |  14 +-
 ...sionless_flux_em_no_by_surfz_3x2v_ser_p1.c |  62 +++---
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c |  62 +++---
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 110 +++++------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 110 +++++------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c |  62 +++---
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 110 +++++------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 110 +++++------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c |  20 +-
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c |  26 +--
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c |  62 +++---
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 110 +++++------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 110 +++++------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...lux_em_star_no_by_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...lux_em_star_no_by_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...lux_em_star_no_by_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...lux_em_star_no_by_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...lux_em_star_no_by_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  38 ++--
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  62 +++---
 ...ess_flux_em_star_no_by_surfx_2x2v_ser_p1.c |  14 +-
 ...ess_flux_em_star_no_by_surfx_3x2v_ser_p1.c |  14 +-
 ...ess_flux_em_star_no_by_surfy_2x2v_ser_p1.c |  38 ++--
 ...ess_flux_em_star_no_by_surfy_3x2v_ser_p1.c |  14 +-
 ...ess_flux_em_star_no_by_surfz_3x2v_ser_p1.c |  62 +++---
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c |  16 +-
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c |  96 +++++-----
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c |  20 +-
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c |  26 +--
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c |  62 +++---
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 110 +++++------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c |  86 ++++-----
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 110 +++++------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  16 +-
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  96 +++++-----
 ..._collisionless_flux_em_surfx_1x1v_ser_p1.c |  20 +-
 ..._collisionless_flux_em_surfx_1x2v_ser_p1.c |  26 +--
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c |  62 +++---
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 110 +++++------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c |  86 ++++-----
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 110 +++++------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 158 +++++++--------
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |  20 +-
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |  26 +--
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |  20 +-
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |  26 +--
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |  14 +-
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c |  14 +-
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |  38 ++--
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c |  14 +-
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c |  62 +++---
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |  38 ++--
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |  14 +-
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |  62 +++---
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |  38 ++--
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |  14 +-
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |  62 +++---
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |  14 +-
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |  14 +-
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |  38 ++--
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |  14 +-
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |  62 +++---
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |  20 +-
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |  26 +--
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c |  14 +-
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |  14 +-
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c |  38 ++--
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |  14 +-
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |  62 +++---
 158 files changed, 3979 insertions(+), 3944 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
index f29ff1cb68..dc08ea1376 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x1v_ser_p1.c
@@ -22,17 +22,17 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   double rdvpar2 = 2.0/dxv[1];
 
 
-  const double *b_x = &b_i[0];
-  const double *b_y = &b_i[2];
-  const double *b_z = &b_i[4];
+  const double *b_1 = &b_i[0];
+  const double *b_2 = &b_i[2];
+  const double *b_3 = &b_i[4];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[2]; 
-  const double *bioverJB_z = &bioverJB[4]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[2]; 
+  const double *bioverJB_3 = &bioverJB[4]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[4]; 
 
   double hamil[6] = {0.}; 
   hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
@@ -47,12 +47,25 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x1v_ser_p1(const double *w, const
   hamil2[1] = hamil[4]*hamil[4]; 
 
   double alphax[6] = {0.}; 
+  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_3[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_3[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_3[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_3[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_3[1]*hamil[4]+1.5811388300841895*apar[0]*dualcurlbhatoverB_3[0]*hamil[4])*rdx2)/(vmap[1]*m_); 
+  alphax[3] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_3[1]*hamil[4]+1.5811388300841895*dualcurlbhatoverB_3[0]*apar[1]*hamil[4])*rdx2)/(vmap[1]*m_); 
 
 
+  out[1] += 0.8660254037844386*(alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[3] += 0.7745966692414834*alphax[3]*fin[5]+0.7745966692414833*alphax[2]*fin[4]+0.8660254037844386*(alphax[1]*fin[3]+fin[1]*alphax[3]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[5] += 0.8660254037844386*alphax[1]*fin[5]+0.8660254037844387*alphax[0]*fin[4]+0.7745966692414834*(alphax[3]*fin[3]+alphax[2]*fin[2]); 
 
   double alphavpar[6] = {0.}; 
+  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_3[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_3[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_3[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_3[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
 
 
+  out[2] += 0.8660254037844386*(alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[3] += 0.8660254037844386*(alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[4] += 1.9364916731037085*(alphavpar[1]*fin[3]+alphavpar[0]*fin[2]); 
+  out[5] += 1.9364916731037085*(alphavpar[0]*fin[3]+alphavpar[1]*fin[2]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
index 7867f153e4..b4adbc1bb1 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_1x2v_ser_p1.c
@@ -23,17 +23,17 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   double rdmu2 = 2.0/dxv[2];
 
 
-  const double *b_x = &b_i[0];
-  const double *b_y = &b_i[2];
-  const double *b_z = &b_i[4];
+  const double *b_1 = &b_i[0];
+  const double *b_2 = &b_i[2];
+  const double *b_3 = &b_i[4];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[2]; 
-  const double *bioverJB_z = &bioverJB[4]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[2]; 
+  const double *bioverJB_3 = &bioverJB[4]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[4]; 
 
   double hamil[12] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
@@ -50,12 +50,34 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_1x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[8]*hamil[8]; 
 
   double alphax[12] = {0.}; 
+  alphax[0] = ((0.7071067811865475*apar[1]*dualcurlbhatoverB_3[1]*hamil[2]+0.7071067811865475*apar[0]*dualcurlbhatoverB_3[0]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[1] = ((0.7071067811865475*apar[0]*dualcurlbhatoverB_3[1]*hamil[2]+0.7071067811865475*dualcurlbhatoverB_3[0]*apar[1]*hamil[2])*rdx2)/(vmap[1]*m_); 
+  alphax[2] = ((1.5811388300841895*apar[1]*dualcurlbhatoverB_3[1]*hamil[8]+1.5811388300841895*apar[0]*dualcurlbhatoverB_3[0]*hamil[8])*rdx2)/(vmap[1]*m_); 
+  alphax[4] = ((1.5811388300841895*apar[0]*dualcurlbhatoverB_3[1]*hamil[8]+1.5811388300841895*dualcurlbhatoverB_3[0]*apar[1]*hamil[8])*rdx2)/(vmap[1]*m_); 
 
 
+  out[1] += 0.6123724356957944*(alphax[4]*fin[4]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
+  out[4] += 0.5477225575051661*(alphax[4]*fin[9]+alphax[2]*fin[8])+0.6123724356957944*(alphax[1]*fin[4]+fin[1]*alphax[4]+alphax[0]*fin[2]+fin[0]*alphax[2]); 
+  out[5] += 0.6123724356957944*(alphax[4]*fin[7]+alphax[2]*fin[6]+alphax[1]*fin[5]+alphax[0]*fin[3]); 
+  out[7] += 0.5477225575051661*(alphax[4]*fin[11]+alphax[2]*fin[10])+0.6123724356957944*(alphax[1]*fin[7]+alphax[0]*fin[6]+alphax[4]*fin[5]+alphax[2]*fin[3]); 
+  out[9] += 0.6123724356957944*(alphax[1]*fin[9]+alphax[0]*fin[8])+0.5477225575051661*(alphax[4]*fin[4]+alphax[2]*fin[2]); 
+  out[11] += 0.6123724356957944*(alphax[1]*fin[11]+alphax[0]*fin[10])+0.5477225575051661*(alphax[4]*fin[7]+alphax[2]*fin[6]); 
 
   double alphavpar[12] = {0.}; 
+  alphavpar[0] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_3[1]*hamil[1])-0.7071067811865475*apar[0]*dualcurlbhatoverB_3[0]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[1] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_3[1]*hamil[1])-0.7071067811865475*dualcurlbhatoverB_3[0]*apar[1]*hamil[1])*rdx2)/(vmap[1]*m_); 
+  alphavpar[3] = ((-(0.7071067811865475*apar[1]*dualcurlbhatoverB_3[1]*hamil[5])-0.7071067811865475*apar[0]*dualcurlbhatoverB_3[0]*hamil[5])*rdx2)/(vmap[1]*m_); 
+  alphavpar[5] = ((-(0.7071067811865475*apar[0]*dualcurlbhatoverB_3[1]*hamil[5])-0.7071067811865475*dualcurlbhatoverB_3[0]*apar[1]*hamil[5])*rdx2)/(vmap[1]*m_); 
 
 
+  out[2] += 0.6123724356957944*(alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
+  out[4] += 0.6123724356957944*(alphavpar[3]*fin[5]+fin[3]*alphavpar[5]+alphavpar[0]*fin[1]+fin[0]*alphavpar[1]); 
+  out[6] += 0.6123724356957944*(alphavpar[1]*fin[5]+fin[1]*alphavpar[5]+alphavpar[0]*fin[3]+fin[0]*alphavpar[3]); 
+  out[7] += 0.6123724356957944*(alphavpar[0]*fin[5]+fin[0]*alphavpar[5]+alphavpar[1]*fin[3]+fin[1]*alphavpar[3]); 
+  out[8] += 1.369306393762915*(alphavpar[5]*fin[7]+alphavpar[3]*fin[6]+alphavpar[1]*fin[4]+alphavpar[0]*fin[2]); 
+  out[9] += 1.369306393762915*(alphavpar[3]*fin[7]+alphavpar[5]*fin[6]+alphavpar[0]*fin[4]+alphavpar[1]*fin[2]); 
+  out[10] += 1.369306393762915*(alphavpar[1]*fin[7]+alphavpar[0]*fin[6]+fin[4]*alphavpar[5]+fin[2]*alphavpar[3]); 
+  out[11] += 1.369306393762915*(alphavpar[0]*fin[7]+alphavpar[1]*fin[6]+fin[2]*alphavpar[5]+alphavpar[3]*fin[4]); 
 
   return 0.; 
 } 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index 57e728ad3b..ee1caa15a7 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -24,17 +24,17 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   double rdmu2 = 2.0/dxv[3];
 
 
-  const double *b_x = &b_i[0];
-  const double *b_y = &b_i[4];
-  const double *b_z = &b_i[8];
+  const double *b_1 = &b_i[0];
+  const double *b_2 = &b_i[4];
+  const double *b_3 = &b_i[8];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[4]; 
-  const double *bioverJB_z = &bioverJB[8]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[4]; 
+  const double *bioverJB_3 = &bioverJB[8]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[4]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[8]; 
 
   double hamil[24] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
@@ -55,14 +55,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = ((-(0.6123724356957944*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]-0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[1] = ((-(1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.6123724356957944*apar[2]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]-0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[3]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[2] = ((-(0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[3] = ((-(1.369306393762915*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[5] = ((-(0.5511351921262146*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3])-0.5511351921262146*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[2]*hamil[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[2]*hamil[3]*jacobtot_inv[3]-1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]-0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]-0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[6] = ((-(2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.369306393762915*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.232375754386623*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]-1.369306393762915*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]-1.232375754386623*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[16]-0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[7] = ((-(0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16])-0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[11] = ((-(1.232375754386623*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16])-1.232375754386623*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[16]-0.6846531968814573*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[16]-2.4647515087732463*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]-1.369306393762915*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]-0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]-0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]-1.369306393762915*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[0] = (((-(0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(1.369306393762915*bioverJB_3[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_3[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[0]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[3])-0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(1.369306393762915*bioverJB_3[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_3[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_3[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_3[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_3[3]*hamil[16])-1.369306393762915*bioverJB_3[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -79,14 +79,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = ((0.6123724356957944*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[1] = ((0.3061862178478971*apar[0]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[1]*b_y[2]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[3]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[2] = ((1.1022703842524295*apar[3]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.6123724356957944*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[3]+0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[3]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[3]+0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[3]+0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[3] = ((1.369306393762915*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[5] = ((0.5511351921262146*apar[2]*b_y[3]*hamil[3]*jacobtot_inv[3]+0.5511351921262146*b_y[2]*apar[3]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[3]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[3]+0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[3]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[3]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[6] = ((0.6846531968814573*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[16]+0.6846531968814573*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[7] = ((2.4647515087732463*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+1.232375754386623*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[16]+1.369306393762915*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+1.232375754386623*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[16]+1.369306393762915*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[16]+0.6846531968814573*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[11] = ((1.232375754386623*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]+1.232375754386623*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.6846531968814573*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+2.4647515087732463*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[16]+0.6846531968814573*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[16]+0.6846531968814573*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]+1.369306393762915*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[16]+1.369306393762915*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[16]+0.6846531968814573*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[16]+0.6846531968814573*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[0] = (((0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((1.369306393762915*bioverJB_3[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_3[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[0]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[3]+0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_3[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_3[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((1.369306393762915*bioverJB_3[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_3[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_3[3]*hamil[16]+1.369306393762915*bioverJB_3[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -103,14 +103,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[5])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[5]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[5]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[5]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[5]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3]-0.6123724356957944*b_y[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*b_y[2]*apar[3]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*jacobtot_inv[2]*apar[3]*b_y[3]-0.6123724356957944*jacobtot_inv[1]*hamil[2]*apar[3]*b_y[3]-0.3061862178478971*apar[0]*hamil[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[0]*apar[2]*hamil[2]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]-0.3061862178478971*b_y[0]*hamil[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*hamil[2]*apar[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[2]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[2]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[2]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[2]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[2]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[1] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[5])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[5]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[5]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[5]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[5]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[5]+1.1022703842524295*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*hamil[2]*b_y[3]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*hamil[2]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[1]*b_y[2]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[1]*apar[2]*hamil[2]*jacobtot_inv[3]+0.6123724356957944*hamil[1]*apar[2]*b_y[2]*jacobtot_inv[3]-0.6123724356957944*jacobtot_inv[0]*hamil[2]*apar[3]*b_y[3]-0.6123724356957944*apar[1]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.6123724356957944*hamil[1]*apar[2]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*jacobtot_inv[1]*apar[2]*hamil[2]*b_y[3]+0.5511351921262146*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]-0.6123724356957944*b_y[1]*hamil[2]*jacobtot_inv[2]*apar[3]+0.6123724356957944*hamil[1]*b_y[2]*jacobtot_inv[2]*apar[3]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*hamil[2]*apar[3]+0.5511351921262146*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[2]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[2]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[2]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[2]+0.3061862178478971*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[2]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[2]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[2] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[5]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[5]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[5]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[5]-1.1022703842524295*hamil[2]*apar[3]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3]-0.5511351921262146*apar[2]*hamil[2]*jacobtot_inv[2]*b_y[3]+0.3061862178478971*apar[1]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.6123724356957944*apar[1]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[0]*hamil[2]*b_y[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3]-0.5511351921262146*b_y[2]*hamil[2]*jacobtot_inv[2]*apar[3]+0.3061862178478971*b_y[1]*hamil[1]*jacobtot_inv[2]*apar[3]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*b_y[2]*apar[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[2]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[2]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[2]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[4] = ((-(0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[12])+0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12]-0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[12]+0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[12]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[12]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[12]-0.6123724356957944*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[9]+0.6123724356957944*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[5] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[5]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[5]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[5]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[5]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[5]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[5]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[5]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[5]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[5]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[5]-0.5511351921262146*apar[2]*hamil[2]*b_y[3]*jacobtot_inv[3]+0.5511351921262146*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]-0.5511351921262146*b_y[2]*hamil[2]*apar[3]*jacobtot_inv[3]+0.5511351921262146*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.3061862178478971*apar[0]*b_y[1]*hamil[2]*jacobtot_inv[3]-0.3061862178478971*b_y[0]*apar[1]*hamil[2]*jacobtot_inv[3]+0.3061862178478971*apar[0]*hamil[1]*b_y[2]*jacobtot_inv[3]+0.3061862178478971*b_y[0]*hamil[1]*apar[2]*jacobtot_inv[3]-1.1022703842524295*hamil[2]*jacobtot_inv[2]*apar[3]*b_y[3]+1.1022703842524295*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3]+0.3061862178478971*apar[0]*hamil[1]*jacobtot_inv[2]*b_y[3]-0.3061862178478971*apar[0]*jacobtot_inv[1]*hamil[2]*b_y[3]-0.6123724356957944*jacobtot_inv[0]*apar[1]*hamil[2]*b_y[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3]+0.3061862178478971*b_y[0]*hamil[1]*jacobtot_inv[2]*apar[3]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*hamil[2]*apar[3]+0.6123724356957944*jacobtot_inv[0]*hamil[1]*b_y[2]*apar[3]-0.6123724356957944*apar[1]*b_y[1]*hamil[2]*jacobtot_inv[2]+0.3061862178478971*apar[1]*hamil[1]*b_y[2]*jacobtot_inv[2]+0.3061862178478971*b_y[1]*hamil[1]*apar[2]*jacobtot_inv[2]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[2]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[2]+0.6123724356957944*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[2])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[8] = ((-(0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12])-0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12]+0.3061862178478971*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[12]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[12]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[12]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[12]-0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[9]-0.3061862178478971*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[9]+1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[8]+0.6123724356957944*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[8]+0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[9] = ((0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12]+1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[2]*hamil[12]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[2]*hamil[12]-1.1022703842524295*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[9]-0.6123724356957944*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[9]-0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[9]-0.6123724356957944*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*apar[1]*b_y[2]*hamil[9]-0.3061862178478971*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[9]+0.3061862178478971*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[1]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[1]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[12] = ((1.1022703842524295*apar[2]*b_y[2]*jacobtot_inv[3]*hamil[12]-1.1022703842524295*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[12]+0.5511351921262146*apar[2]*jacobtot_inv[2]*b_y[3]*hamil[12]-0.5511351921262146*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.5511351921262146*b_y[2]*jacobtot_inv[2]*apar[3]*hamil[12]-0.5511351921262146*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[2]*hamil[12]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[2]*hamil[12]+0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[2]*hamil[12]+0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.5511351921262146*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[9]-0.5511351921262146*b_y[2]*apar[3]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[9]-0.3061862178478971*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[9]-1.1022703842524295*jacobtot_inv[2]*apar[3]*b_y[3]*hamil[9]-0.3061862178478971*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[9]-0.3061862178478971*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[9]-0.6123724356957944*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*b_y[1]*jacobtot_inv[2]*hamil[9]-0.3061862178478971*apar[1]*jacobtot_inv[1]*b_y[2]*hamil[9]-0.3061862178478971*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[9]+0.5511351921262146*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]+0.5511351921262146*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*apar[0]*b_y[2]*jacobtot_inv[3]*hamil[8]+0.3061862178478971*b_y[0]*apar[2]*jacobtot_inv[3]*hamil[8]+1.1022703842524295*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[8]+0.3061862178478971*apar[0]*jacobtot_inv[2]*b_y[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[8]+0.3061862178478971*b_y[0]*jacobtot_inv[2]*apar[3]*hamil[8]+0.6123724356957944*jacobtot_inv[0]*b_y[2]*apar[3]*hamil[8]+0.3061862178478971*apar[1]*b_y[2]*jacobtot_inv[2]*hamil[8]+0.3061862178478971*b_y[1]*apar[2]*jacobtot_inv[2]*hamil[8]+0.6123724356957944*jacobtot_inv[1]*apar[2]*b_y[2]*hamil[8])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[5]-0.6123724356957944*bioverJB_3[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_3[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_3[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_3[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[5]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_3[3]+0.6123724356957944*bioverJB_3[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[2]+0.6123724356957944*bioverJB_3[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_1[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[5])+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_3[3]-0.6123724356957944*bioverJB_3[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_3[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[12]-0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[5])+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_3[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_3[3]-0.6123724356957944*bioverJB_3[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_3[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[12]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[9]+0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[12])+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[12])+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[9]-0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[8]+0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
index 2cbc2e69ad..4dbf7f2db6 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_3x2v_ser_p1.c
@@ -25,17 +25,17 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   double rdmu2 = 2.0/dxv[4];
 
 
-  const double *b_x = &b_i[0];
-  const double *b_y = &b_i[8];
-  const double *b_z = &b_i[16];
+  const double *b_1 = &b_i[0];
+  const double *b_2 = &b_i[8];
+  const double *b_3 = &b_i[16];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[8]; 
-  const double *bioverJB_z = &bioverJB[16]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[8]; 
+  const double *bioverJB_3 = &bioverJB[16]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[8]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[16]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[16]; 
 
   double hamil[48] = {0.}; 
   hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
@@ -60,22 +60,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (((-(0.21650635094610965*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]-0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]+0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5])-0.21650635094610965*apar[3]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_z[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]+0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[2] = ((-(0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]-0.21650635094610965*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[3] = (((-(0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[4] = (((-(0.4841229182759271*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[6] = ((-(0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7])-0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.21650635094610965*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[7] = (((-(0.19485571585149863*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5])-0.19485571585149863*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[3]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]+0.19485571585149863*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[2]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[8] = ((-(0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]-0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[9] = (((-(0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.43571062644833425*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]+0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[10] = ((-(0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]-0.4841229182759271*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[11] = (((-(0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]+0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[16] = ((-(0.19485571585149863*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]-0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_y[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[17] = ((-(0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.4841229182759271*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[18] = (((-(0.43571062644833425*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.7842791276070014*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]+0.43571062644833425*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]+0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]+0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphax[19] = ((-(0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphax[26] = ((-(0.43571062644833425*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]-0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]-0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]-0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphax[0] = (((-(0.3061862178478971*bioverJB_2[1]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*bioverJB_3[5]*apar[7]+0.3061862178478971*bioverJB_3[3]*hamil[4]*apar[6]+0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_1[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_1[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.3061862178478971*bioverJB_2[0]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_3[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_3[5]*apar[6]+0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[4]+0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_1[5]+0.1767766952966368*dualcurlbhatoverB_1[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.3061862178478971*bioverJB_2[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_2[0]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_1[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_1[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_2[5])-0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_3[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_3[0]*hamil[4]*apar[6]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_3[5]+0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_1[5]+0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[4] = (((-(0.6846531968814573*bioverJB_2[1]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_2[0]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_3[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_3[3]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_3[1]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_3[0]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_1[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_1[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_1[0]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(0.3061862178478971*bioverJB_2[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_2[1]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_1[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_1[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(0.3061862178478971*apar[3]*hamil[4]*bioverJB_2[5])-0.3061862178478971*bioverJB_2[3]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_3[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_3[1]*hamil[4]*apar[6]+0.3061862178478971*apar[2]*hamil[4]*bioverJB_3[5]+0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_1[5]+0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[8] = (((-(0.3061862178478971*hamil[4]*bioverJB_2[5]*apar[7])-0.3061862178478971*bioverJB_2[3]*hamil[4]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_1[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[9] = (((-(0.6846531968814573*bioverJB_2[0]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_2[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_3[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_3[5]*apar[6]*hamil[32]+0.6846531968814573*bioverJB_3[0]*apar[4]*hamil[32]+0.6846531968814573*bioverJB_3[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_1[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[1]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[10] = (((-(0.6846531968814573*bioverJB_2[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_2[0]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_1[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(0.6846531968814573*apar[5]*bioverJB_2[5]*hamil[32])-0.6846531968814573*apar[3]*bioverJB_2[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_3[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_3[0]*apar[6]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_3[5]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_3[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_1[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[16] = (((-(0.3061862178478971*bioverJB_2[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_2[5]*apar[6])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_1[5]+0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[4])*rdx2)/vmap[1])/m_; 
+  alphax[17] = (((-(0.6846531968814573*bioverJB_2[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_2[1]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_1[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[1]*apar[2]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[18] = (((-(0.6846531968814573*apar[3]*bioverJB_2[5]*hamil[32])-0.6846531968814573*bioverJB_2[3]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_3[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_3[1]*apar[6]*hamil[32]+0.6846531968814573*apar[2]*bioverJB_3[5]*hamil[32]+0.6846531968814573*bioverJB_3[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_1[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[1]*apar[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[19] = (((-(0.6846531968814573*bioverJB_2[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_2[3]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_1[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_1[3]*hamil[32])*rdx2)/vmap[1])/m_; 
+  alphax[26] = (((-(0.6846531968814573*bioverJB_2[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_2[5]*apar[6]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_1[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_1[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_1[3]*apar[4]*hamil[32])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.3061862178478971*(alphax[26]*fin[26]+alphax[19]*fin[19]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[11]*fin[11]+alphax[10]*fin[10]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -104,22 +104,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphax[1]*fin[47]+alphax[0]*fin[46]+alphax[6]*fin[45]+alphax[7]*fin[44]+alphax[2]*fin[42]+alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[8]*fin[36])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[17]*fin[29]+alphax[18]*fin[28]+fin[23]*alphax[26]+alphax[10]*fin[25]+alphax[11]*fin[24]+fin[15]*alphax[19]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (((0.21650635094610965*apar[3]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*b_x[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[5]+0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[4]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*apar[1]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*b_z[1]*hamil[4]*apar[5]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[4]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[1] = (((0.38971143170299727*hamil[4]*apar[5]*b_x[5]*jacobtot_inv[5]+0.21650635094610965*apar[3]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*apar[3]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[4]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_x[5]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[0]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.10825317547305482*b_z[0]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_z[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[3]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[2] = (((0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]+0.21650635094610965*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.21650635094610965*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.21650635094610965*apar[4]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[3] = (((0.10825317547305482*apar[0]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[1]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[1]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*apar[5]*b_z[5]*jacobtot_inv[5])-0.21650635094610965*apar[1]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_z[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_z[5]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[5]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[5]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[5]-0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[4] = (((0.4841229182759271*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[6] = (((0.38971143170299727*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7]+0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.21650635094610965*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_z[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_z[5]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*hamil[4]*apar[7]-0.10825317547305482*b_z[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[7] = (((0.19485571585149863*apar[1]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[3]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*apar[5]*b_x[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.21650635094610965*jacobtot_inv[0]*apar[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[3]*hamil[4]*b_z[5]*jacobtot_inv[5])-0.19485571585149863*b_z[3]*hamil[4]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_z[1]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*apar[1]*hamil[4]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_z[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_z[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[5]-0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[4]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[8] = (((0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.38971143170299727*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[6]-0.21650635094610965*b_z[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_z[5]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[4]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[9] = (((0.8714212528966685*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.43571062644833425*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.24206145913796356*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[10] = (((0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]+0.4841229182759271*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.4841229182759271*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.4841229182759271*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.24206145913796356*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[11] = (((0.24206145913796356*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[32]-0.4841229182759271*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[32]-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[16] = (((0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]+0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]+0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_z[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_z[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_z[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_z[5]-0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[17] = (((0.8714212528966685*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.4841229182759271*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]+0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.24206145913796356*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.4841229182759271*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[18] = (((0.43571062644833425*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[32])-0.43571062644833425*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[32]-0.8714212528966685*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[32]-0.24206145913796356*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[32]-0.4841229182759271*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[19] = (((0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.8714212528966685*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[32]-0.4841229182759271*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
-  alphay[26] = (((0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]+0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]+0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]+0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]+0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.43571062644833425*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.8714212528966685*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[32]-0.24206145913796356*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[32]-0.43571062644833425*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.4841229182759271*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[32]-0.4841229182759271*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1])/m_; 
+  alphay[0] = (((0.3061862178478971*bioverJB_1[1]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_1[0]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[3]*hamil[4]*apar[5])-0.3061862178478971*bioverJB_3[0]*apar[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_2[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_2[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_2[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_2[0]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[1] = (((0.3061862178478971*bioverJB_1[0]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_1[1]*apar[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*apar[5]*bioverJB_3[5])-0.3061862178478971*apar[1]*bioverJB_3[1]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_2[5]+0.1767766952966368*dualcurlbhatoverB_2[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_2[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_2[0]*apar[1]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[2] = (((0.3061862178478971*bioverJB_1[1]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_1[0]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[3]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_2[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_2[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_2[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_2[0]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[3] = (((0.3061862178478971*hamil[4]*apar[5]*bioverJB_1[5]+0.3061862178478971*apar[3]*bioverJB_1[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[0]*hamil[4]*apar[5])-0.3061862178478971*apar[1]*bioverJB_3[3]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_2[5]+0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_2[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_2[0]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[4] = (((0.6846531968814573*bioverJB_1[1]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_1[0]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[3]*apar[5]*hamil[32])-0.6846531968814573*bioverJB_3[0]*apar[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_2[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_2[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_2[0]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[6] = (((0.3061862178478971*bioverJB_1[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_1[1]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*hamil[4]*bioverJB_3[5]*apar[7])-0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_2[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_2[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_2[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_2[1]*apar[2]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[7] = (((0.3061862178478971*apar[3]*hamil[4]*bioverJB_1[5]+0.3061862178478971*bioverJB_1[3]*hamil[4]*apar[5])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*hamil[4]*bioverJB_3[5])-0.3061862178478971*bioverJB_3[1]*hamil[4]*apar[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_2[5]+0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_2[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_2[1]*apar[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[8] = (((0.3061862178478971*hamil[4]*bioverJB_1[5]*apar[7]+0.3061862178478971*bioverJB_1[3]*hamil[4]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[4])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_2[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_2[3]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[9] = (((0.6846531968814573*bioverJB_1[0]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_1[1]*apar[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[5]*bioverJB_3[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_3[1]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_2[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[1]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[10] = (((0.6846531968814573*bioverJB_1[1]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_1[0]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_3[0]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_2[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[11] = (((0.6846531968814573*apar[5]*bioverJB_1[5]*hamil[32]+0.6846531968814573*apar[3]*bioverJB_1[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[0]*apar[5]*hamil[32])-0.6846531968814573*apar[1]*bioverJB_3[3]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_2[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[16] = (((0.3061862178478971*bioverJB_1[3]*hamil[4]*apar[7]+0.3061862178478971*hamil[4]*bioverJB_1[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[1]*hamil[4]*apar[7])-0.3061862178478971*apar[4]*hamil[4]*bioverJB_3[5])*rdx2*rdy2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_2[5]+0.1767766952966368*dualcurlbhatoverB_2[3]*apar[4]*hamil[4])*rdy2)/vmap[1])/m_; 
+  alphay[17] = (((0.6846531968814573*bioverJB_1[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_1[1]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_3[1]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_2[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[1]*apar[2]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[18] = (((0.6846531968814573*apar[3]*bioverJB_1[5]*hamil[32]+0.6846531968814573*bioverJB_1[3]*apar[5]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*apar[1]*bioverJB_3[5]*hamil[32])-0.6846531968814573*bioverJB_3[1]*apar[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_2[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[1]*apar[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[19] = (((0.6846531968814573*bioverJB_1[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_1[3]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_3[3]*apar[4]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_2[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_2[3]*hamil[32])*rdy2)/vmap[1])/m_; 
+  alphay[26] = (((0.6846531968814573*bioverJB_1[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_1[5]*apar[6]*hamil[32])*rdy2*rdz2)/vmap[1]+((-(0.6846531968814573*bioverJB_3[1]*apar[7]*hamil[32])-0.6846531968814573*apar[4]*bioverJB_3[5]*hamil[32])*rdx2*rdy2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_2[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_2[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_2[3]*apar[4]*hamil[32])*rdy2)/vmap[1])/m_; 
 
 
   out[2] += 0.3061862178478971*(alphay[26]*fin[26]+alphay[19]*fin[19]+alphay[18]*fin[18]+alphay[17]*fin[17]+alphay[16]*fin[16]+alphay[11]*fin[11]+alphay[10]*fin[10]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -148,22 +148,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46]+alphay[0]*fin[45]+alphay[8]*fin[44]+alphay[1]*fin[42]+alphay[16]*fin[41]+alphay[3]*fin[40]+alphay[7]*fin[36])+0.273861278752583*(alphay[10]*fin[31]+alphay[17]*fin[30]+alphay[4]*fin[29]+alphay[19]*fin[28]+fin[24]*alphay[26]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (((-(0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[7])-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[6]-0.10825317547305482*apar[2]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[3]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[3]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[4]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.21650635094610965*apar[1]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*b_y[1]*hamil[4]*apar[5]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[4]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((-(0.19485571585149863*b_x[1]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[1]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*hamil[4]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[4]*apar[6]-0.19485571585149863*apar[4]*hamil[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*b_x[3]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_x[5]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[4]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.10825317547305482*apar[0]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*b_y[3]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[3]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*apar[5]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[5]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[2] = ((0.21650635094610965*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[6]+0.21650635094610965*apar[4]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[4]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[3] = (((-(0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[7])-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[7]-0.19485571585149863*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[6]-0.10825317547305482*b_x[0]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*apar[2]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*hamil[4]*apar[5]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.19485571585149863*apar[3]*jacobtot_inv[3]*hamil[4]*b_y[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[4]*b_y[5]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[5]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[5]+0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[4] = (((-(0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[32])-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[32]-0.24206145913796356*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.4841229182759271*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[6] = ((0.10825317547305482*b_y[0]*hamil[4]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[4]*b_y[5]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*hamil[4]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[4]*apar[7]+0.10825317547305482*b_y[1]*hamil[4]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*apar[2]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[3]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[3]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[4]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[7] = (((-(0.35074028853269745*hamil[4]*b_x[5]*jacobtot_inv[5]*apar[7])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*hamil[4]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[4]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[4]*apar[7]-0.19485571585149863*b_x[3]*hamil[4]*jacobtot_inv[5]*apar[6]-0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[4]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[4]*apar[6]-0.19485571585149863*b_x[1]*apar[4]*hamil[4]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*apar[2]*hamil[4]*jacobtot_inv[5]-0.19485571585149863*jacobtot_inv[1]*apar[4]*hamil[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[4]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[4]-0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*hamil[4]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*b_y[3]*hamil[4]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_y[1]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*apar[1]*hamil[4]*jacobtot_inv[5]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[4]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[5]+0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[4]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[4]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[4])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[8] = ((0.38971143170299727*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*hamil[4]*apar[7]+0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[4]*apar[7]+0.19485571585149863*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[6]+0.21650635094610965*b_y[1]*apar[4]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[4]*b_y[5]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[4]+0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[9] = (((-(0.43571062644833425*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[32]-0.43571062644833425*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[32]-0.24206145913796356*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.24206145913796356*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[10] = ((0.4841229182759271*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[32]+0.4841229182759271*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.24206145913796356*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[11] = (((-(0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[32]-0.43571062644833425*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.8714212528966685*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[32]+0.4841229182759271*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[16] = ((0.19485571585149863*b_y[3]*hamil[4]*jacobtot_inv[5]*apar[7]+0.38971143170299727*jacobtot_inv[3]*hamil[4]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[4]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[4]*apar[7]+0.19485571585149863*hamil[4]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[4]*apar[6]+0.10825317547305482*b_y[0]*apar[4]*hamil[4]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*apar[2]*hamil[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*apar[4]*hamil[4]*b_y[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[4]*b_y[5]+0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[4]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[4])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[17] = ((0.24206145913796356*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[18] = (((-(0.7842791276070014*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[32])-0.43571062644833425*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[32]-0.43571062644833425*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[32]-0.43571062644833425*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[32]-0.43571062644833425*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[32]-0.43571062644833425*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[32]-0.24206145913796356*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[32]-0.43571062644833425*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[32]-0.24206145913796356*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[32]-0.24206145913796356*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[32]-0.24206145913796356*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[32]-0.24206145913796356*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.43571062644833425*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[32]+0.43571062644833425*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[32]+0.24206145913796356*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[32]+0.4841229182759271*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[32]+0.24206145913796356*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[32])*rdx2*rdz2)/vmap[1])/m_; 
-  alphaz[19] = ((0.8714212528966685*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[32]+0.43571062644833425*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[32]+0.43571062644833425*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[32]+0.4841229182759271*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphaz[26] = ((0.43571062644833425*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[32]+0.8714212528966685*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[32]+0.24206145913796356*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[32]+0.43571062644833425*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[32]+0.24206145913796356*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[32]+0.24206145913796356*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[32]+0.24206145913796356*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[32]+0.4841229182759271*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[32]+0.4841229182759271*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[32]+0.24206145913796356*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[32])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphaz[0] = (((-(0.3061862178478971*hamil[4]*bioverJB_1[5]*apar[7])-0.3061862178478971*bioverJB_1[3]*hamil[4]*apar[6]-0.3061862178478971*bioverJB_1[1]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[3]*hamil[4]*apar[5]+0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*apar[5]*dualcurlbhatoverB_3[5]+0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[4]+0.1767766952966368*apar[1]*dualcurlbhatoverB_3[1]*hamil[4]+0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((-(0.3061862178478971*bioverJB_1[3]*hamil[4]*apar[7])-0.3061862178478971*hamil[4]*bioverJB_1[5]*apar[6]-0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[4]-0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*hamil[4]*apar[5]*bioverJB_2[5]+0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[3]*hamil[4]*dualcurlbhatoverB_3[5]+0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.3061862178478971*bioverJB_2[3]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*hamil[4]*dualcurlbhatoverB_3[5]*apar[7]+0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[4]*apar[6]+0.1767766952966368*dualcurlbhatoverB_3[1]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((-(0.3061862178478971*bioverJB_1[1]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_1[0]*hamil[4]*apar[6]-0.3061862178478971*apar[4]*hamil[4]*bioverJB_1[5]-0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[0]*hamil[4]*apar[5]+0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[1]*hamil[4]*dualcurlbhatoverB_3[5]+0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[4]*apar[5]+0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[4] = (((-(0.6846531968814573*bioverJB_1[5]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_1[3]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_1[1]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_1[0]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_2[3]*apar[5]*hamil[32]+0.6846531968814573*bioverJB_2[0]*apar[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[5]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*apar[3]*dualcurlbhatoverB_3[3]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_3[1]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_3[0]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((0.3061862178478971*hamil[4]*bioverJB_2[5]*apar[7]+0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[4]*apar[7]+0.1767766952966368*hamil[4]*dualcurlbhatoverB_3[5]*apar[6]+0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((-(0.3061862178478971*bioverJB_1[0]*hamil[4]*apar[7])-0.3061862178478971*bioverJB_1[1]*hamil[4]*apar[6]-0.3061862178478971*apar[2]*hamil[4]*bioverJB_1[5]-0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*hamil[4]*bioverJB_2[5]+0.3061862178478971*bioverJB_2[1]*hamil[4]*apar[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*apar[0]*hamil[4]*dualcurlbhatoverB_3[5]+0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[4]*apar[5]+0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[4]+0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[8] = (((0.3061862178478971*bioverJB_2[0]*hamil[4]*apar[7]+0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[4])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[4]*apar[6]+0.1767766952966368*apar[4]*hamil[4]*dualcurlbhatoverB_3[5]+0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[9] = (((-(0.6846531968814573*bioverJB_1[3]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_1[5]*apar[6]*hamil[32]-0.6846531968814573*bioverJB_1[0]*apar[4]*hamil[32]-0.6846531968814573*bioverJB_1[1]*apar[2]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[5]*bioverJB_2[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_2[1]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[3]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[3]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_3[1]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[1]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[10] = (((0.6846531968814573*bioverJB_2[3]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_2[0]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_3[5]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[3]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[1]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((-(0.6846531968814573*bioverJB_1[1]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_1[0]*apar[6]*hamil[32]-0.6846531968814573*apar[4]*bioverJB_1[5]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_1[3]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*bioverJB_2[0]*apar[5]*hamil[32]+0.6846531968814573*apar[1]*bioverJB_2[3]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[1]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[1]*apar[5]*hamil[32]+0.3952847075210473*apar[0]*dualcurlbhatoverB_3[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[16] = (((0.3061862178478971*bioverJB_2[1]*hamil[4]*apar[7]+0.3061862178478971*apar[4]*hamil[4]*bioverJB_2[5])*rdx2*rdz2)/vmap[1]+((0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[4]*apar[7]+0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[4]*apar[6]+0.1767766952966368*apar[2]*hamil[4]*dualcurlbhatoverB_3[5]+0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[4])*rdz2)/vmap[1])/m_; 
+  alphaz[17] = (((0.6846531968814573*bioverJB_2[5]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_2[1]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_3[3]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[5]*apar[6]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[4]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[1]*apar[2]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[18] = (((-(0.6846531968814573*bioverJB_1[0]*apar[7]*hamil[32])-0.6846531968814573*bioverJB_1[1]*apar[6]*hamil[32]-0.6846531968814573*apar[2]*bioverJB_1[5]*hamil[32]-0.6846531968814573*bioverJB_1[3]*apar[4]*hamil[32])*rdy2*rdz2)/vmap[1]+((0.6846531968814573*apar[1]*bioverJB_2[5]*hamil[32]+0.6846531968814573*bioverJB_2[1]*apar[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*apar[0]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[5]*hamil[32]+0.3952847075210473*apar[1]*dualcurlbhatoverB_3[3]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[1]*apar[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[19] = (((0.6846531968814573*bioverJB_2[0]*apar[7]*hamil[32]+0.6846531968814573*bioverJB_2[3]*apar[4]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_3[1]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[0]*apar[6]*hamil[32]+0.3952847075210473*apar[4]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_3[3]*hamil[32])*rdz2)/vmap[1])/m_; 
+  alphaz[26] = (((0.6846531968814573*bioverJB_2[1]*apar[7]*hamil[32]+0.6846531968814573*apar[4]*bioverJB_2[5]*hamil[32])*rdx2*rdz2)/vmap[1]+((0.3952847075210473*dualcurlbhatoverB_3[0]*apar[7]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[1]*apar[6]*hamil[32]+0.3952847075210473*apar[2]*dualcurlbhatoverB_3[5]*hamil[32]+0.3952847075210473*dualcurlbhatoverB_3[3]*apar[4]*hamil[32])*rdz2)/vmap[1])/m_; 
 
 
   out[3] += 0.3061862178478971*(alphaz[26]*fin[26]+alphaz[19]*fin[19]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[11]*fin[11]+alphaz[10]*fin[10]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -192,22 +192,22 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_3x2v_ser_p1(const double *w, const
   out[47] += 0.3061862178478971*(alphaz[3]*fin[47]+alphaz[7]*fin[46]+alphaz[8]*fin[45]+alphaz[0]*fin[44]+alphaz[16]*fin[42]+alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[6]*fin[36])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[19]*fin[29]+alphaz[4]*fin[28]+fin[25]*alphaz[26]+alphaz[9]*fin[24]+alphaz[10]*fin[23]+fin[15]*alphaz[17]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (((-(0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[7]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.21650635094610965*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[6]+0.10825317547305482*apar[2]*hamil[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[5]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*b_x[3]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[5]*b_x[5]+0.10825317547305482*hamil[3]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[5]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[5]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[4]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[3]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[3]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[3]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[8]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[6]*apar[7]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[6]-0.21650635094610965*apar[1]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*b_y[3]*apar[5]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*apar[5]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[5]*b_y[5]-0.10825317547305482*apar[0]*hamil[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[3]*hamil[3]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[3]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[3]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[3]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[3]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[3]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[16]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[16]+0.38971143170299727*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.21650635094610965*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[8]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[7]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[7]+0.10825317547305482*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[6]+0.21650635094610965*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[6]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[6]+0.21650635094610965*apar[1]*hamil[2]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[5]*jacobtot_inv[5]+0.21650635094610965*b_z[1]*hamil[2]*apar[5]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[5]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[3]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[4]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[3]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[3]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[2]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[2]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[1] = (((-(0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[16]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[16]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[8]+0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[7]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[7]+0.19485571585149863*b_x[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[7]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[6]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[6]-0.21650635094610965*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[6]-0.38971143170299727*hamil[2]*apar[5]*b_x[5]*jacobtot_inv[5]+0.19485571585149863*hamil[3]*apar[4]*b_x[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*b_x[3]*hamil[3]*jacobtot_inv[5]-0.21650635094610965*hamil[2]*apar[3]*b_x[3]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_x[5]-0.21650635094610965*hamil[2]*apar[3]*jacobtot_inv[3]*b_x[5]-0.19485571585149863*apar[1]*jacobtot_inv[1]*hamil[2]*b_x[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_x[5]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[5]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[5]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[5]+0.10825317547305482*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[4]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[3]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_x[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_x[3]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[3]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[16])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[16]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[8]-0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[7]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[7]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*hamil[6]*apar[7]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[6]*apar[7]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[6]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[6]+0.38971143170299727*hamil[1]*apar[5]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[1]*b_y[3]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[3]*hamil[3]*jacobtot_inv[5]+0.21650635094610965*hamil[1]*apar[3]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[5]*b_y[5]-0.21650635094610965*apar[1]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.21650635094610965*hamil[1]*apar[3]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[3]*hamil[3]*b_y[5]+0.19485571585149863*apar[1]*hamil[1]*jacobtot_inv[1]*b_y[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[1]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[5]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[5]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[5]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[3]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[3]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[1]*b_y[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[1]*b_y[3]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[3]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[16]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[7]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[7]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[5]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[6]-0.19485571585149863*hamil[1]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[2]*b_z[3]*jacobtot_inv[5]-0.10825317547305482*hamil[1]*apar[2]*b_z[3]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*hamil[2]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_z[5]+0.21650635094610965*apar[1]*hamil[2]*jacobtot_inv[3]*b_z[5]-0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*apar[3]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[5]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[5]-0.10825317547305482*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[4]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[4]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[2]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[2]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[2]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[2]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[16])-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[8]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*hamil[6]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[6]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[7]-0.21650635094610965*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[16])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[16]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[16]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[16]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[7]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[7]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[6]+0.21650635094610965*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[6]-0.10825317547305482*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[6]-0.21650635094610965*hamil[3]*apar[4]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_y[5]-0.10825317547305482*apar[2]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[4]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[4]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[4]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[3]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[16]+0.38971143170299727*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[8]+0.21650635094610965*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[6]+0.21650635094610965*hamil[2]*apar[4]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_z[5]+0.10825317547305482*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[4]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[3] = (((-(0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[16]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[16]-0.38971143170299727*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[8]-0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[8]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[7]-0.19485571585149863*apar[1]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[5]*b_x[5]*hamil[6]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[5]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[1]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[1]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[6]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[6]-0.10825317547305482*apar[0]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[5]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[5]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[1]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[16]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[16]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[16]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[16]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[8]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[7]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[7]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[6]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[6]-0.38971143170299727*hamil[3]*apar[5]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[5]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[5]*jacobtot_inv[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[5]*b_y[5]-0.19485571585149863*apar[3]*hamil[3]*jacobtot_inv[3]*b_y[5]+0.10825317547305482*apar[1]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[3]*b_y[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[5]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[5]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[5]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[5]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[3]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[3]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[16]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[16]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[16]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[16]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[16]+0.38971143170299727*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[8]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[8]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[8]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[7]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[7]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[7]+0.19485571585149863*apar[3]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[3]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[3]*apar[5]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[5]*hamil[6]+0.21650635094610965*apar[1]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_z[3]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[6]+0.38971143170299727*hamil[2]*apar[5]*b_z[5]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[4]*jacobtot_inv[5]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[4]*b_z[5]+0.19485571585149863*hamil[2]*apar[3]*jacobtot_inv[3]*b_z[5]+0.21650635094610965*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[0]*hamil[2]*b_z[5]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[5]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[5]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[5]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[5]-0.10825317547305482*b_z[1]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*b_z[3]*apar[4]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[3]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[3]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[3]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[5] = (((0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[21]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[14]+0.10825317547305482*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[21]-0.21650635094610965*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[14]+0.21650635094610965*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[21]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[12]-0.10825317547305482*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[6] = (((-(0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[16])-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[3]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*hamil[6]*apar[7]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*hamil[6]*apar[7]-0.38971143170299727*hamil[2]*b_x[5]*jacobtot_inv[5]*apar[7]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[2]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.38971143170299727*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[6]-0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[6]-0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[6]-0.21650635094610965*hamil[2]*b_x[3]*jacobtot_inv[5]*apar[6]-0.21650635094610965*hamil[2]*jacobtot_inv[3]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[2]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[2]*apar[6]-0.19485571585149863*jacobtot_inv[1]*hamil[2]*apar[4]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_x[5]-0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_x[3])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[16])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[16]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[16]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[8]-0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[7]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[7]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[7]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[7]+0.38971143170299727*hamil[1]*b_y[5]*jacobtot_inv[5]*apar[7]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*b_y[5]*apar[7]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[7]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[1]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[6]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[6]-0.10825317547305482*b_y[1]*hamil[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*b_y[3]*jacobtot_inv[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[3]*b_y[5]*apar[6]-0.10825317547305482*jacobtot_inv[1]*hamil[3]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[1]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[1]*apar[6]-0.10825317547305482*apar[2]*hamil[3]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[3]*hamil[3]*apar[4]*jacobtot_inv[5]-0.21650635094610965*hamil[3]*jacobtot_inv[3]*apar[4]*b_y[5]+0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_y[5]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_y[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[4]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[4]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[3]+0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[16]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[16]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[16]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[16]+0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[8]+0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[8]+0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_z[5]*apar[7]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[7]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[6]+0.10825317547305482*b_z[1]*hamil[2]*jacobtot_inv[5]*apar[6]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[5]*apar[6]+0.10825317547305482*apar[2]*hamil[2]*b_z[5]*jacobtot_inv[5]+0.10825317547305482*hamil[2]*b_z[3]*apar[4]*jacobtot_inv[5]+0.21650635094610965*hamil[2]*jacobtot_inv[3]*apar[4]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[4]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[4]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[2])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[7] = (((-(0.7014805770653949*apar[3]*b_x[5]*jacobtot_inv[5]*hamil[16])-0.7014805770653949*b_x[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.7014805770653949*jacobtot_inv[3]*apar[5]*b_x[5]*hamil[16]-0.19485571585149863*apar[0]*jacobtot_inv[1]*b_x[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*apar[1]*b_x[5]*hamil[16]-0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[5]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[5]*hamil[16]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[3]*hamil[16]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[3]*hamil[16]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[3]*hamil[16]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.7014805770653949*apar[5]*b_x[5]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*b_x[3]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*apar[3]*jacobtot_inv[3]*b_x[5]*hamil[8]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_x[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_x[5]*hamil[8]-0.38971143170299727*b_x[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_x[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_x[3]*hamil[8]-0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[3]*hamil[8]+0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[7]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[7]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[7]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[7]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[7]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[7]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[7]+0.35074028853269745*hamil[3]*b_x[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*hamil[3]*apar[7]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*hamil[3]*apar[7]-0.19485571585149863*apar[0]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[0]*apar[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*apar[1]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[1]*apar[3]*jacobtot_inv[5]*hamil[6]-0.38971143170299727*jacobtot_inv[0]*apar[5]*b_x[5]*hamil[6]-0.19485571585149863*apar[1]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*apar[3]*b_x[5]*hamil[6]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[5]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*apar[5]*hamil[6]-0.10825317547305482*apar[0]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*apar[3]*jacobtot_inv[3]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*apar[3]*b_x[3]*hamil[6]+0.19485571585149863*b_x[3]*hamil[3]*jacobtot_inv[5]*apar[6]+0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_x[5]*apar[6]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*hamil[3]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*hamil[3]*apar[6]-0.19485571585149863*apar[1]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.19485571585149863*b_x[1]*hamil[2]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_x[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_x[0]*apar[2]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*apar[0]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*b_x[0]*hamil[2]*apar[3]*jacobtot_inv[5]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*apar[5]*b_x[5]+0.19485571585149863*jacobtot_inv[1]*hamil[3]*apar[4]*b_x[5]-0.10825317547305482*apar[0]*hamil[2]*jacobtot_inv[3]*b_x[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_x[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[3]*b_x[5]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[5]+0.10825317547305482*b_x[0]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*hamil[3]*apar[4]+0.10825317547305482*b_x[1]*apar[2]*hamil[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*hamil[2]*b_x[3]*jacobtot_inv[3]-0.10825317547305482*b_x[1]*hamil[2]*apar[3]*jacobtot_inv[3]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[3]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[3]*b_x[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[16]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[16]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[16]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[16]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[16]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[8]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[8]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[8]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[8]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[7]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[7]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[7]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[7]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[7]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[7]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[7]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*hamil[6]*apar[7]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*hamil[6]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*hamil[6]*apar[7]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[6]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.19485571585149863*apar[3]*hamil[3]*b_y[5]*jacobtot_inv[5]+0.19485571585149863*apar[1]*hamil[1]*b_y[5]*jacobtot_inv[5]-0.19485571585149863*b_y[3]*hamil[3]*apar[5]*jacobtot_inv[5]+0.19485571585149863*b_y[1]*hamil[1]*apar[5]*jacobtot_inv[5]-0.10825317547305482*apar[0]*b_y[1]*hamil[3]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*apar[1]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*apar[0]*hamil[1]*b_y[3]*jacobtot_inv[5]+0.10825317547305482*b_y[0]*hamil[1]*apar[3]*jacobtot_inv[5]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*apar[5]*b_y[5]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*apar[5]*b_y[5]+0.10825317547305482*apar[0]*hamil[1]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[3]*b_y[5]-0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[3]*b_y[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*apar[3]*b_y[5]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[5]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[5]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[5]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[5]-0.21650635094610965*apar[1]*b_y[1]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*apar[1]*hamil[1]*b_y[3]*jacobtot_inv[3]+0.10825317547305482*b_y[1]*hamil[1]*apar[3]*jacobtot_inv[3]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[3]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[3]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*apar[3]*b_y[3])*rdx2*rdz2)/vmap[1]+((0.7014805770653949*apar[1]*b_z[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*b_z[1]*apar[5]*jacobtot_inv[5]*hamil[16]+0.7014805770653949*jacobtot_inv[1]*apar[5]*b_z[5]*hamil[16]+0.19485571585149863*apar[0]*jacobtot_inv[3]*b_z[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*apar[3]*b_z[5]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[5]*hamil[16]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[5]*hamil[16]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[3]*hamil[16]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[3]*hamil[16]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[1]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[1]*hamil[16]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[1]*hamil[16]+0.19485571585149863*apar[0]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[0]*apar[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[1]*b_z[3]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[1]*apar[3]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*apar[5]*b_z[5]*hamil[8]+0.38971143170299727*apar[1]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*apar[3]*b_z[5]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[5]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[5]*hamil[8]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[1]*hamil[8]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[1]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*apar[1]*b_z[1]*hamil[8]-0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[7]-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[7]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[7]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[7]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[7]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[7]-0.35074028853269745*hamil[1]*b_z[5]*jacobtot_inv[5]*apar[7]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[3]*apar[7]-0.19485571585149863*b_z[1]*hamil[1]*jacobtot_inv[1]*apar[7]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[1]*apar[7]+0.7014805770653949*apar[5]*b_z[5]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*apar[1]*b_z[1]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_z[5]*hamil[6]+0.38971143170299727*apar[1]*jacobtot_inv[1]*b_z[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_z[5]*hamil[6]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[5]*hamil[6]+0.38971143170299727*b_z[1]*jacobtot_inv[1]*apar[5]*hamil[6]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_z[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_z[0]*apar[1]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_z[3]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[3]*hamil[6]-0.19485571585149863*hamil[1]*b_z[3]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[1]*jacobtot_inv[3]*b_z[5]*apar[6]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[1]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[1]*apar[6]+0.19485571585149863*hamil[2]*apar[3]*b_z[5]*jacobtot_inv[5]+0.19485571585149863*hamil[2]*b_z[3]*apar[5]*jacobtot_inv[5]-0.19485571585149863*b_z[1]*hamil[1]*apar[4]*jacobtot_inv[5]+0.10825317547305482*apar[0]*b_z[1]*hamil[2]*jacobtot_inv[5]+0.10825317547305482*b_z[0]*apar[1]*hamil[2]*jacobtot_inv[5]-0.10825317547305482*b_z[0]*hamil[1]*apar[2]*jacobtot_inv[5]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*apar[5]*b_z[5]-0.19485571585149863*hamil[1]*jacobtot_inv[1]*apar[4]*b_z[5]+0.10825317547305482*apar[0]*jacobtot_inv[1]*hamil[2]*b_z[5]+0.21650635094610965*jacobtot_inv[0]*apar[1]*hamil[2]*b_z[5]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*apar[2]*b_z[5]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[5]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[5]-0.10825317547305482*b_z[0]*hamil[1]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*hamil[1]*b_z[3]*apar[4]+0.21650635094610965*apar[1]*b_z[1]*hamil[2]*jacobtot_inv[3]-0.10825317547305482*b_z[1]*hamil[1]*apar[2]*jacobtot_inv[3]+0.10825317547305482*apar[1]*jacobtot_inv[1]*hamil[2]*b_z[3]-0.10825317547305482*hamil[1]*jacobtot_inv[1]*apar[2]*b_z[3]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[8] = (((-(0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[16])-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[16]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[16]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[8]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*hamil[6]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*hamil[6]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[7]-0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[6]-0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[6]-0.10825317547305482*apar[2]*hamil[2]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*b_x[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*hamil[2]*jacobtot_inv[3]*apar[4]*b_x[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[3])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[16]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[16]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[16]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[16]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[8]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[8]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[8]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[8]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[7]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[7]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[7]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[7]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[7]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[7]-0.38971143170299727*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[3]*apar[7]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[7]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*hamil[3]*apar[7]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[7]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[6]-0.19485571585149863*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[6]+0.10825317547305482*hamil[1]*apar[2]*b_y[5]*jacobtot_inv[5]-0.21650635094610965*b_y[1]*hamil[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*b_y[3]*apar[4]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*jacobtot_inv[3]*apar[4]*b_y[5]-0.21650635094610965*jacobtot_inv[1]*hamil[3]*apar[4]*b_y[5]-0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[3]*b_y[5]-0.10825317547305482*b_y[0]*hamil[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*hamil[3]*apar[4]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[3]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[3])*rdx2*rdz2)/vmap[1]+((0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[16]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[16]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[16]+0.38971143170299727*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[8]+0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[8]+0.38971143170299727*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[8]+0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[8]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[8]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[8]+0.19485571585149863*jacobtot_inv[3]*b_z[5]*hamil[6]*apar[7]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[6]*apar[7]+0.38971143170299727*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[3]*apar[7]+0.21650635094610965*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[0]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[6]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[6]+0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[6]+0.10825317547305482*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[6]+0.21650635094610965*b_z[1]*hamil[2]*apar[4]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[1]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[0]*apar[2]*hamil[2]*b_z[5]+0.10825317547305482*b_z[0]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[0]*hamil[2]*b_z[3]*apar[4]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[3])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[12] = (((0.19485571585149863*b_x[0]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[21]+0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[2]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[2]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[5]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[6]*hamil[14]+0.19485571585149863*apar[4]*b_x[5]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_x[5]*hamil[14]+0.10825317547305482*b_x[3]*jacobtot_inv[3]*apar[4]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[2]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[21])-0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[1]*hamil[21]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[1]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[1]*hamil[21]-0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[1]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[1]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[1]*hamil[14]+0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[21]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[12]-0.19485571585149863*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[12]-0.10825317547305482*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[13] = ((-(0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[21]-0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[14]-0.21650635094610965*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[14]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[12]+0.21650635094610965*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[14] = (((0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[14]+0.19485571585149863*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[21]+0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[3]*hamil[21]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[3]*hamil[21]-0.38971143170299727*apar[5]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[14]-0.21650635094610965*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[0]*b_y[5]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[1]*b_y[3]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[3]*hamil[14]+0.10825317547305482*apar[0]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[1]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[21])-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[6]*hamil[21]-0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[2]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[7]*hamil[12]-0.19485571585149863*b_z[5]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[6]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[1]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[16] = (((-(0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[16])-0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[16]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[16]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[16]-0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[8]-0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[8]-0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[8]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[8]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[8]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[8]-0.19485571585149863*b_x[0]*jacobtot_inv[5]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[0]*b_x[5]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[3]*hamil[6]*apar[7]-0.38971143170299727*jacobtot_inv[1]*b_x[3]*hamil[6]*apar[7]-0.19485571585149863*b_x[1]*hamil[2]*jacobtot_inv[5]*apar[7]-0.38971143170299727*jacobtot_inv[1]*hamil[2]*b_x[5]*apar[7]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[3]*apar[7]-0.19485571585149863*b_x[1]*jacobtot_inv[5]*apar[6]*hamil[6]-0.38971143170299727*jacobtot_inv[1]*b_x[5]*apar[6]*hamil[6]-0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[6]*hamil[6]-0.21650635094610965*jacobtot_inv[0]*b_x[3]*apar[6]*hamil[6]-0.19485571585149863*apar[2]*b_x[5]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*b_x[3]*apar[4]*jacobtot_inv[5]*hamil[6]-0.19485571585149863*jacobtot_inv[3]*apar[4]*b_x[5]*hamil[6]-0.10825317547305482*apar[2]*b_x[3]*jacobtot_inv[3]*hamil[6]-0.10825317547305482*b_x[0]*hamil[2]*jacobtot_inv[5]*apar[6]-0.21650635094610965*jacobtot_inv[0]*hamil[2]*b_x[5]*apar[6]-0.10825317547305482*b_x[1]*hamil[2]*jacobtot_inv[3]*apar[6]-0.21650635094610965*jacobtot_inv[1]*hamil[2]*b_x[3]*apar[6]-0.19485571585149863*hamil[2]*apar[4]*b_x[5]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*b_x[3]*jacobtot_inv[5]-0.10825317547305482*apar[2]*hamil[2]*jacobtot_inv[3]*b_x[5]-0.10825317547305482*hamil[2]*b_x[3]*jacobtot_inv[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[16]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[16]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[16]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[16]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[16]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[16]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[16]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[16]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[16]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[8]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[8]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[8]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[8]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[8]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[8]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[8]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[8]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[8]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[8]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[7]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[7]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[7]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[7]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[7]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[7]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[7]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[7]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[7]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[7]-0.19485571585149863*b_y[3]*hamil[3]*jacobtot_inv[5]*apar[7]+0.19485571585149863*b_y[1]*hamil[1]*jacobtot_inv[5]*apar[7]-0.38971143170299727*hamil[3]*jacobtot_inv[3]*b_y[5]*apar[7]+0.38971143170299727*hamil[1]*jacobtot_inv[1]*b_y[5]*apar[7]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[3]*apar[7]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*hamil[3]*apar[7]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*hamil[3]*apar[7]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[3]*apar[7]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[6]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[6]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[6]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[6]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[6]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[6]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[6]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[6]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[6]-0.19485571585149863*hamil[3]*b_y[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_y[0]*hamil[1]*jacobtot_inv[5]*apar[6]+0.21650635094610965*jacobtot_inv[0]*hamil[1]*b_y[5]*apar[6]+0.10825317547305482*b_y[1]*hamil[1]*jacobtot_inv[3]*apar[6]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*hamil[3]*apar[6]+0.21650635094610965*hamil[1]*jacobtot_inv[1]*b_y[3]*apar[6]+0.19485571585149863*hamil[1]*apar[4]*b_y[5]*jacobtot_inv[5]-0.10825317547305482*b_y[0]*hamil[3]*apar[4]*jacobtot_inv[5]-0.10825317547305482*b_y[1]*apar[2]*hamil[3]*jacobtot_inv[5]+0.10825317547305482*hamil[1]*apar[2]*b_y[3]*jacobtot_inv[5]-0.21650635094610965*jacobtot_inv[0]*hamil[3]*apar[4]*b_y[5]+0.10825317547305482*hamil[1]*apar[2]*jacobtot_inv[3]*b_y[5]-0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[3]*b_y[5]-0.21650635094610965*b_y[1]*hamil[3]*jacobtot_inv[3]*apar[4]+0.10825317547305482*hamil[1]*b_y[3]*jacobtot_inv[3]*apar[4]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[16]+0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[16]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[16]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[16]+0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[16]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[16]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[16]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[16]+0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[7]*hamil[8]+0.38971143170299727*jacobtot_inv[0]*b_z[5]*apar[7]*hamil[8]+0.38971143170299727*b_z[1]*jacobtot_inv[3]*apar[7]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[7]*hamil[8]+0.19485571585149863*b_z[1]*jacobtot_inv[5]*apar[6]*hamil[8]+0.19485571585149863*jacobtot_inv[1]*b_z[5]*apar[6]*hamil[8]+0.19485571585149863*apar[2]*b_z[5]*jacobtot_inv[5]*hamil[8]+0.19485571585149863*b_z[3]*apar[4]*jacobtot_inv[5]*hamil[8]+0.38971143170299727*jacobtot_inv[3]*apar[4]*b_z[5]*hamil[8]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[4]*hamil[8]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*apar[4]*hamil[8]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*apar[2]*hamil[8]+0.35074028853269745*b_z[5]*jacobtot_inv[5]*hamil[6]*apar[7]+0.19485571585149863*b_z[1]*jacobtot_inv[1]*hamil[6]*apar[7]+0.19485571585149863*hamil[2]*b_z[3]*jacobtot_inv[5]*apar[7]+0.38971143170299727*hamil[2]*jacobtot_inv[3]*b_z[5]*apar[7]+0.10825317547305482*b_z[0]*jacobtot_inv[1]*hamil[2]*apar[7]+0.21650635094610965*jacobtot_inv[0]*b_z[1]*hamil[2]*apar[7]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[6]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[6]+0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[6]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[6]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[6]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[6]+0.19485571585149863*hamil[2]*b_z[5]*jacobtot_inv[5]*apar[6]+0.10825317547305482*b_z[1]*jacobtot_inv[1]*hamil[2]*apar[6]+0.10825317547305482*b_z[0]*hamil[2]*apar[4]*jacobtot_inv[5]+0.10825317547305482*b_z[1]*apar[2]*hamil[2]*jacobtot_inv[5]+0.21650635094610965*jacobtot_inv[0]*hamil[2]*apar[4]*b_z[5]+0.10825317547305482*jacobtot_inv[1]*apar[2]*hamil[2]*b_z[5]+0.21650635094610965*b_z[1]*hamil[2]*jacobtot_inv[3]*apar[4]+0.10825317547305482*jacobtot_inv[1]*hamil[2]*b_z[3]*apar[4])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[20] = ((-(0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[21])+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[21]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[21]-0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[21]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*b_y[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[2]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[4]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[2]*hamil[14]+0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[12]+0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[12]+0.21650635094610965*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[12]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[12]+0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[12]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[21] = (((0.35074028853269745*b_x[3]*jacobtot_inv[5]*apar[7]*hamil[21]+0.35074028853269745*jacobtot_inv[3]*b_x[5]*apar[7]*hamil[21]+0.19485571585149863*b_x[0]*jacobtot_inv[1]*apar[7]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*b_x[1]*apar[7]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[6]*hamil[21]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[6]*hamil[21]+0.19485571585149863*b_x[0]*apar[4]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*b_x[1]*apar[2]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*jacobtot_inv[0]*apar[4]*b_x[5]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*apar[2]*b_x[5]*hamil[21]+0.19485571585149863*b_x[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.19485571585149863*jacobtot_inv[1]*b_x[3]*apar[4]*hamil[21]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[3]*hamil[21]+0.35074028853269745*b_x[5]*jacobtot_inv[5]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[3]*apar[7]*hamil[14]+0.19485571585149863*b_x[1]*jacobtot_inv[1]*apar[7]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[0]*apar[7]*hamil[14]+0.19485571585149863*b_x[3]*jacobtot_inv[5]*apar[6]*hamil[14]+0.19485571585149863*jacobtot_inv[3]*b_x[5]*apar[6]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[1]*apar[6]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[1]*apar[6]*hamil[14]+0.19485571585149863*b_x[1]*apar[4]*jacobtot_inv[5]*hamil[14]+0.10825317547305482*b_x[0]*apar[2]*jacobtot_inv[5]*hamil[14]+0.19485571585149863*jacobtot_inv[1]*apar[4]*b_x[5]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_x[5]*hamil[14]+0.10825317547305482*b_x[0]*jacobtot_inv[3]*apar[4]*hamil[14]+0.10825317547305482*jacobtot_inv[0]*b_x[3]*apar[4]*hamil[14]+0.10825317547305482*b_x[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_x[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.38971143170299727*apar[3]*b_y[3]*jacobtot_inv[5]*hamil[21]-0.38971143170299727*apar[1]*b_y[1]*jacobtot_inv[5]*hamil[21]+0.19485571585149863*apar[3]*jacobtot_inv[3]*b_y[5]*hamil[21]-0.19485571585149863*apar[1]*jacobtot_inv[1]*b_y[5]*hamil[21]+0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[5]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[5]*hamil[21]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[3]*hamil[21]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[3]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[3]*hamil[21]-0.19485571585149863*apar[3]*b_y[5]*jacobtot_inv[5]*hamil[14]-0.19485571585149863*b_y[3]*apar[5]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*apar[0]*b_y[1]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[0]*apar[1]*jacobtot_inv[5]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*apar[5]*b_y[5]*hamil[14]-0.10825317547305482*apar[0]*jacobtot_inv[1]*b_y[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[1]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[5]*hamil[14]-0.21650635094610965*apar[1]*b_y[1]*jacobtot_inv[3]*hamil[14]-0.10825317547305482*apar[1]*jacobtot_inv[1]*b_y[3]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[3]*hamil[14]+0.19485571585149863*apar[1]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.19485571585149863*b_y[1]*apar[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[0]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[0]*apar[3]*jacobtot_inv[5]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*apar[5]*b_y[5]*hamil[12]+0.10825317547305482*apar[0]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*apar[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[5]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[5]*hamil[12]+0.10825317547305482*apar[1]*b_y[3]*jacobtot_inv[3]*hamil[12]+0.10825317547305482*b_y[1]*apar[3]*jacobtot_inv[3]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*apar[3]*b_y[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.35074028853269745*b_z[1]*jacobtot_inv[5]*apar[7]*hamil[21])-0.35074028853269745*jacobtot_inv[1]*b_z[5]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[3]*apar[7]*hamil[21]-0.19485571585149863*b_z[0]*jacobtot_inv[5]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[0]*b_z[5]*apar[6]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[3]*apar[6]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*b_z[3]*apar[6]*hamil[21]-0.35074028853269745*apar[4]*b_z[5]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*b_z[3]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*apar[2]*jacobtot_inv[3]*b_z[5]*hamil[21]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[4]*hamil[21]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[4]*hamil[21]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[2]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[2]*hamil[21]-0.35074028853269745*b_z[5]*jacobtot_inv[5]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[3]*apar[7]*hamil[12]-0.19485571585149863*b_z[1]*jacobtot_inv[1]*apar[7]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[0]*apar[7]*hamil[12]-0.19485571585149863*b_z[3]*jacobtot_inv[5]*apar[6]*hamil[12]-0.19485571585149863*jacobtot_inv[3]*b_z[5]*apar[6]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[1]*apar[6]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[1]*apar[6]*hamil[12]-0.19485571585149863*b_z[1]*apar[4]*jacobtot_inv[5]*hamil[12]-0.10825317547305482*b_z[0]*apar[2]*jacobtot_inv[5]*hamil[12]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_z[5]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_z[5]*hamil[12]-0.10825317547305482*b_z[0]*jacobtot_inv[3]*apar[4]*hamil[12]-0.10825317547305482*jacobtot_inv[0]*b_z[3]*apar[4]*hamil[12]-0.10825317547305482*b_z[1]*apar[2]*jacobtot_inv[3]*hamil[12]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_z[3]*hamil[12])*rdx2*rdy2)/vmap[1])/m_; 
-  alphavpar[22] = ((0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[21]+0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[3]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[6]*hamil[21]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[21]-0.10825317547305482*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[21]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[21]+0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[3]*hamil[21]-0.38971143170299727*b_y[5]*jacobtot_inv[5]*apar[7]*hamil[14]-0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[0]*apar[7]*hamil[14]-0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[1]*apar[6]*hamil[14]-0.21650635094610965*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*apar[2]*b_y[5]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[0]*b_y[3]*apar[4]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[14]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[6]*hamil[12]+0.10825317547305482*apar[2]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*b_y[3]*apar[4]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*jacobtot_inv[3]*apar[4]*b_y[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[3]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
-  alphavpar[27] = ((0.19485571585149863*b_y[3]*jacobtot_inv[3]*apar[7]*hamil[21]-0.19485571585149863*b_y[1]*jacobtot_inv[1]*apar[7]*hamil[21]+0.38971143170299727*b_y[3]*jacobtot_inv[5]*apar[6]*hamil[21]+0.19485571585149863*jacobtot_inv[3]*b_y[5]*apar[6]*hamil[21]+0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[6]*hamil[21]-0.38971143170299727*b_y[1]*apar[4]*jacobtot_inv[5]*hamil[21]-0.19485571585149863*jacobtot_inv[1]*apar[4]*b_y[5]*hamil[21]-0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[4]*hamil[21]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[3]*hamil[21]+0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[3]*hamil[21]-0.19485571585149863*b_y[3]*jacobtot_inv[5]*apar[7]*hamil[14]-0.38971143170299727*jacobtot_inv[3]*b_y[5]*apar[7]*hamil[14]-0.10825317547305482*b_y[0]*jacobtot_inv[1]*apar[7]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*b_y[1]*apar[7]*hamil[14]-0.19485571585149863*b_y[5]*jacobtot_inv[5]*apar[6]*hamil[14]-0.10825317547305482*b_y[1]*jacobtot_inv[1]*apar[6]*hamil[14]-0.10825317547305482*b_y[0]*apar[4]*jacobtot_inv[5]*hamil[14]-0.10825317547305482*b_y[1]*apar[2]*jacobtot_inv[5]*hamil[14]-0.21650635094610965*jacobtot_inv[0]*apar[4]*b_y[5]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*apar[2]*b_y[5]*hamil[14]-0.21650635094610965*b_y[1]*jacobtot_inv[3]*apar[4]*hamil[14]-0.10825317547305482*jacobtot_inv[1]*b_y[3]*apar[4]*hamil[14]+0.19485571585149863*b_y[1]*jacobtot_inv[5]*apar[7]*hamil[12]+0.38971143170299727*jacobtot_inv[1]*b_y[5]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[3]*apar[7]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[3]*apar[7]*hamil[12]+0.10825317547305482*b_y[0]*jacobtot_inv[5]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[0]*b_y[5]*apar[6]*hamil[12]+0.10825317547305482*b_y[1]*jacobtot_inv[3]*apar[6]*hamil[12]+0.21650635094610965*jacobtot_inv[1]*b_y[3]*apar[6]*hamil[12]+0.19485571585149863*apar[4]*b_y[5]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*b_y[3]*jacobtot_inv[5]*hamil[12]+0.10825317547305482*apar[2]*jacobtot_inv[3]*b_y[5]*hamil[12]+0.10825317547305482*b_y[3]*jacobtot_inv[3]*apar[4]*hamil[12])*rdx2*rdz2)/(vmap[1]*m_); 
+  alphavpar[0] = (((-(0.3061862178478971*apar[3]*bioverJB_1[5]*hamil[16])-0.3061862178478971*bioverJB_1[3]*apar[5]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_1[5]*hamil[8]-0.3061862178478971*apar[3]*bioverJB_1[3]*hamil[8]+0.3061862178478971*bioverJB_1[3]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_1[5]*apar[6]*hamil[7]+0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[7]+0.3061862178478971*hamil[3]*bioverJB_1[5]*apar[7]-0.3061862178478971*bioverJB_1[0]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_1[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_1[3]*hamil[3]*apar[6]-0.3061862178478971*bioverJB_1[1]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_1[1]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_1[0]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[3]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_2[3]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[7]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[7]+0.3061862178478971*bioverJB_2[1]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_2[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_2[3]*hamil[3]*apar[5]+0.3061862178478971*bioverJB_2[1]*hamil[1]*apar[5]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[3]+0.3061862178478971*bioverJB_2[0]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_3[3]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[7]-0.1767766952966368*hamil[3]*apar[5]*dualcurlbhatoverB_3[5]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[1]*hamil[3]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*apar[1]*bioverJB_3[5]*hamil[16]+0.3061862178478971*bioverJB_3[1]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_3[0]*apar[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_3[3]*hamil[8]-0.3061862178478971*bioverJB_3[1]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_3[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_3[5]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_3[5]*apar[7]+0.3061862178478971*apar[5]*bioverJB_3[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_3[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_3[3]*apar[6]+0.3061862178478971*hamil[2]*bioverJB_3[3]*apar[5]-0.3061862178478971*bioverJB_3[1]*hamil[1]*apar[4]+0.3061862178478971*bioverJB_3[0]*apar[1]*hamil[2]-0.3061862178478971*bioverJB_3[0]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_2[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[3]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_2[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[2]*apar[5]*dualcurlbhatoverB_2[5]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_2[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[1]*hamil[2]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[0]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_1[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[6]*hamil[16]-0.1767766952966368*apar[4]*dualcurlbhatoverB_1[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[5]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[5]*dualcurlbhatoverB_1[5]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_1[3]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[1]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((-(0.5511351921262146*apar[5]*bioverJB_1[5]*hamil[16])-0.3061862178478971*apar[3]*bioverJB_1[3]*hamil[16]-0.3061862178478971*apar[3]*bioverJB_1[5]*hamil[8]-0.3061862178478971*bioverJB_1[3]*apar[5]*hamil[8]+0.5511351921262146*bioverJB_1[5]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_1[3]*apar[6]*hamil[7]+0.5511351921262146*bioverJB_1[1]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[7]+0.3061862178478971*bioverJB_1[3]*hamil[3]*apar[7]-0.5511351921262146*bioverJB_1[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_1[0]*apar[3]*hamil[6]+0.3061862178478971*hamil[3]*bioverJB_1[5]*apar[6]-0.3061862178478971*bioverJB_1[0]*hamil[2]*apar[5]+0.3061862178478971*bioverJB_1[0]*hamil[3]*apar[4]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[3]-0.3061862178478971*bioverJB_1[1]*hamil[2]*apar[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[5]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_2[5]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[8]+0.3061862178478971*apar[3]*bioverJB_2[5]*hamil[7]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[7]+0.3061862178478971*bioverJB_2[0]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_2[1]*apar[6]*hamil[6]-0.3061862178478971*hamil[3]*apar[5]*bioverJB_2[5]+0.3061862178478971*bioverJB_2[0]*hamil[1]*apar[5]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[3]+0.3061862178478971*bioverJB_2[1]*hamil[1]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_3[5]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_3[5]*hamil[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[7]-0.31819805153394626*apar[1]*dualcurlbhatoverB_3[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[7]-0.1767766952966368*apar[3]*hamil[3]*dualcurlbhatoverB_3[5]-0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[3])*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_3[0]*apar[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_3[3]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_3[5]*hamil[8]+0.3061862178478971*bioverJB_3[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_3[0]*apar[7]*hamil[7]-0.3061862178478971*bioverJB_3[1]*apar[6]*hamil[7]-0.3061862178478971*apar[2]*bioverJB_3[5]*hamil[7]-0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[7]-0.3061862178478971*hamil[1]*bioverJB_3[3]*apar[7]+0.3061862178478971*bioverJB_3[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_3[0]*apar[1]*hamil[6]-0.3061862178478971*hamil[1]*bioverJB_3[5]*apar[6]+0.3061862178478971*hamil[2]*apar[5]*bioverJB_3[5]-0.3061862178478971*bioverJB_3[0]*hamil[1]*apar[4]+0.3061862178478971*apar[1]*bioverJB_3[1]*hamil[2]-0.3061862178478971*bioverJB_3[1]*hamil[1]*apar[2])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_2[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_2[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[3]*hamil[8]-0.31819805153394626*apar[5]*dualcurlbhatoverB_2[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_2[3]*hamil[6]-0.31819805153394626*apar[1]*dualcurlbhatoverB_2[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[0]*hamil[6]-0.1767766952966368*hamil[2]*apar[3]*dualcurlbhatoverB_2[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[1]*hamil[2]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[1]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_1[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[3]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_1[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[1]*apar[3]*dualcurlbhatoverB_1[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[1]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_1[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[8]-0.3061862178478971*bioverJB_1[0]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_1[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_1[1]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_1[0]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[16]-0.3061862178478971*bioverJB_2[3]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[8]+0.3061862178478971*bioverJB_2[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_2[3]*hamil[3]*apar[7]+0.3061862178478971*bioverJB_2[1]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_2[1]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_2[0]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_2[0]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_3[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[16]-0.1767766952966368*apar[5]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_3[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[0]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[16]+0.3061862178478971*bioverJB_3[0]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_3[3]*apar[7]-0.3061862178478971*bioverJB_3[3]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_3[0]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_2[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_2[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[3]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[5]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[5]*apar[6]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_1[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[6]*hamil[7]-0.1767766952966368*apar[4]*dualcurlbhatoverB_1[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[5]*apar[7]-0.1767766952966368*apar[5]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*apar[3]*dualcurlbhatoverB_1[3]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[3]*apar[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[3] = (((-(0.3061862178478971*bioverJB_1[0]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_1[1]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_1[1]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_1[0]*apar[3]*hamil[8]+0.3061862178478971*bioverJB_1[0]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_1[1]*apar[6]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_1[5]*hamil[7]+0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[7]+0.3061862178478971*bioverJB_1[1]*hamil[3]*apar[7]-0.3061862178478971*apar[3]*bioverJB_1[5]*hamil[6]-0.3061862178478971*bioverJB_1[3]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_1[0]*hamil[3]*apar[6]-0.3061862178478971*hamil[2]*apar[5]*bioverJB_1[5]+0.3061862178478971*hamil[3]*apar[4]*bioverJB_1[5]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[3]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_1[3])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[0]*apar[6]*hamil[16]-0.3061862178478971*apar[4]*bioverJB_2[5]*hamil[16]-0.3061862178478971*bioverJB_2[0]*apar[7]*hamil[8]-0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_2[5]*hamil[7]+0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_2[5]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_2[3]*apar[6]*hamil[6]+0.3061862178478971*hamil[1]*apar[5]*bioverJB_2[5]-0.3061862178478971*bioverJB_2[0]*hamil[3]*apar[5]-0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[3]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_2[3])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_3[0]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[6]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[5]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[6]*hamil[8]-0.1767766952966368*apar[4]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[5]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[7]-0.1767766952966368*apar[1]*hamil[3]*dualcurlbhatoverB_3[5]-0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[3]*apar[5]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*apar[5]*bioverJB_3[5]*hamil[16]+0.3061862178478971*apar[1]*bioverJB_3[1]*hamil[16]+0.5511351921262146*bioverJB_3[3]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_3[0]*apar[1]*hamil[8]-0.5511351921262146*bioverJB_3[5]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_3[3]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_3[1]*hamil[1]*apar[7]+0.3061862178478971*apar[1]*bioverJB_3[5]*hamil[6]+0.3061862178478971*bioverJB_3[1]*apar[5]*hamil[6]-0.3061862178478971*bioverJB_3[0]*hamil[1]*apar[6]-0.3061862178478971*hamil[1]*apar[4]*bioverJB_3[5]+0.3061862178478971*bioverJB_3[0]*hamil[2]*apar[5]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_3[3]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_3[3])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_2[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_2[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[1]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_2[5]*hamil[8]-0.31819805153394626*apar[3]*dualcurlbhatoverB_2[3]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[1]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[0]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_2[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_2[5]-0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[2]*apar[5]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_2[3]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_1[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[16]-0.31819805153394626*apar[5]*dualcurlbhatoverB_1[5]*hamil[7]-0.31819805153394626*apar[3]*dualcurlbhatoverB_1[3]*hamil[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[6]*hamil[6]-0.1767766952966368*apar[4]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[6]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_1[5]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[5]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_1[3]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((0.3061862178478971*bioverJB_1[3]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_1[5]*apar[6]*hamil[21]+0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_1[5]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_1[3]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_1[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[21]-0.3061862178478971*bioverJB_2[3]*apar[5]*hamil[14]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[14]+0.3061862178478971*bioverJB_2[1]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[3]*dualcurlbhatoverB_3[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[1]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[1]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_3[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_3[5]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[21]-0.3061862178478971*bioverJB_3[5]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_3[3]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[1]*dualcurlbhatoverB_1[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[21]-0.1767766952966368*apar[5]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*apar[3]*dualcurlbhatoverB_1[3]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[6] = (((0.5511351921262146*bioverJB_1[1]*apar[4]*hamil[16]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[16]+0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[8]-0.5511351921262146*bioverJB_1[1]*hamil[6]*apar[7]-0.3061862178478971*bioverJB_1[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_1[0]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_1[1]*hamil[2]*apar[6])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_2[5]*hamil[16]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[16]-0.3061862178478971*apar[5]*bioverJB_2[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[8]+0.3061862178478971*bioverJB_2[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[7]-0.3061862178478971*hamil[3]*bioverJB_2[5]*apar[7]+0.3061862178478971*bioverJB_2[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_2[0]*apar[5]*hamil[6]+0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[6]+0.3061862178478971*bioverJB_2[1]*hamil[1]*apar[6]-0.3061862178478971*bioverJB_2[1]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_3[5]*hamil[16])-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_3[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[16]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_3[5]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[6]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[3]*apar[7]-0.1767766952966368*hamil[3]*dualcurlbhatoverB_3[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[3]*apar[4]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[3])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[1]*apar[6]*hamil[16])-0.3061862178478971*apar[2]*bioverJB_3[5]*hamil[16]+0.3061862178478971*bioverJB_3[1]*apar[7]*hamil[8]+0.3061862178478971*apar[4]*bioverJB_3[5]*hamil[8]+0.3061862178478971*hamil[2]*bioverJB_3[5]*apar[7]-0.3061862178478971*bioverJB_3[5]*apar[6]*hamil[6]-0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[6]+0.3061862178478971*bioverJB_3[1]*hamil[2]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_2[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_2[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[3]*apar[4]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_2[5]*hamil[6]*apar[7]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[3]*apar[6]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_2[1]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[2]*hamil[6]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[2]*apar[4]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[2]*hamil[2])*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_1[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[7]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[3]*apar[7]-0.1767766952966368*apar[3]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[6]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[5]*apar[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[4]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[7] = (((-(0.5511351921262146*bioverJB_1[1]*apar[5]*hamil[16])-0.3061862178478971*bioverJB_1[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_1[0]*apar[5]*hamil[8]-0.3061862178478971*bioverJB_1[1]*apar[3]*hamil[8]+0.5511351921262146*bioverJB_1[1]*apar[7]*hamil[7]+0.3061862178478971*bioverJB_1[0]*apar[6]*hamil[7]+0.5511351921262146*apar[4]*bioverJB_1[5]*hamil[7]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[7]+0.3061862178478971*bioverJB_1[0]*hamil[3]*apar[7]-0.5511351921262146*apar[5]*bioverJB_1[5]*hamil[6]-0.3061862178478971*apar[3]*bioverJB_1[3]*hamil[6]+0.3061862178478971*bioverJB_1[1]*hamil[3]*apar[6]+0.3061862178478971*apar[2]*hamil[3]*bioverJB_1[5]-0.3061862178478971*hamil[2]*apar[3]*bioverJB_1[5]-0.3061862178478971*hamil[2]*bioverJB_1[3]*apar[5]+0.3061862178478971*bioverJB_1[3]*hamil[3]*apar[4])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*bioverJB_2[1]*apar[6]*hamil[16]-0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[16]-0.3061862178478971*bioverJB_2[1]*apar[7]*hamil[8]-0.3061862178478971*apar[4]*bioverJB_2[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[7]+0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[7]+0.3061862178478971*bioverJB_2[3]*hamil[6]*apar[7]+0.3061862178478971*bioverJB_2[5]*apar[6]*hamil[6]-0.3061862178478971*apar[1]*hamil[3]*bioverJB_2[5]+0.3061862178478971*hamil[1]*apar[3]*bioverJB_2[5]-0.3061862178478971*bioverJB_2[1]*hamil[3]*apar[5]+0.3061862178478971*hamil[1]*bioverJB_2[3]*apar[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_3[1]*apar[7]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[6]*hamil[16]-0.31819805153394626*apar[4]*dualcurlbhatoverB_3[5]*hamil[16]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[7]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[6]*hamil[8]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_3[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[7]-0.1767766952966368*apar[0]*hamil[3]*dualcurlbhatoverB_3[5]-0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[3]*apar[5]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[3]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[3])*rdz2)/vmap[1]+((0.5511351921262146*bioverJB_3[3]*apar[5]*hamil[16]+0.3061862178478971*bioverJB_3[0]*apar[1]*hamil[16]+0.5511351921262146*apar[5]*bioverJB_3[5]*hamil[8]+0.3061862178478971*apar[1]*bioverJB_3[1]*hamil[8]-0.5511351921262146*bioverJB_3[3]*apar[7]*hamil[7]-0.5511351921262146*bioverJB_3[5]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[7]-0.3061862178478971*bioverJB_3[0]*hamil[1]*apar[7]+0.3061862178478971*bioverJB_3[0]*apar[5]*hamil[6]+0.3061862178478971*apar[1]*bioverJB_3[3]*hamil[6]-0.3061862178478971*bioverJB_3[1]*hamil[1]*apar[6]+0.3061862178478971*apar[1]*hamil[2]*bioverJB_3[5]-0.3061862178478971*hamil[1]*apar[2]*bioverJB_3[5]+0.3061862178478971*bioverJB_3[1]*hamil[2]*apar[5]-0.3061862178478971*hamil[1]*bioverJB_3[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*apar[5]*dualcurlbhatoverB_2[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_2[3]*hamil[16]-0.31819805153394626*apar[1]*dualcurlbhatoverB_2[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[0]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_2[5]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_2[3]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[1]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[1]*hamil[8]-0.31819805153394626*apar[1]*dualcurlbhatoverB_2[5]*hamil[6]-0.31819805153394626*dualcurlbhatoverB_2[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_2[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[3]*hamil[6]-0.1767766952966368*apar[0]*hamil[2]*dualcurlbhatoverB_2[5]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[2]*apar[5]-0.1767766952966368*apar[1]*hamil[2]*dualcurlbhatoverB_2[3]-0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[2]*apar[3])*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_1[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_1[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[16]-0.31819805153394626*apar[3]*dualcurlbhatoverB_1[5]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[5]*hamil[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[6]-0.1767766952966368*apar[0]*hamil[1]*dualcurlbhatoverB_1[5]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[5]-0.1767766952966368*apar[1]*hamil[1]*dualcurlbhatoverB_1[3]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.3061862178478971*apar[2]*bioverJB_1[5]*hamil[16]+0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[16]+0.3061862178478971*apar[4]*bioverJB_1[5]*hamil[8]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[8]-0.3061862178478971*bioverJB_1[3]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_1[5]*apar[7]-0.3061862178478971*bioverJB_1[5]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_1[3]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_2[5]*hamil[16])+0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[16]-0.3061862178478971*bioverJB_2[0]*apar[5]*hamil[8]-0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[8]+0.3061862178478971*bioverJB_2[0]*apar[6]*hamil[7]-0.3061862178478971*apar[4]*bioverJB_2[5]*hamil[7]+0.3061862178478971*hamil[1]*bioverJB_2[5]*apar[7]-0.3061862178478971*bioverJB_2[0]*hamil[3]*apar[7]+0.3061862178478971*apar[5]*bioverJB_2[5]*hamil[6]+0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_2[3]*apar[6]-0.3061862178478971*bioverJB_2[3]*hamil[3]*apar[4])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_3[5]*hamil[16])-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[5]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[5]*hamil[8]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[6]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[5]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[3]*apar[6]-0.1767766952966368*hamil[3]*apar[4]*dualcurlbhatoverB_3[5]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[3])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_3[3]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_3[3]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_3[0]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_3[0]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[6]+0.3061862178478971*hamil[2]*bioverJB_3[3]*apar[4])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_2[3]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_2[5]*apar[6]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_2[5]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_2[3]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[2]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[6]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[3]*apar[4]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[2]*apar[6]-0.1767766952966368*hamil[2]*apar[4]*dualcurlbhatoverB_2[5]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_2[3])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_1[5]*hamil[16])-0.31819805153394626*apar[3]*dualcurlbhatoverB_1[3]*hamil[16]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_1[5]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[7]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[5]*hamil[6]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[4]*dualcurlbhatoverB_1[5]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_1[3])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((0.5511351921262146*bioverJB_1[5]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_1[3]*apar[6]*hamil[21]+0.5511351921262146*bioverJB_1[1]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_1[0]*apar[2]*hamil[21]+0.3061862178478971*bioverJB_1[3]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_1[5]*apar[6]*hamil[14]+0.3061862178478971*bioverJB_1[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_1[1]*apar[2]*hamil[14])*rdy2*rdz2)/vmap[1]+((0.3061862178478971*apar[3]*bioverJB_2[5]*hamil[21]-0.3061862178478971*bioverJB_2[0]*apar[1]*hamil[21]-0.3061862178478971*apar[5]*bioverJB_2[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_2[1]*hamil[14]+0.3061862178478971*bioverJB_2[0]*apar[5]*hamil[12]+0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_3[5]*hamil[21])-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[3]*hamil[21]-0.31819805153394626*apar[1]*dualcurlbhatoverB_3[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[0]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[1]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[1]*hamil[14])*rdz2)/vmap[1]+((-(0.3061862178478971*bioverJB_3[0]*apar[7]*hamil[21])-0.3061862178478971*bioverJB_3[1]*apar[6]*hamil[21]-0.3061862178478971*apar[2]*bioverJB_3[5]*hamil[21]-0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_3[3]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_3[5]*apar[6]*hamil[12]-0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[12]-0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_1[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[21]-0.1767766952966368*apar[3]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[13] = (((0.3061862178478971*bioverJB_2[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_2[3]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_2[1]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_2[0]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_3[3]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_1[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[6]*hamil[21]-0.1767766952966368*apar[4]*dualcurlbhatoverB_1[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[5]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[14] = (((0.3061862178478971*bioverJB_1[0]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_1[1]*apar[6]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_1[5]*hamil[21]+0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[21]+0.3061862178478971*bioverJB_1[1]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_1[0]*apar[6]*hamil[14]+0.3061862178478971*apar[4]*bioverJB_1[5]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_2[5]*hamil[21])+0.3061862178478971*bioverJB_2[0]*apar[3]*hamil[21]-0.3061862178478971*bioverJB_2[0]*apar[5]*hamil[14]-0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[14]+0.3061862178478971*apar[5]*bioverJB_2[5]*hamil[12]+0.3061862178478971*apar[3]*bioverJB_2[3]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*apar[0]*dualcurlbhatoverB_3[5]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[5]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[5]*hamil[14]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_3[5]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_3[3]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_3[0]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_3[1]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_3[0]*apar[6]*hamil[12]-0.3061862178478971*apar[4]*bioverJB_3[5]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_3[3]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[5]*dualcurlbhatoverB_1[5]*hamil[21])-0.31819805153394626*apar[3]*dualcurlbhatoverB_1[3]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[0]*hamil[21]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[5]*hamil[12]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[16] = (((0.5511351921262146*apar[4]*bioverJB_1[5]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[16]+0.3061862178478971*apar[2]*bioverJB_1[5]*hamil[8]+0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[8]-0.5511351921262146*bioverJB_1[5]*hamil[6]*apar[7]-0.3061862178478971*hamil[2]*bioverJB_1[3]*apar[7]-0.3061862178478971*bioverJB_1[3]*apar[6]*hamil[6]-0.3061862178478971*hamil[2]*bioverJB_1[5]*apar[6])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[16])+0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[16]-0.3061862178478971*apar[1]*bioverJB_2[5]*hamil[8]-0.3061862178478971*bioverJB_2[1]*apar[5]*hamil[8]+0.3061862178478971*bioverJB_2[1]*apar[6]*hamil[7]-0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[7]-0.3061862178478971*bioverJB_2[1]*hamil[3]*apar[7]+0.3061862178478971*hamil[1]*bioverJB_2[3]*apar[7]+0.3061862178478971*apar[3]*bioverJB_2[5]*hamil[6]+0.3061862178478971*bioverJB_2[3]*apar[5]*hamil[6]+0.3061862178478971*hamil[1]*bioverJB_2[5]*apar[6]-0.3061862178478971*hamil[3]*apar[4]*bioverJB_2[5])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_3[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[5]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[5]*hamil[8]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[7]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[6]*hamil[7]-0.31819805153394626*apar[4]*dualcurlbhatoverB_3[5]*hamil[7]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_3[0]*hamil[3]*apar[7]-0.1767766952966368*dualcurlbhatoverB_3[1]*hamil[3]*apar[6]-0.1767766952966368*apar[2]*hamil[3]*dualcurlbhatoverB_3[5]-0.1767766952966368*dualcurlbhatoverB_3[3]*hamil[3]*apar[4])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_3[5]*apar[6]*hamil[16])-0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[16]+0.5511351921262146*bioverJB_3[5]*apar[7]*hamil[8]+0.3061862178478971*bioverJB_3[1]*apar[4]*hamil[8]+0.3061862178478971*bioverJB_3[1]*hamil[2]*apar[7]-0.3061862178478971*bioverJB_3[1]*apar[6]*hamil[6]-0.3061862178478971*apar[2]*bioverJB_3[5]*hamil[6]+0.3061862178478971*hamil[2]*apar[4]*bioverJB_3[5])*rdx2*rdy2)/vmap[1]+((-(0.5727564927611033*dualcurlbhatoverB_2[5]*apar[7]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_2[3]*apar[6]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_2[1]*apar[4]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[2]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_2[3]*apar[7]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_2[5]*apar[6]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[4]*hamil[8]-0.1767766952966368*dualcurlbhatoverB_2[1]*apar[2]*hamil[8]-0.31819805153394626*dualcurlbhatoverB_2[1]*hamil[6]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[0]*hamil[2]*apar[7]-0.1767766952966368*dualcurlbhatoverB_2[0]*apar[6]*hamil[6]-0.31819805153394626*apar[4]*dualcurlbhatoverB_2[5]*hamil[6]-0.1767766952966368*apar[2]*dualcurlbhatoverB_2[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_2[1]*hamil[2]*apar[6]-0.1767766952966368*apar[2]*hamil[2]*dualcurlbhatoverB_2[5]-0.1767766952966368*hamil[2]*dualcurlbhatoverB_2[3]*apar[4])*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_1[5]*hamil[16])-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[5]*hamil[16]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[16]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[16]-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[7]*hamil[7]-0.31819805153394626*dualcurlbhatoverB_1[5]*apar[6]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[7]-0.1767766952966368*dualcurlbhatoverB_1[0]*hamil[1]*apar[7]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[5]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[5]*hamil[6]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[6]-0.1767766952966368*dualcurlbhatoverB_1[1]*hamil[1]*apar[6]-0.1767766952966368*hamil[1]*apar[2]*dualcurlbhatoverB_1[5]-0.1767766952966368*hamil[1]*dualcurlbhatoverB_1[3]*apar[4])*rdx2)/vmap[1])/m_; 
+  alphavpar[20] = (((0.3061862178478971*bioverJB_2[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_2[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_2[5]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_2[1]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_2[0]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_2[1]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_3[5]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[6]*hamil[21]-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[5]*apar[6]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[4]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[2]*hamil[14])*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_1[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[5]*apar[6]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[21] = (((0.5511351921262146*bioverJB_1[1]*apar[7]*hamil[21]+0.3061862178478971*bioverJB_1[0]*apar[6]*hamil[21]+0.5511351921262146*apar[4]*bioverJB_1[5]*hamil[21]+0.3061862178478971*apar[2]*bioverJB_1[3]*hamil[21]+0.3061862178478971*bioverJB_1[0]*apar[7]*hamil[14]+0.3061862178478971*bioverJB_1[1]*apar[6]*hamil[14]+0.3061862178478971*apar[2]*bioverJB_1[5]*hamil[14]+0.3061862178478971*bioverJB_1[3]*apar[4]*hamil[14])*rdy2*rdz2)/vmap[1]+((-(0.3061862178478971*apar[1]*bioverJB_2[3]*hamil[21])+0.3061862178478971*bioverJB_2[1]*apar[3]*hamil[21]-0.3061862178478971*apar[1]*bioverJB_2[5]*hamil[14]-0.3061862178478971*bioverJB_2[1]*apar[5]*hamil[14]+0.3061862178478971*apar[3]*bioverJB_2[5]*hamil[12]+0.3061862178478971*bioverJB_2[3]*apar[5]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*apar[1]*dualcurlbhatoverB_3[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_3[1]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[3]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[5]*hamil[14]-0.1767766952966368*apar[1]*dualcurlbhatoverB_3[3]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[3]*hamil[14])*rdz2)/vmap[1]+((-(0.5511351921262146*bioverJB_3[3]*apar[7]*hamil[21])-0.5511351921262146*bioverJB_3[5]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_3[0]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_3[1]*apar[2]*hamil[21]-0.3061862178478971*bioverJB_3[0]*apar[7]*hamil[12]-0.3061862178478971*bioverJB_3[1]*apar[6]*hamil[12]-0.3061862178478971*apar[2]*bioverJB_3[5]*hamil[12]-0.3061862178478971*bioverJB_3[3]*apar[4]*hamil[12])*rdx2*rdy2)/vmap[1]+((-(0.31819805153394626*apar[3]*dualcurlbhatoverB_1[5]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[5]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[1]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[1]*hamil[21]-0.1767766952966368*apar[0]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[5]*hamil[12]-0.1767766952966368*apar[1]*dualcurlbhatoverB_1[3]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[22] = (((0.3061862178478971*bioverJB_2[0]*apar[6]*hamil[21]-0.3061862178478971*apar[4]*bioverJB_2[5]*hamil[21]-0.3061862178478971*bioverJB_2[0]*apar[7]*hamil[14]-0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[14]+0.3061862178478971*bioverJB_2[5]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_2[3]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.1767766952966368*dualcurlbhatoverB_3[0]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[6]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[5]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[6]*hamil[14]-0.1767766952966368*apar[4]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_1[5]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_1[3]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[6]*hamil[12]-0.1767766952966368*apar[4]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[3]*hamil[12])*rdx2)/vmap[1])/m_; 
+  alphavpar[27] = (((0.3061862178478971*bioverJB_2[1]*apar[6]*hamil[21]-0.3061862178478971*bioverJB_2[3]*apar[4]*hamil[21]-0.3061862178478971*bioverJB_2[1]*apar[7]*hamil[14]-0.3061862178478971*apar[4]*bioverJB_2[5]*hamil[14]+0.3061862178478971*bioverJB_2[3]*apar[7]*hamil[12]+0.3061862178478971*bioverJB_2[5]*apar[6]*hamil[12])*rdx2*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_3[1]*apar[7]*hamil[21])-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[6]*hamil[21]-0.31819805153394626*apar[4]*dualcurlbhatoverB_3[5]*hamil[21]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[3]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_3[0]*apar[7]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[1]*apar[6]*hamil[14]-0.1767766952966368*apar[2]*dualcurlbhatoverB_3[5]*hamil[14]-0.1767766952966368*dualcurlbhatoverB_3[3]*apar[4]*hamil[14])*rdz2)/vmap[1]+((-(0.31819805153394626*dualcurlbhatoverB_1[3]*apar[7]*hamil[21])-0.31819805153394626*dualcurlbhatoverB_1[5]*apar[6]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[4]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[2]*hamil[21]-0.1767766952966368*dualcurlbhatoverB_1[0]*apar[7]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[1]*apar[6]*hamil[12]-0.1767766952966368*apar[2]*dualcurlbhatoverB_1[5]*hamil[12]-0.1767766952966368*dualcurlbhatoverB_1[3]*apar[4]*hamil[12])*rdx2)/vmap[1])/m_; 
 
 
   out[4] += 0.3061862178478971*(alphavpar[27]*fin[27]+alphavpar[22]*fin[22]+alphavpar[21]*fin[21]+alphavpar[20]*fin[20]+alphavpar[16]*fin[16]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_2x2v_ser_p1.c
index 58845cb3d4..a7f6cd3f9e 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_2x2v_ser_p1.c
@@ -22,13 +22,13 @@ GKYL_CU_DH double dg_gyrokinetic_no_by_vol_2x2v_ser_p1(const double *w, const do
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[2]*dxv[2];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[4]; 
-  const double *bioverJB_z = &bioverJB[8]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[4]; 
+  const double *bioverJB_3 = &bioverJB[8]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[4]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[8]; 
 
   double hamil[24] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_3x2v_ser_p1.c
index 759613f79d..534609df37 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_no_by_vol_3x2v_ser_p1.c
@@ -23,13 +23,13 @@ GKYL_CU_DH double dg_gyrokinetic_no_by_vol_3x2v_ser_p1(const double *w, const do
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[3]*dxv[3];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[8]; 
-  const double *bioverJB_z = &bioverJB[16]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[8]; 
+  const double *bioverJB_3 = &bioverJB[16]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[8]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[16]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[16]; 
 
   double hamil[48] = {0.}; 
   hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x1v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x1v_ser_p1.c
index bc8b9fcdef..584dd57402 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x1v_ser_p1.c
@@ -20,13 +20,13 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x1v_ser_p1(const double *w, const double *
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[1]*dxv[1];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[2]; 
-  const double *bioverJB_z = &bioverJB[4]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[2]; 
+  const double *bioverJB_3 = &bioverJB[4]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[4]; 
 
   double hamil[6] = {0.}; 
   hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
@@ -41,12 +41,12 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x1v_ser_p1(const double *w, const double *
   hamil2[1] = hamil[4]*hamil[4]; 
 
   double alphax[6] = {0.}; 
-  alphax[0] = (rdx2*((3.5355339059327373*dualcurlbhatoverB_z[0]*hamil2[1])/vmap2+(0.7071067811865475*dualcurlbhatoverB_z[0]*hamil2[0])/vmap2))/(m_*q_)+(rtg33inv[0]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
-  alphax[1] = (rdx2*((3.5355339059327373*dualcurlbhatoverB_z[1]*hamil2[1])/vmap2+(0.7071067811865475*hamil2[0]*dualcurlbhatoverB_z[1])/vmap2))/(m_*q_)+(rtg33inv[1]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
-  alphax[2] = (3.1622776601683795*dualcurlbhatoverB_z[0]*hamil[2]*hamil[4]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[0]*vmap[1]*hamil[4]*rdx2)/(m_*vmap2); 
-  alphax[3] = (3.1622776601683795*dualcurlbhatoverB_z[1]*hamil[2]*hamil[4]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[1]*vmap[1]*hamil[4]*rdx2)/(m_*vmap2); 
-  alphax[4] = (3.1622776601683795*dualcurlbhatoverB_z[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[5] = (3.16227766016838*dualcurlbhatoverB_z[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[0] = (rdx2*((3.5355339059327373*dualcurlbhatoverB_3[0]*hamil2[1])/vmap2+(0.7071067811865475*dualcurlbhatoverB_3[0]*hamil2[0])/vmap2))/(m_*q_)+(rtg33inv[0]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
+  alphax[1] = (rdx2*((3.5355339059327373*dualcurlbhatoverB_3[1]*hamil2[1])/vmap2+(0.7071067811865475*hamil2[0]*dualcurlbhatoverB_3[1])/vmap2))/(m_*q_)+(rtg33inv[1]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
+  alphax[2] = (3.1622776601683795*dualcurlbhatoverB_3[0]*hamil[2]*hamil[4]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[0]*vmap[1]*hamil[4]*rdx2)/(m_*vmap2); 
+  alphax[3] = (3.1622776601683795*dualcurlbhatoverB_3[1]*hamil[2]*hamil[4]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[1]*vmap[1]*hamil[4]*rdx2)/(m_*vmap2); 
+  alphax[4] = (3.1622776601683795*dualcurlbhatoverB_3[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[5] = (3.16227766016838*dualcurlbhatoverB_3[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
 
 
   out[1] += 0.8660254037844386*(alphax[5]*fin[5]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -54,10 +54,10 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x1v_ser_p1(const double *w, const double *
   out[5] += 0.5532833351724881*alphax[5]*fin[5]+0.8660254037844386*(alphax[1]*fin[5]+fin[1]*alphax[5])+0.5532833351724881*alphax[4]*fin[4]+0.8660254037844387*(alphax[0]*fin[4]+fin[0]*alphax[4])+0.7745966692414834*(alphax[3]*fin[3]+alphax[2]*fin[2]); 
 
   double alphavpar[6] = {0.}; 
-  alphavpar[0] = -((0.7071067811865475*dualcurlbhatoverB_z[0]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*hamil[1]*vmap[1]*rdx2)/(m_*vmap2); 
-  alphavpar[1] = -((0.7071067811865475*dualcurlbhatoverB_z[1]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*hamil[1]*rtg33inv[1]*vmap[1]*rdx2)/(m_*vmap2); 
-  alphavpar[2] = -((1.5811388300841895*dualcurlbhatoverB_z[0]*hamil[1]*hamil[4]*rdx2)/(m_*q_*vmap2)); 
-  alphavpar[3] = -((1.5811388300841895*dualcurlbhatoverB_z[1]*hamil[1]*hamil[4]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[0] = -((0.7071067811865475*dualcurlbhatoverB_3[0]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*hamil[1]*vmap[1]*rdx2)/(m_*vmap2); 
+  alphavpar[1] = -((0.7071067811865475*dualcurlbhatoverB_3[1]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*hamil[1]*rtg33inv[1]*vmap[1]*rdx2)/(m_*vmap2); 
+  alphavpar[2] = -((1.5811388300841895*dualcurlbhatoverB_3[0]*hamil[1]*hamil[4]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[3] = -((1.5811388300841895*dualcurlbhatoverB_3[1]*hamil[1]*hamil[4]*rdx2)/(m_*q_*vmap2)); 
 
 
   out[2] += 0.8660254037844386*(alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x2v_ser_p1.c
index d1a6d34223..e8c0bb028d 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_1x2v_ser_p1.c
@@ -21,13 +21,13 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x2v_ser_p1(const double *w, const double *
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[1]*dxv[1];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[2]; 
-  const double *bioverJB_z = &bioverJB[4]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[2]; 
+  const double *bioverJB_3 = &bioverJB[4]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[2]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[2]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[4]; 
 
   double hamil[12] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
@@ -44,12 +44,12 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x2v_ser_p1(const double *w, const double *
   hamil2[1] = hamil[8]*hamil[8]; 
 
   double alphax[12] = {0.}; 
-  alphax[0] = (rdx2*((2.5*dualcurlbhatoverB_z[0]*hamil2[1])/vmap2+(0.5*dualcurlbhatoverB_z[0]*hamil2[0])/vmap2))/(m_*q_)+(rtg33inv[0]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
-  alphax[1] = (rdx2*((2.5*dualcurlbhatoverB_z[1]*hamil2[1])/vmap2+(0.5*hamil2[0]*dualcurlbhatoverB_z[1])/vmap2))/(m_*q_)+(rtg33inv[1]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
-  alphax[2] = (2.23606797749979*dualcurlbhatoverB_z[0]*hamil[2]*hamil[8]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[0]*vmap[1]*hamil[8]*rdx2)/(m_*vmap2); 
-  alphax[4] = (2.23606797749979*dualcurlbhatoverB_z[1]*hamil[2]*hamil[8]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[1]*vmap[1]*hamil[8]*rdx2)/(m_*vmap2); 
-  alphax[8] = (2.23606797749979*dualcurlbhatoverB_z[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[9] = (2.2360679774997902*dualcurlbhatoverB_z[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[0] = (rdx2*((2.5*dualcurlbhatoverB_3[0]*hamil2[1])/vmap2+(0.5*dualcurlbhatoverB_3[0]*hamil2[0])/vmap2))/(m_*q_)+(rtg33inv[0]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
+  alphax[1] = (rdx2*((2.5*dualcurlbhatoverB_3[1]*hamil2[1])/vmap2+(0.5*hamil2[0]*dualcurlbhatoverB_3[1])/vmap2))/(m_*q_)+(rtg33inv[1]*vmap[1]*hamil[2]*rdx2)/(m_*vmap2); 
+  alphax[2] = (2.23606797749979*dualcurlbhatoverB_3[0]*hamil[2]*hamil[8]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[0]*vmap[1]*hamil[8]*rdx2)/(m_*vmap2); 
+  alphax[4] = (2.23606797749979*dualcurlbhatoverB_3[1]*hamil[2]*hamil[8]*rdx2)/(m_*q_*vmap2)+(2.23606797749979*rtg33inv[1]*vmap[1]*hamil[8]*rdx2)/(m_*vmap2); 
+  alphax[8] = (2.23606797749979*dualcurlbhatoverB_3[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[9] = (2.2360679774997902*dualcurlbhatoverB_3[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
 
 
   out[1] += 0.6123724356957944*(alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[4]*fin[4]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -60,14 +60,14 @@ GKYL_CU_DH double dg_gyrokinetic_vol_1x2v_ser_p1(const double *w, const double *
   out[11] += (0.39123039821797573*alphax[9]+0.6123724356957944*alphax[1])*fin[11]+0.39123039821797573*alphax[8]*fin[10]+0.6123724356957944*(alphax[0]*fin[10]+fin[5]*alphax[9]+fin[3]*alphax[8])+0.5477225575051661*(alphax[4]*fin[7]+alphax[2]*fin[6]); 
 
   double alphavpar[12] = {0.}; 
-  alphavpar[0] = -((0.5*dualcurlbhatoverB_z[0]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*hamil[1]*vmap[1]*rdx2)/(m_*vmap2); 
-  alphavpar[1] = -((0.5*dualcurlbhatoverB_z[1]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*hamil[1]*rtg33inv[1]*vmap[1]*rdx2)/(m_*vmap2); 
-  alphavpar[2] = -((1.118033988749895*dualcurlbhatoverB_z[0]*hamil[1]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
-  alphavpar[3] = -((0.5*dualcurlbhatoverB_z[0]*hamil[2]*hamil[5]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*vmap[1]*hamil[5]*rdx2)/(m_*vmap2); 
-  alphavpar[4] = -((1.118033988749895*dualcurlbhatoverB_z[1]*hamil[1]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
-  alphavpar[5] = -((0.5*dualcurlbhatoverB_z[1]*hamil[2]*hamil[5]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[1]*vmap[1]*hamil[5]*rdx2)/(m_*vmap2); 
-  alphavpar[6] = -((1.118033988749895*dualcurlbhatoverB_z[0]*hamil[5]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
-  alphavpar[7] = -((1.118033988749895*dualcurlbhatoverB_z[1]*hamil[5]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[0] = -((0.5*dualcurlbhatoverB_3[0]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*hamil[1]*vmap[1]*rdx2)/(m_*vmap2); 
+  alphavpar[1] = -((0.5*dualcurlbhatoverB_3[1]*hamil[1]*hamil[2]*rdx2)/(m_*q_*vmap2))-(1.0*hamil[1]*rtg33inv[1]*vmap[1]*rdx2)/(m_*vmap2); 
+  alphavpar[2] = -((1.118033988749895*dualcurlbhatoverB_3[0]*hamil[1]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[3] = -((0.5*dualcurlbhatoverB_3[0]*hamil[2]*hamil[5]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[0]*vmap[1]*hamil[5]*rdx2)/(m_*vmap2); 
+  alphavpar[4] = -((1.118033988749895*dualcurlbhatoverB_3[1]*hamil[1]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[5] = -((0.5*dualcurlbhatoverB_3[1]*hamil[2]*hamil[5]*rdx2)/(m_*q_*vmap2))-(1.0*rtg33inv[1]*vmap[1]*hamil[5]*rdx2)/(m_*vmap2); 
+  alphavpar[6] = -((1.118033988749895*dualcurlbhatoverB_3[0]*hamil[5]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
+  alphavpar[7] = -((1.118033988749895*dualcurlbhatoverB_3[1]*hamil[5]*hamil[8]*rdx2)/(m_*q_*vmap2)); 
 
 
   out[2] += 0.6123724356957944*(alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_2x2v_ser_p1.c
index ca50761939..96f313faa4 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_2x2v_ser_p1.c
@@ -22,13 +22,13 @@ GKYL_CU_DH double dg_gyrokinetic_vol_2x2v_ser_p1(const double *w, const double *
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[2]*dxv[2];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[4]; 
-  const double *bioverJB_z = &bioverJB[8]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[4]; 
+  const double *bioverJB_3 = &bioverJB[8]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[4]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[4]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[8]; 
 
   double hamil[24] = {0.}; 
   hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
@@ -49,22 +49,22 @@ GKYL_CU_DH double dg_gyrokinetic_vol_2x2v_ser_p1(const double *w, const double *
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = (rdx2*((1.25*dualcurlbhatoverB_x[0]*hamil2[1])/vmap2+(0.25*dualcurlbhatoverB_x[0]*hamil2[0])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_y[1]*hamil[5]+0.8660254037844386*bioverJB_y[0]*hamil[2])*rdx2*rdz2)/q_; 
-  alphax[1] = (rdx2*((1.25*dualcurlbhatoverB_x[1]*hamil2[1])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_x[1])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_y[0]*hamil[5]+0.8660254037844386*bioverJB_y[1]*hamil[2])*rdx2*rdz2)/q_; 
-  alphax[2] = (rdx2*((1.25*hamil2[1]*dualcurlbhatoverB_x[2])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_x[2])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_y[3]*hamil[5]+0.8660254037844386*bioverJB_y[2]*hamil[2])*rdx2*rdz2)/q_; 
-  alphax[3] = (1.118033988749895*dualcurlbhatoverB_x[0]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
-  alphax[4] = ((0.8660254037844386*bioverJB_y[1]*hamil[12]+0.8660254037844386*bioverJB_y[0]*hamil[9])*rdx2*rdz2)/q_; 
-  alphax[5] = (rdx2*((1.25*hamil2[1]*dualcurlbhatoverB_x[3])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_x[3])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_y[2]*hamil[5]+0.8660254037844386*hamil[2]*bioverJB_y[3])*rdx2*rdz2)/q_; 
-  alphax[6] = (1.118033988749895*dualcurlbhatoverB_x[1]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
-  alphax[7] = (1.118033988749895*dualcurlbhatoverB_x[2]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
-  alphax[8] = ((0.8660254037844386*bioverJB_y[0]*hamil[12]+0.8660254037844386*bioverJB_y[1]*hamil[9])*rdx2*rdz2)/q_; 
-  alphax[9] = ((0.8660254037844386*bioverJB_y[3]*hamil[12]+0.8660254037844386*bioverJB_y[2]*hamil[9])*rdx2*rdz2)/q_; 
-  alphax[11] = (1.118033988749895*dualcurlbhatoverB_x[3]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
-  alphax[12] = ((0.8660254037844386*bioverJB_y[2]*hamil[12]+0.8660254037844386*bioverJB_y[3]*hamil[9])*rdx2*rdz2)/q_; 
-  alphax[16] = (1.118033988749895*dualcurlbhatoverB_x[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[17] = (1.1180339887498951*dualcurlbhatoverB_x[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[18] = (1.1180339887498951*hamil2[1]*dualcurlbhatoverB_x[2]*rdx2)/(m_*q_*vmap2); 
-  alphax[20] = (1.118033988749895*hamil2[1]*dualcurlbhatoverB_x[3]*rdx2)/(m_*q_*vmap2); 
+  alphax[0] = (rdx2*((1.25*dualcurlbhatoverB_1[0]*hamil2[1])/vmap2+(0.25*dualcurlbhatoverB_1[0]*hamil2[0])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_2[1]*hamil[5]+0.8660254037844386*bioverJB_2[0]*hamil[2])*rdx2*rdz2)/q_; 
+  alphax[1] = (rdx2*((1.25*dualcurlbhatoverB_1[1]*hamil2[1])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_1[1])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_2[0]*hamil[5]+0.8660254037844386*bioverJB_2[1]*hamil[2])*rdx2*rdz2)/q_; 
+  alphax[2] = (rdx2*((1.25*hamil2[1]*dualcurlbhatoverB_1[2])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_1[2])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_2[3]*hamil[5]+0.8660254037844386*bioverJB_2[2]*hamil[2])*rdx2*rdz2)/q_; 
+  alphax[3] = (1.118033988749895*dualcurlbhatoverB_1[0]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
+  alphax[4] = ((0.8660254037844386*bioverJB_2[1]*hamil[12]+0.8660254037844386*bioverJB_2[0]*hamil[9])*rdx2*rdz2)/q_; 
+  alphax[5] = (rdx2*((1.25*hamil2[1]*dualcurlbhatoverB_1[3])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_1[3])/vmap2))/(m_*q_)+((0.8660254037844386*bioverJB_2[2]*hamil[5]+0.8660254037844386*hamil[2]*bioverJB_2[3])*rdx2*rdz2)/q_; 
+  alphax[6] = (1.118033988749895*dualcurlbhatoverB_1[1]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
+  alphax[7] = (1.118033988749895*dualcurlbhatoverB_1[2]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
+  alphax[8] = ((0.8660254037844386*bioverJB_2[0]*hamil[12]+0.8660254037844386*bioverJB_2[1]*hamil[9])*rdx2*rdz2)/q_; 
+  alphax[9] = ((0.8660254037844386*bioverJB_2[3]*hamil[12]+0.8660254037844386*bioverJB_2[2]*hamil[9])*rdx2*rdz2)/q_; 
+  alphax[11] = (1.118033988749895*dualcurlbhatoverB_1[3]*hamil[3]*hamil[16]*rdx2)/(m_*q_*vmap2); 
+  alphax[12] = ((0.8660254037844386*bioverJB_2[2]*hamil[12]+0.8660254037844386*bioverJB_2[3]*hamil[9])*rdx2*rdz2)/q_; 
+  alphax[16] = (1.118033988749895*dualcurlbhatoverB_1[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[17] = (1.1180339887498951*dualcurlbhatoverB_1[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[18] = (1.1180339887498951*hamil2[1]*dualcurlbhatoverB_1[2]*rdx2)/(m_*q_*vmap2); 
+  alphax[20] = (1.118033988749895*hamil2[1]*dualcurlbhatoverB_1[3]*rdx2)/(m_*q_*vmap2); 
 
 
   out[1] += 0.4330127018922193*(alphax[20]*fin[20]+alphax[18]*fin[18]+alphax[17]*fin[17]+alphax[16]*fin[16]+alphax[12]*fin[12]+alphax[11]*fin[11]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -81,22 +81,22 @@ GKYL_CU_DH double dg_gyrokinetic_vol_2x2v_ser_p1(const double *w, const double *
   out[23] += (0.27664166758624403*alphax[17]+0.4330127018922193*alphax[1])*fin[23]+(0.27664166758624403*alphax[16]+0.43301270189221935*alphax[0])*fin[22]+0.27664166758624403*alphax[20]*fin[21]+0.43301270189221935*(alphax[5]*fin[21]+alphax[8]*fin[20]+fin[8]*alphax[20])+0.27664166758624403*alphax[18]*fin[19]+0.4330127018922193*(alphax[2]*fin[19]+alphax[4]*fin[18]+fin[4]*alphax[18]+alphax[12]*fin[17]+fin[12]*alphax[17])+0.43301270189221935*(alphax[9]*fin[16]+fin[9]*alphax[16])+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = (rdz2*((1.25*dualcurlbhatoverB_z[0]*hamil2[1])/vmap2+(0.25*dualcurlbhatoverB_z[0]*hamil2[0])/vmap2))/(m_*q_)+(0.7071067811865475*rtg33inv[0]*vmap[1]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_y[2]*hamil[5])-0.8660254037844386*bioverJB_y[0]*hamil[1])*rdx2*rdz2)/q_; 
-  alphaz[1] = (rdz2*((1.25*dualcurlbhatoverB_z[1]*hamil2[1])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_z[1])/vmap2))/(m_*q_)+(0.7071067811865475*rtg33inv[1]*vmap[1]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_y[3]*hamil[5])-0.8660254037844386*bioverJB_y[1]*hamil[1])*rdx2*rdz2)/q_; 
-  alphaz[2] = (rdz2*((1.25*hamil2[1]*dualcurlbhatoverB_z[2])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_z[2])/vmap2))/(m_*q_)+(0.7071067811865475*vmap[1]*rtg33inv[2]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_y[0]*hamil[5])-0.8660254037844386*hamil[1]*bioverJB_y[2])*rdx2*rdz2)/q_; 
-  alphaz[3] = (1.118033988749895*dualcurlbhatoverB_z[0]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*rtg33inv[0]*vmap[1]*hamil[16]*rdz2)/(m_*vmap2); 
-  alphaz[4] = ((-(0.8660254037844386*bioverJB_y[2]*hamil[12])-0.8660254037844386*bioverJB_y[0]*hamil[8])*rdx2*rdz2)/q_; 
-  alphaz[5] = (rdz2*((1.25*hamil2[1]*dualcurlbhatoverB_z[3])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_z[3])/vmap2))/(m_*q_)+(0.7071067811865475*vmap[1]*hamil[3]*rtg33inv[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_y[1]*hamil[5])-0.8660254037844386*hamil[1]*bioverJB_y[3])*rdx2*rdz2)/q_; 
-  alphaz[6] = (1.118033988749895*dualcurlbhatoverB_z[1]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*rtg33inv[1]*vmap[1]*hamil[16]*rdz2)/(m_*vmap2); 
-  alphaz[7] = (1.118033988749895*dualcurlbhatoverB_z[2]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*vmap[1]*rtg33inv[2]*hamil[16]*rdz2)/(m_*vmap2); 
-  alphaz[8] = ((-(0.8660254037844386*bioverJB_y[3]*hamil[12])-0.8660254037844386*bioverJB_y[1]*hamil[8])*rdx2*rdz2)/q_; 
-  alphaz[9] = ((-(0.8660254037844386*bioverJB_y[0]*hamil[12])-0.8660254037844386*bioverJB_y[2]*hamil[8])*rdx2*rdz2)/q_; 
-  alphaz[11] = (1.118033988749895*dualcurlbhatoverB_z[3]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*vmap[1]*rtg33inv[3]*hamil[16]*rdz2)/(m_*vmap2); 
-  alphaz[12] = ((-(0.8660254037844386*bioverJB_y[1]*hamil[12])-0.8660254037844386*bioverJB_y[3]*hamil[8])*rdx2*rdz2)/q_; 
-  alphaz[16] = (1.118033988749895*dualcurlbhatoverB_z[0]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
-  alphaz[17] = (1.1180339887498951*dualcurlbhatoverB_z[1]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
-  alphaz[18] = (1.1180339887498951*hamil2[1]*dualcurlbhatoverB_z[2]*rdz2)/(m_*q_*vmap2); 
-  alphaz[20] = (1.118033988749895*hamil2[1]*dualcurlbhatoverB_z[3]*rdz2)/(m_*q_*vmap2); 
+  alphaz[0] = (rdz2*((1.25*dualcurlbhatoverB_3[0]*hamil2[1])/vmap2+(0.25*dualcurlbhatoverB_3[0]*hamil2[0])/vmap2))/(m_*q_)+(0.7071067811865475*rtg33inv[0]*vmap[1]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_2[2]*hamil[5])-0.8660254037844386*bioverJB_2[0]*hamil[1])*rdx2*rdz2)/q_; 
+  alphaz[1] = (rdz2*((1.25*dualcurlbhatoverB_3[1]*hamil2[1])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_3[1])/vmap2))/(m_*q_)+(0.7071067811865475*rtg33inv[1]*vmap[1]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_2[3]*hamil[5])-0.8660254037844386*bioverJB_2[1]*hamil[1])*rdx2*rdz2)/q_; 
+  alphaz[2] = (rdz2*((1.25*hamil2[1]*dualcurlbhatoverB_3[2])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_3[2])/vmap2))/(m_*q_)+(0.7071067811865475*vmap[1]*rtg33inv[2]*hamil[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_2[0]*hamil[5])-0.8660254037844386*hamil[1]*bioverJB_2[2])*rdx2*rdz2)/q_; 
+  alphaz[3] = (1.118033988749895*dualcurlbhatoverB_3[0]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*rtg33inv[0]*vmap[1]*hamil[16]*rdz2)/(m_*vmap2); 
+  alphaz[4] = ((-(0.8660254037844386*bioverJB_2[2]*hamil[12])-0.8660254037844386*bioverJB_2[0]*hamil[8])*rdx2*rdz2)/q_; 
+  alphaz[5] = (rdz2*((1.25*hamil2[1]*dualcurlbhatoverB_3[3])/vmap2+(0.25*hamil2[0]*dualcurlbhatoverB_3[3])/vmap2))/(m_*q_)+(0.7071067811865475*vmap[1]*hamil[3]*rtg33inv[3]*rdz2)/(m_*vmap2)+((-(0.8660254037844386*bioverJB_2[1]*hamil[5])-0.8660254037844386*hamil[1]*bioverJB_2[3])*rdx2*rdz2)/q_; 
+  alphaz[6] = (1.118033988749895*dualcurlbhatoverB_3[1]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*rtg33inv[1]*vmap[1]*hamil[16]*rdz2)/(m_*vmap2); 
+  alphaz[7] = (1.118033988749895*dualcurlbhatoverB_3[2]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*vmap[1]*rtg33inv[2]*hamil[16]*rdz2)/(m_*vmap2); 
+  alphaz[8] = ((-(0.8660254037844386*bioverJB_2[3]*hamil[12])-0.8660254037844386*bioverJB_2[1]*hamil[8])*rdx2*rdz2)/q_; 
+  alphaz[9] = ((-(0.8660254037844386*bioverJB_2[0]*hamil[12])-0.8660254037844386*bioverJB_2[2]*hamil[8])*rdx2*rdz2)/q_; 
+  alphaz[11] = (1.118033988749895*dualcurlbhatoverB_3[3]*hamil[3]*hamil[16]*rdz2)/(m_*q_*vmap2)+(1.5811388300841895*vmap[1]*rtg33inv[3]*hamil[16]*rdz2)/(m_*vmap2); 
+  alphaz[12] = ((-(0.8660254037844386*bioverJB_2[1]*hamil[12])-0.8660254037844386*bioverJB_2[3]*hamil[8])*rdx2*rdz2)/q_; 
+  alphaz[16] = (1.118033988749895*dualcurlbhatoverB_3[0]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
+  alphaz[17] = (1.1180339887498951*dualcurlbhatoverB_3[1]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
+  alphaz[18] = (1.1180339887498951*hamil2[1]*dualcurlbhatoverB_3[2]*rdz2)/(m_*q_*vmap2); 
+  alphaz[20] = (1.118033988749895*hamil2[1]*dualcurlbhatoverB_3[3]*rdz2)/(m_*q_*vmap2); 
 
 
   out[2] += 0.4330127018922193*(alphaz[20]*fin[20]+alphaz[18]*fin[18]+alphaz[17]*fin[17]+alphaz[16]*fin[16]+alphaz[12]*fin[12]+alphaz[11]*fin[11]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -113,22 +113,22 @@ GKYL_CU_DH double dg_gyrokinetic_vol_2x2v_ser_p1(const double *w, const double *
   out[23] += (0.27664166758624403*alphaz[18]+0.4330127018922193*alphaz[2])*fin[23]+(0.27664166758624403*alphaz[20]+0.43301270189221935*alphaz[5])*fin[22]+0.27664166758624403*alphaz[16]*fin[21]+0.43301270189221935*(alphaz[0]*fin[21]+alphaz[9]*fin[20]+fin[9]*alphaz[20])+0.27664166758624403*alphaz[17]*fin[19]+0.4330127018922193*(alphaz[1]*fin[19]+alphaz[12]*fin[18]+fin[12]*alphaz[18]+alphaz[4]*fin[17]+fin[4]*alphaz[17])+0.43301270189221935*(alphaz[8]*fin[16]+fin[8]*alphaz[16])+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = (rdx2*(-((0.25*dualcurlbhatoverB_x[2]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_x[0]*hamil[1]*hamil[3])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_z[1]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_z[0]*hamil[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[1]*hamil[5])/vmap2)-(0.7071067811865475*rtg33inv[0]*hamil[2])/vmap2))/m_; 
-  alphavpar[1] = (rdx2*(-((0.25*dualcurlbhatoverB_x[3]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_x[1]*hamil[1]*hamil[3])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_z[0]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_z[1]*hamil[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[0]*hamil[5])/vmap2)-(0.7071067811865475*rtg33inv[1]*hamil[2])/vmap2))/m_; 
-  alphavpar[2] = (rdz2*(-((0.25*dualcurlbhatoverB_z[3]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_z[2]*hamil[2]*hamil[3])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_x[0]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[1]*dualcurlbhatoverB_x[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[3]*hamil[5])/vmap2)-(0.7071067811865475*hamil[2]*rtg33inv[2])/vmap2))/m_; 
-  alphavpar[3] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[2]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[0]*hamil[1]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[1]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[0]*hamil[2]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[4] = (rdx2*(-((0.25*dualcurlbhatoverB_x[2]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_x[0]*hamil[3]*hamil[8])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_z[1]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_z[0]*hamil[3]*hamil[9])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[1]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[0]*hamil[9])/vmap2))/m_; 
-  alphavpar[5] = (rdz2*(-((0.25*dualcurlbhatoverB_z[2]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[2]*dualcurlbhatoverB_z[3]*hamil[3])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_x[1]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[1]*dualcurlbhatoverB_x[3]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[2]*hamil[5])/vmap2)-(0.7071067811865475*hamil[2]*rtg33inv[3])/vmap2))/m_; 
-  alphavpar[6] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[3]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[1]*hamil[1]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[0]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[1]*hamil[2]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[7] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[3]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[2]*hamil[2]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[0]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[1]*dualcurlbhatoverB_x[2]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[8] = (rdx2*(-((0.25*dualcurlbhatoverB_x[3]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_x[1]*hamil[3]*hamil[8])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_z[0]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_z[1]*hamil[3]*hamil[9])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[0]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[1]*hamil[9])/vmap2))/m_; 
-  alphavpar[9] = (rdz2*(-((0.25*dualcurlbhatoverB_z[3]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_z[2]*hamil[3]*hamil[9])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_x[0]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_x[2]*hamil[3]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[3]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[2]*hamil[9])/vmap2))/m_; 
-  alphavpar[10] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[2]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[0]*hamil[8]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[1]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[0]*hamil[9]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[11] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[2]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[2]*dualcurlbhatoverB_z[3]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[1]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[1]*dualcurlbhatoverB_x[3]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[12] = (rdz2*(-((0.25*dualcurlbhatoverB_z[2]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_z[3]*hamil[3]*hamil[9])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_x[1]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_x[3]*hamil[3]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[2]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[3]*hamil[9])/vmap2))/m_; 
-  alphavpar[13] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[3]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[1]*hamil[8]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[0]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[1]*hamil[9]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[14] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[3]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[2]*hamil[9]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[0]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[2]*hamil[8]*hamil[16])/vmap2))/(m_*q_); 
-  alphavpar[15] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_z[2]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_z[3]*hamil[9]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_x[1]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_x[3]*hamil[8]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[0] = (rdx2*(-((0.25*dualcurlbhatoverB_1[2]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_1[0]*hamil[1]*hamil[3])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_3[1]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_3[0]*hamil[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[1]*hamil[5])/vmap2)-(0.7071067811865475*rtg33inv[0]*hamil[2])/vmap2))/m_; 
+  alphavpar[1] = (rdx2*(-((0.25*dualcurlbhatoverB_1[3]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_1[1]*hamil[1]*hamil[3])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_3[0]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_3[1]*hamil[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[0]*hamil[5])/vmap2)-(0.7071067811865475*rtg33inv[1]*hamil[2])/vmap2))/m_; 
+  alphavpar[2] = (rdz2*(-((0.25*dualcurlbhatoverB_3[3]*hamil[3]*hamil[5])/vmap2)-(0.25*dualcurlbhatoverB_3[2]*hamil[2]*hamil[3])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_1[0]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[1]*dualcurlbhatoverB_1[2]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[3]*hamil[5])/vmap2)-(0.7071067811865475*hamil[2]*rtg33inv[2])/vmap2))/m_; 
+  alphavpar[3] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[2]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[0]*hamil[1]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[1]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[0]*hamil[2]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[4] = (rdx2*(-((0.25*dualcurlbhatoverB_1[2]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_1[0]*hamil[3]*hamil[8])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_3[1]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_3[0]*hamil[3]*hamil[9])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[1]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[0]*hamil[9])/vmap2))/m_; 
+  alphavpar[5] = (rdz2*(-((0.25*dualcurlbhatoverB_3[2]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[2]*dualcurlbhatoverB_3[3]*hamil[3])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_1[1]*hamil[3]*hamil[5])/vmap2)-(0.25*hamil[1]*dualcurlbhatoverB_1[3]*hamil[3])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[2]*hamil[5])/vmap2)-(0.7071067811865475*hamil[2]*rtg33inv[3])/vmap2))/m_; 
+  alphavpar[6] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[3]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[1]*hamil[1]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[0]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[1]*hamil[2]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[7] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[3]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[2]*hamil[2]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[0]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[1]*dualcurlbhatoverB_1[2]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[8] = (rdx2*(-((0.25*dualcurlbhatoverB_1[3]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_1[1]*hamil[3]*hamil[8])/vmap2)+rdz2*(-((0.25*dualcurlbhatoverB_3[0]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_3[1]*hamil[3]*hamil[9])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[0]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[1]*hamil[9])/vmap2))/m_; 
+  alphavpar[9] = (rdz2*(-((0.25*dualcurlbhatoverB_3[3]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_3[2]*hamil[3]*hamil[9])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_1[0]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_1[2]*hamil[3]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[3]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[2]*hamil[9])/vmap2))/m_; 
+  alphavpar[10] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[2]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[0]*hamil[8]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[1]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[0]*hamil[9]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[11] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[2]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[2]*dualcurlbhatoverB_3[3]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[1]*hamil[5]*hamil[16])/vmap2)-(0.5590169943749475*hamil[1]*dualcurlbhatoverB_1[3]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[12] = (rdz2*(-((0.25*dualcurlbhatoverB_3[2]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_3[3]*hamil[3]*hamil[9])/vmap2)+rdx2*(-((0.25*dualcurlbhatoverB_1[1]*hamil[3]*hamil[12])/vmap2)-(0.25*dualcurlbhatoverB_1[3]*hamil[3]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.7071067811865475*rtg33inv[2]*hamil[12])/vmap2)-(0.7071067811865475*rtg33inv[3]*hamil[9])/vmap2))/m_; 
+  alphavpar[13] = (rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[3]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[1]*hamil[8]*hamil[16])/vmap2)+rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[0]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[1]*hamil[9]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[14] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[3]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[2]*hamil[9]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[0]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[2]*hamil[8]*hamil[16])/vmap2))/(m_*q_); 
+  alphavpar[15] = (rdz2*(-((0.5590169943749475*dualcurlbhatoverB_3[2]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_3[3]*hamil[9]*hamil[16])/vmap2)+rdx2*(-((0.5590169943749475*dualcurlbhatoverB_1[1]*hamil[12]*hamil[16])/vmap2)-(0.5590169943749475*dualcurlbhatoverB_1[3]*hamil[8]*hamil[16])/vmap2))/(m_*q_); 
 
 
   out[3] += 0.4330127018922193*(alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[13]*fin[13]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_3x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_3x2v_ser_p1.c
index ab026b29b6..9575cc5f86 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_vol_3x2v_ser_p1.c
@@ -23,13 +23,13 @@ GKYL_CU_DH double dg_gyrokinetic_vol_3x2v_ser_p1(const double *w, const double *
   double rdvpar2Sq = rdvpar2*rdvpar2;
   double dvparSq = dxv[3]*dxv[3];
 
-  const double *bioverJB_x = &bioverJB[0]; 
-  const double *bioverJB_y = &bioverJB[8]; 
-  const double *bioverJB_z = &bioverJB[16]; 
+  const double *bioverJB_1 = &bioverJB[0]; 
+  const double *bioverJB_2 = &bioverJB[8]; 
+  const double *bioverJB_3 = &bioverJB[16]; 
 
-  const double *dualcurlbhatoverB_x = &dualcurlbhatoverB[0]; 
-  const double *dualcurlbhatoverB_y = &dualcurlbhatoverB[8]; 
-  const double *dualcurlbhatoverB_z = &dualcurlbhatoverB[16]; 
+  const double *dualcurlbhatoverB_1 = &dualcurlbhatoverB[0]; 
+  const double *dualcurlbhatoverB_2 = &dualcurlbhatoverB[8]; 
+  const double *dualcurlbhatoverB_3 = &dualcurlbhatoverB[16]; 
 
   double hamil[48] = {0.}; 
   hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
@@ -54,26 +54,26 @@ GKYL_CU_DH double dg_gyrokinetic_vol_3x2v_ser_p1(const double *w, const double *
   hamil2[1] = hamil[32]*hamil[32]; 
 
   double alphax[48] = {0.}; 
-  alphax[0] = (rdx2*((0.625*dualcurlbhatoverB_x[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_x[0]*hamil2[0])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_y[1]*hamil[7]+0.6123724356957944*bioverJB_y[0]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_z[5]*hamil[16])-0.6123724356957944*bioverJB_z[3]*hamil[8]-0.6123724356957944*bioverJB_z[1]*hamil[6]-0.6123724356957944*bioverJB_z[0]*hamil[2])*rdx2*rdy2)/q_; 
-  alphax[1] = (rdx2*((0.625*dualcurlbhatoverB_x[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_x[1])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_y[0]*hamil[7]+0.6123724356957944*bioverJB_y[1]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_z[3]*hamil[16])-0.6123724356957944*bioverJB_z[5]*hamil[8]-0.6123724356957944*bioverJB_z[0]*hamil[6]-0.6123724356957944*bioverJB_z[1]*hamil[2])*rdx2*rdy2)/q_; 
-  alphax[2] = ((0.6123724356957944*bioverJB_y[1]*hamil[16]+0.6123724356957944*bioverJB_y[0]*hamil[8])*rdx2*rdz2)/q_; 
-  alphax[3] = (rdx2*((0.625*hamil2[1]*dualcurlbhatoverB_x[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_x[3])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_y[5]*hamil[7]+0.6123724356957944*bioverJB_y[3]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_z[1]*hamil[16])-0.6123724356957944*bioverJB_z[0]*hamil[8]-0.6123724356957944*bioverJB_z[5]*hamil[6]-0.6123724356957944*hamil[2]*bioverJB_z[3])*rdx2*rdy2)/q_; 
-  alphax[4] = (0.5590169943749475*dualcurlbhatoverB_x[0]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
-  alphax[5] = ((0.6123724356957944*bioverJB_y[1]*hamil[21]+0.6123724356957944*bioverJB_y[0]*hamil[14])*rdx2*rdz2)/q_; 
-  alphax[6] = ((0.6123724356957944*bioverJB_y[0]*hamil[16]+0.6123724356957944*bioverJB_y[1]*hamil[8])*rdx2*rdz2)/q_; 
-  alphax[7] = (rdx2*((0.625*hamil2[1]*dualcurlbhatoverB_x[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_x[5])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_y[3]*hamil[7]+0.6123724356957944*hamil[3]*bioverJB_y[5])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_z[0]*hamil[16])-0.6123724356957944*bioverJB_z[1]*hamil[8]-0.6123724356957944*bioverJB_z[3]*hamil[6]-0.6123724356957944*hamil[2]*bioverJB_z[5])*rdx2*rdy2)/q_; 
-  alphax[8] = ((0.6123724356957944*bioverJB_y[5]*hamil[16]+0.6123724356957944*bioverJB_y[3]*hamil[8])*rdx2*rdz2)/q_; 
-  alphax[9] = (0.5590169943749475*dualcurlbhatoverB_x[1]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
-  alphax[11] = (0.5590169943749475*dualcurlbhatoverB_x[3]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
-  alphax[12] = ((0.6123724356957944*bioverJB_y[0]*hamil[21]+0.6123724356957944*bioverJB_y[1]*hamil[14])*rdx2*rdz2)/q_; 
-  alphax[14] = ((0.6123724356957944*bioverJB_y[5]*hamil[21]+0.6123724356957944*bioverJB_y[3]*hamil[14])*rdx2*rdz2)/q_; 
-  alphax[16] = ((0.6123724356957944*bioverJB_y[3]*hamil[16]+0.6123724356957944*bioverJB_y[5]*hamil[8])*rdx2*rdz2)/q_; 
-  alphax[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_x[5]*hamil[32]*rdx2)/(m_*q_*vmap2); 
-  alphax[21] = ((0.6123724356957944*bioverJB_y[3]*hamil[21]+0.6123724356957944*bioverJB_y[5]*hamil[14])*rdx2*rdz2)/q_; 
-  alphax[32] = (0.5590169943749475*dualcurlbhatoverB_x[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[33] = (0.5590169943749476*dualcurlbhatoverB_x[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
-  alphax[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_x[3]*rdx2)/(m_*q_*vmap2); 
-  alphax[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_x[5]*rdx2)/(m_*q_*vmap2); 
+  alphax[0] = (rdx2*((0.625*dualcurlbhatoverB_1[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_1[0]*hamil2[0])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_2[1]*hamil[7]+0.6123724356957944*bioverJB_2[0]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_3[5]*hamil[16])-0.6123724356957944*bioverJB_3[3]*hamil[8]-0.6123724356957944*bioverJB_3[1]*hamil[6]-0.6123724356957944*bioverJB_3[0]*hamil[2])*rdx2*rdy2)/q_; 
+  alphax[1] = (rdx2*((0.625*dualcurlbhatoverB_1[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_1[1])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_2[0]*hamil[7]+0.6123724356957944*bioverJB_2[1]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_3[3]*hamil[16])-0.6123724356957944*bioverJB_3[5]*hamil[8]-0.6123724356957944*bioverJB_3[0]*hamil[6]-0.6123724356957944*bioverJB_3[1]*hamil[2])*rdx2*rdy2)/q_; 
+  alphax[2] = ((0.6123724356957944*bioverJB_2[1]*hamil[16]+0.6123724356957944*bioverJB_2[0]*hamil[8])*rdx2*rdz2)/q_; 
+  alphax[3] = (rdx2*((0.625*hamil2[1]*dualcurlbhatoverB_1[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_1[3])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_2[5]*hamil[7]+0.6123724356957944*bioverJB_2[3]*hamil[3])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_3[1]*hamil[16])-0.6123724356957944*bioverJB_3[0]*hamil[8]-0.6123724356957944*bioverJB_3[5]*hamil[6]-0.6123724356957944*hamil[2]*bioverJB_3[3])*rdx2*rdy2)/q_; 
+  alphax[4] = (0.5590169943749475*dualcurlbhatoverB_1[0]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
+  alphax[5] = ((0.6123724356957944*bioverJB_2[1]*hamil[21]+0.6123724356957944*bioverJB_2[0]*hamil[14])*rdx2*rdz2)/q_; 
+  alphax[6] = ((0.6123724356957944*bioverJB_2[0]*hamil[16]+0.6123724356957944*bioverJB_2[1]*hamil[8])*rdx2*rdz2)/q_; 
+  alphax[7] = (rdx2*((0.625*hamil2[1]*dualcurlbhatoverB_1[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_1[5])/vmap2))/(m_*q_)+((0.6123724356957944*bioverJB_2[3]*hamil[7]+0.6123724356957944*hamil[3]*bioverJB_2[5])*rdx2*rdz2+(-(0.6123724356957944*bioverJB_3[0]*hamil[16])-0.6123724356957944*bioverJB_3[1]*hamil[8]-0.6123724356957944*bioverJB_3[3]*hamil[6]-0.6123724356957944*hamil[2]*bioverJB_3[5])*rdx2*rdy2)/q_; 
+  alphax[8] = ((0.6123724356957944*bioverJB_2[5]*hamil[16]+0.6123724356957944*bioverJB_2[3]*hamil[8])*rdx2*rdz2)/q_; 
+  alphax[9] = (0.5590169943749475*dualcurlbhatoverB_1[1]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
+  alphax[11] = (0.5590169943749475*dualcurlbhatoverB_1[3]*hamil[4]*hamil[32]*rdx2)/(m_*q_*vmap2); 
+  alphax[12] = ((0.6123724356957944*bioverJB_2[0]*hamil[21]+0.6123724356957944*bioverJB_2[1]*hamil[14])*rdx2*rdz2)/q_; 
+  alphax[14] = ((0.6123724356957944*bioverJB_2[5]*hamil[21]+0.6123724356957944*bioverJB_2[3]*hamil[14])*rdx2*rdz2)/q_; 
+  alphax[16] = ((0.6123724356957944*bioverJB_2[3]*hamil[16]+0.6123724356957944*bioverJB_2[5]*hamil[8])*rdx2*rdz2)/q_; 
+  alphax[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_1[5]*hamil[32]*rdx2)/(m_*q_*vmap2); 
+  alphax[21] = ((0.6123724356957944*bioverJB_2[3]*hamil[21]+0.6123724356957944*bioverJB_2[5]*hamil[14])*rdx2*rdz2)/q_; 
+  alphax[32] = (0.5590169943749475*dualcurlbhatoverB_1[0]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[33] = (0.5590169943749476*dualcurlbhatoverB_1[1]*hamil2[1]*rdx2)/(m_*q_*vmap2); 
+  alphax[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_1[3]*rdx2)/(m_*q_*vmap2); 
+  alphax[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_1[5]*rdx2)/(m_*q_*vmap2); 
 
 
   out[1] += 0.3061862178478971*(alphax[38]*fin[38]+alphax[35]*fin[35]+alphax[33]*fin[33]+alphax[32]*fin[32]+alphax[21]*fin[21]+alphax[18]*fin[18]+alphax[16]*fin[16]+alphax[14]*fin[14]+alphax[12]*fin[12]+alphax[11]*fin[11]+alphax[9]*fin[9]+alphax[8]*fin[8]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[4]*fin[4]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -102,26 +102,26 @@ GKYL_CU_DH double dg_gyrokinetic_vol_3x2v_ser_p1(const double *w, const double *
   out[47] += (0.19561519910898784*alphax[33]+0.3061862178478971*alphax[1])*fin[47]+0.19561519910898784*alphax[32]*fin[46]+0.3061862178478971*(alphax[0]*fin[46]+alphax[6]*fin[45])+0.19561519910898784*alphax[38]*fin[44]+0.3061862178478971*(alphax[7]*fin[44]+alphax[12]*fin[43]+alphax[2]*fin[42])+0.19561519910898784*alphax[35]*fin[41]+0.3061862178478971*(alphax[3]*fin[41]+alphax[16]*fin[40]+alphax[5]*fin[39]+fin[20]*alphax[38]+alphax[21]*fin[37]+alphax[8]*fin[36]+fin[13]*alphax[35]+alphax[14]*fin[34]+fin[27]*alphax[33]+fin[22]*alphax[32])+0.273861278752583*(alphax[9]*fin[31]+alphax[4]*fin[30]+alphax[18]*fin[28]+alphax[11]*fin[24]); 
 
   double alphay[48] = {0.}; 
-  alphay[0] = (rdy2*((0.625*dualcurlbhatoverB_y[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_y[0]*hamil2[0])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_x[1]*hamil[7])-0.6123724356957944*bioverJB_x[0]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[3]*hamil[7]+0.6123724356957944*bioverJB_z[0]*hamil[1])*rdx2*rdy2)/q_; 
-  alphay[1] = (rdy2*((0.625*dualcurlbhatoverB_y[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_y[1])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_x[0]*hamil[7])-0.6123724356957944*bioverJB_x[1]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[5]*hamil[7]+0.6123724356957944*bioverJB_z[1]*hamil[1])*rdx2*rdy2)/q_; 
-  alphay[2] = ((-(0.6123724356957944*bioverJB_x[1]*hamil[16])-0.6123724356957944*bioverJB_x[0]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[3]*hamil[16]+0.6123724356957944*bioverJB_z[0]*hamil[6])*rdx2*rdy2)/q_; 
-  alphay[3] = (rdy2*((0.625*hamil2[1]*dualcurlbhatoverB_y[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_y[3])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_x[5]*hamil[7])-0.6123724356957944*bioverJB_x[3]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[0]*hamil[7]+0.6123724356957944*hamil[1]*bioverJB_z[3])*rdx2*rdy2)/q_; 
-  alphay[4] = (0.5590169943749475*dualcurlbhatoverB_y[0]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
-  alphay[5] = ((-(0.6123724356957944*bioverJB_x[1]*hamil[21])-0.6123724356957944*bioverJB_x[0]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[3]*hamil[21]+0.6123724356957944*bioverJB_z[0]*hamil[12])*rdx2*rdy2)/q_; 
-  alphay[6] = ((-(0.6123724356957944*bioverJB_x[0]*hamil[16])-0.6123724356957944*bioverJB_x[1]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[5]*hamil[16]+0.6123724356957944*bioverJB_z[1]*hamil[6])*rdx2*rdy2)/q_; 
-  alphay[7] = (rdy2*((0.625*hamil2[1]*dualcurlbhatoverB_y[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_y[5])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_x[3]*hamil[7])-0.6123724356957944*hamil[3]*bioverJB_x[5])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[1]*hamil[7]+0.6123724356957944*hamil[1]*bioverJB_z[5])*rdx2*rdy2)/q_; 
-  alphay[8] = ((-(0.6123724356957944*bioverJB_x[5]*hamil[16])-0.6123724356957944*bioverJB_x[3]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[0]*hamil[16]+0.6123724356957944*bioverJB_z[3]*hamil[6])*rdx2*rdy2)/q_; 
-  alphay[9] = (0.5590169943749475*dualcurlbhatoverB_y[1]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
-  alphay[11] = (0.5590169943749475*dualcurlbhatoverB_y[3]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
-  alphay[12] = ((-(0.6123724356957944*bioverJB_x[0]*hamil[21])-0.6123724356957944*bioverJB_x[1]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[5]*hamil[21]+0.6123724356957944*bioverJB_z[1]*hamil[12])*rdx2*rdy2)/q_; 
-  alphay[14] = ((-(0.6123724356957944*bioverJB_x[5]*hamil[21])-0.6123724356957944*bioverJB_x[3]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[0]*hamil[21]+0.6123724356957944*bioverJB_z[3]*hamil[12])*rdx2*rdy2)/q_; 
-  alphay[16] = ((-(0.6123724356957944*bioverJB_x[3]*hamil[16])-0.6123724356957944*bioverJB_x[5]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[1]*hamil[16]+0.6123724356957944*bioverJB_z[5]*hamil[6])*rdx2*rdy2)/q_; 
-  alphay[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_y[5]*hamil[32]*rdy2)/(m_*q_*vmap2); 
-  alphay[21] = ((-(0.6123724356957944*bioverJB_x[3]*hamil[21])-0.6123724356957944*bioverJB_x[5]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_z[1]*hamil[21]+0.6123724356957944*bioverJB_z[5]*hamil[12])*rdx2*rdy2)/q_; 
-  alphay[32] = (0.5590169943749475*dualcurlbhatoverB_y[0]*hamil2[1]*rdy2)/(m_*q_*vmap2); 
-  alphay[33] = (0.5590169943749476*dualcurlbhatoverB_y[1]*hamil2[1]*rdy2)/(m_*q_*vmap2); 
-  alphay[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_y[3]*rdy2)/(m_*q_*vmap2); 
-  alphay[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_y[5]*rdy2)/(m_*q_*vmap2); 
+  alphay[0] = (rdy2*((0.625*dualcurlbhatoverB_2[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_2[0]*hamil2[0])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_1[1]*hamil[7])-0.6123724356957944*bioverJB_1[0]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[3]*hamil[7]+0.6123724356957944*bioverJB_3[0]*hamil[1])*rdx2*rdy2)/q_; 
+  alphay[1] = (rdy2*((0.625*dualcurlbhatoverB_2[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_2[1])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_1[0]*hamil[7])-0.6123724356957944*bioverJB_1[1]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[5]*hamil[7]+0.6123724356957944*bioverJB_3[1]*hamil[1])*rdx2*rdy2)/q_; 
+  alphay[2] = ((-(0.6123724356957944*bioverJB_1[1]*hamil[16])-0.6123724356957944*bioverJB_1[0]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[3]*hamil[16]+0.6123724356957944*bioverJB_3[0]*hamil[6])*rdx2*rdy2)/q_; 
+  alphay[3] = (rdy2*((0.625*hamil2[1]*dualcurlbhatoverB_2[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_2[3])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_1[5]*hamil[7])-0.6123724356957944*bioverJB_1[3]*hamil[3])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[0]*hamil[7]+0.6123724356957944*hamil[1]*bioverJB_3[3])*rdx2*rdy2)/q_; 
+  alphay[4] = (0.5590169943749475*dualcurlbhatoverB_2[0]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
+  alphay[5] = ((-(0.6123724356957944*bioverJB_1[1]*hamil[21])-0.6123724356957944*bioverJB_1[0]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[3]*hamil[21]+0.6123724356957944*bioverJB_3[0]*hamil[12])*rdx2*rdy2)/q_; 
+  alphay[6] = ((-(0.6123724356957944*bioverJB_1[0]*hamil[16])-0.6123724356957944*bioverJB_1[1]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[5]*hamil[16]+0.6123724356957944*bioverJB_3[1]*hamil[6])*rdx2*rdy2)/q_; 
+  alphay[7] = (rdy2*((0.625*hamil2[1]*dualcurlbhatoverB_2[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_2[5])/vmap2))/(m_*q_)+((-(0.6123724356957944*bioverJB_1[3]*hamil[7])-0.6123724356957944*hamil[3]*bioverJB_1[5])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[1]*hamil[7]+0.6123724356957944*hamil[1]*bioverJB_3[5])*rdx2*rdy2)/q_; 
+  alphay[8] = ((-(0.6123724356957944*bioverJB_1[5]*hamil[16])-0.6123724356957944*bioverJB_1[3]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[0]*hamil[16]+0.6123724356957944*bioverJB_3[3]*hamil[6])*rdx2*rdy2)/q_; 
+  alphay[9] = (0.5590169943749475*dualcurlbhatoverB_2[1]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
+  alphay[11] = (0.5590169943749475*dualcurlbhatoverB_2[3]*hamil[4]*hamil[32]*rdy2)/(m_*q_*vmap2); 
+  alphay[12] = ((-(0.6123724356957944*bioverJB_1[0]*hamil[21])-0.6123724356957944*bioverJB_1[1]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[5]*hamil[21]+0.6123724356957944*bioverJB_3[1]*hamil[12])*rdx2*rdy2)/q_; 
+  alphay[14] = ((-(0.6123724356957944*bioverJB_1[5]*hamil[21])-0.6123724356957944*bioverJB_1[3]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[0]*hamil[21]+0.6123724356957944*bioverJB_3[3]*hamil[12])*rdx2*rdy2)/q_; 
+  alphay[16] = ((-(0.6123724356957944*bioverJB_1[3]*hamil[16])-0.6123724356957944*bioverJB_1[5]*hamil[8])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[1]*hamil[16]+0.6123724356957944*bioverJB_3[5]*hamil[6])*rdx2*rdy2)/q_; 
+  alphay[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_2[5]*hamil[32]*rdy2)/(m_*q_*vmap2); 
+  alphay[21] = ((-(0.6123724356957944*bioverJB_1[3]*hamil[21])-0.6123724356957944*bioverJB_1[5]*hamil[14])*rdy2*rdz2+(0.6123724356957944*bioverJB_3[1]*hamil[21]+0.6123724356957944*bioverJB_3[5]*hamil[12])*rdx2*rdy2)/q_; 
+  alphay[32] = (0.5590169943749475*dualcurlbhatoverB_2[0]*hamil2[1]*rdy2)/(m_*q_*vmap2); 
+  alphay[33] = (0.5590169943749476*dualcurlbhatoverB_2[1]*hamil2[1]*rdy2)/(m_*q_*vmap2); 
+  alphay[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_2[3]*rdy2)/(m_*q_*vmap2); 
+  alphay[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_2[5]*rdy2)/(m_*q_*vmap2); 
 
 
   out[2] += 0.3061862178478971*(alphay[38]*fin[38]+alphay[35]*fin[35]+alphay[33]*fin[33]+alphay[32]*fin[32]+alphay[21]*fin[21]+alphay[18]*fin[18]+alphay[16]*fin[16]+alphay[14]*fin[14]+alphay[12]*fin[12]+alphay[11]*fin[11]+alphay[9]*fin[9]+alphay[8]*fin[8]+alphay[7]*fin[7]+alphay[6]*fin[6]+alphay[5]*fin[5]+alphay[4]*fin[4]+alphay[3]*fin[3]+alphay[2]*fin[2]+alphay[1]*fin[1]+alphay[0]*fin[0]); 
@@ -150,26 +150,26 @@ GKYL_CU_DH double dg_gyrokinetic_vol_3x2v_ser_p1(const double *w, const double *
   out[47] += 0.3061862178478971*(alphay[2]*fin[47]+alphay[6]*fin[46])+0.19561519910898784*alphay[32]*fin[45]+0.3061862178478971*(alphay[0]*fin[45]+alphay[8]*fin[44])+0.19561519910898784*alphay[33]*fin[42]+0.3061862178478971*(alphay[1]*fin[42]+alphay[16]*fin[41])+0.19561519910898784*alphay[35]*fin[40]+0.3061862178478971*(alphay[3]*fin[40]+alphay[5]*fin[38])+0.19561519910898784*fin[36]*alphay[38]+0.3061862178478971*(fin[5]*alphay[38]+alphay[7]*fin[36]+alphay[12]*fin[35]+fin[12]*alphay[35]+alphay[14]*fin[33]+fin[14]*alphay[33]+alphay[21]*fin[32]+fin[21]*alphay[32])+0.273861278752583*(alphay[4]*fin[29]+alphay[9]*fin[25]+alphay[11]*fin[23]+fin[15]*alphay[18]); 
 
   double alphaz[48] = {0.}; 
-  alphaz[0] = (rdz2*((0.625*dualcurlbhatoverB_z[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_z[0]*hamil2[0])/vmap2))/(m_*q_)+(0.5*rtg33inv[0]*vmap[1]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_x[5]*hamil[16]+0.6123724356957944*bioverJB_x[3]*hamil[8]+0.6123724356957944*bioverJB_x[1]*hamil[6]+0.6123724356957944*bioverJB_x[0]*hamil[2])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_y[3]*hamil[7])-0.6123724356957944*bioverJB_y[0]*hamil[1])*rdx2*rdz2)/q_; 
-  alphaz[1] = (rdz2*((0.625*dualcurlbhatoverB_z[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_z[1])/vmap2))/(m_*q_)+(0.5*rtg33inv[1]*vmap[1]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_x[3]*hamil[16]+0.6123724356957944*bioverJB_x[5]*hamil[8]+0.6123724356957944*bioverJB_x[0]*hamil[6]+0.6123724356957944*bioverJB_x[1]*hamil[2])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_y[5]*hamil[7])-0.6123724356957944*bioverJB_y[1]*hamil[1])*rdx2*rdz2)/q_; 
-  alphaz[2] = ((-(0.6123724356957944*bioverJB_y[3]*hamil[16])-0.6123724356957944*bioverJB_y[0]*hamil[6])*rdx2*rdz2)/q_; 
-  alphaz[3] = (rdz2*((0.625*hamil2[1]*dualcurlbhatoverB_z[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_z[3])/vmap2))/(m_*q_)+(0.5*vmap[1]*rtg33inv[3]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_x[1]*hamil[16]+0.6123724356957944*bioverJB_x[0]*hamil[8]+0.6123724356957944*bioverJB_x[5]*hamil[6]+0.6123724356957944*hamil[2]*bioverJB_x[3])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_y[0]*hamil[7])-0.6123724356957944*hamil[1]*bioverJB_y[3])*rdx2*rdz2)/q_; 
-  alphaz[4] = (0.5590169943749475*dualcurlbhatoverB_z[0]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*rtg33inv[0]*vmap[1]*hamil[32]*rdz2)/(m_*vmap2); 
-  alphaz[5] = ((-(0.6123724356957944*bioverJB_y[3]*hamil[21])-0.6123724356957944*bioverJB_y[0]*hamil[12])*rdx2*rdz2)/q_; 
-  alphaz[6] = ((-(0.6123724356957944*bioverJB_y[5]*hamil[16])-0.6123724356957944*bioverJB_y[1]*hamil[6])*rdx2*rdz2)/q_; 
-  alphaz[7] = (rdz2*((0.625*hamil2[1]*dualcurlbhatoverB_z[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_z[5])/vmap2))/(m_*q_)+(0.5*vmap[1]*hamil[4]*rtg33inv[5]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_x[0]*hamil[16]+0.6123724356957944*bioverJB_x[1]*hamil[8]+0.6123724356957944*bioverJB_x[3]*hamil[6]+0.6123724356957944*hamil[2]*bioverJB_x[5])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_y[1]*hamil[7])-0.6123724356957944*hamil[1]*bioverJB_y[5])*rdx2*rdz2)/q_; 
-  alphaz[8] = ((-(0.6123724356957944*bioverJB_y[0]*hamil[16])-0.6123724356957944*bioverJB_y[3]*hamil[6])*rdx2*rdz2)/q_; 
-  alphaz[9] = (0.5590169943749475*dualcurlbhatoverB_z[1]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*rtg33inv[1]*vmap[1]*hamil[32]*rdz2)/(m_*vmap2); 
-  alphaz[11] = (0.5590169943749475*dualcurlbhatoverB_z[3]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*vmap[1]*rtg33inv[3]*hamil[32]*rdz2)/(m_*vmap2); 
-  alphaz[12] = ((-(0.6123724356957944*bioverJB_y[5]*hamil[21])-0.6123724356957944*bioverJB_y[1]*hamil[12])*rdx2*rdz2)/q_; 
-  alphaz[14] = ((-(0.6123724356957944*bioverJB_y[0]*hamil[21])-0.6123724356957944*bioverJB_y[3]*hamil[12])*rdx2*rdz2)/q_; 
-  alphaz[16] = ((-(0.6123724356957944*bioverJB_y[1]*hamil[16])-0.6123724356957944*bioverJB_y[5]*hamil[6])*rdx2*rdz2)/q_; 
-  alphaz[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_z[5]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*vmap[1]*rtg33inv[5]*hamil[32]*rdz2)/(m_*vmap2); 
-  alphaz[21] = ((-(0.6123724356957944*bioverJB_y[1]*hamil[21])-0.6123724356957944*bioverJB_y[5]*hamil[12])*rdx2*rdz2)/q_; 
-  alphaz[32] = (0.5590169943749475*dualcurlbhatoverB_z[0]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
-  alphaz[33] = (0.5590169943749476*dualcurlbhatoverB_z[1]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
-  alphaz[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_z[3]*rdz2)/(m_*q_*vmap2); 
-  alphaz[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_z[5]*rdz2)/(m_*q_*vmap2); 
+  alphaz[0] = (rdz2*((0.625*dualcurlbhatoverB_3[0]*hamil2[1])/vmap2+(0.125*dualcurlbhatoverB_3[0]*hamil2[0])/vmap2))/(m_*q_)+(0.5*rtg33inv[0]*vmap[1]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_1[5]*hamil[16]+0.6123724356957944*bioverJB_1[3]*hamil[8]+0.6123724356957944*bioverJB_1[1]*hamil[6]+0.6123724356957944*bioverJB_1[0]*hamil[2])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_2[3]*hamil[7])-0.6123724356957944*bioverJB_2[0]*hamil[1])*rdx2*rdz2)/q_; 
+  alphaz[1] = (rdz2*((0.625*dualcurlbhatoverB_3[1]*hamil2[1])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_3[1])/vmap2))/(m_*q_)+(0.5*rtg33inv[1]*vmap[1]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_1[3]*hamil[16]+0.6123724356957944*bioverJB_1[5]*hamil[8]+0.6123724356957944*bioverJB_1[0]*hamil[6]+0.6123724356957944*bioverJB_1[1]*hamil[2])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_2[5]*hamil[7])-0.6123724356957944*bioverJB_2[1]*hamil[1])*rdx2*rdz2)/q_; 
+  alphaz[2] = ((-(0.6123724356957944*bioverJB_2[3]*hamil[16])-0.6123724356957944*bioverJB_2[0]*hamil[6])*rdx2*rdz2)/q_; 
+  alphaz[3] = (rdz2*((0.625*hamil2[1]*dualcurlbhatoverB_3[3])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_3[3])/vmap2))/(m_*q_)+(0.5*vmap[1]*rtg33inv[3]*hamil[4]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_1[1]*hamil[16]+0.6123724356957944*bioverJB_1[0]*hamil[8]+0.6123724356957944*bioverJB_1[5]*hamil[6]+0.6123724356957944*hamil[2]*bioverJB_1[3])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_2[0]*hamil[7])-0.6123724356957944*hamil[1]*bioverJB_2[3])*rdx2*rdz2)/q_; 
+  alphaz[4] = (0.5590169943749475*dualcurlbhatoverB_3[0]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*rtg33inv[0]*vmap[1]*hamil[32]*rdz2)/(m_*vmap2); 
+  alphaz[5] = ((-(0.6123724356957944*bioverJB_2[3]*hamil[21])-0.6123724356957944*bioverJB_2[0]*hamil[12])*rdx2*rdz2)/q_; 
+  alphaz[6] = ((-(0.6123724356957944*bioverJB_2[5]*hamil[16])-0.6123724356957944*bioverJB_2[1]*hamil[6])*rdx2*rdz2)/q_; 
+  alphaz[7] = (rdz2*((0.625*hamil2[1]*dualcurlbhatoverB_3[5])/vmap2+(0.125*hamil2[0]*dualcurlbhatoverB_3[5])/vmap2))/(m_*q_)+(0.5*vmap[1]*hamil[4]*rtg33inv[5]*rdz2)/(m_*vmap2)+((0.6123724356957944*bioverJB_1[0]*hamil[16]+0.6123724356957944*bioverJB_1[1]*hamil[8]+0.6123724356957944*bioverJB_1[3]*hamil[6]+0.6123724356957944*hamil[2]*bioverJB_1[5])*rdy2*rdz2+(-(0.6123724356957944*bioverJB_2[1]*hamil[7])-0.6123724356957944*hamil[1]*bioverJB_2[5])*rdx2*rdz2)/q_; 
+  alphaz[8] = ((-(0.6123724356957944*bioverJB_2[0]*hamil[16])-0.6123724356957944*bioverJB_2[3]*hamil[6])*rdx2*rdz2)/q_; 
+  alphaz[9] = (0.5590169943749475*dualcurlbhatoverB_3[1]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*rtg33inv[1]*vmap[1]*hamil[32]*rdz2)/(m_*vmap2); 
+  alphaz[11] = (0.5590169943749475*dualcurlbhatoverB_3[3]*hamil[4]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*vmap[1]*rtg33inv[3]*hamil[32]*rdz2)/(m_*vmap2); 
+  alphaz[12] = ((-(0.6123724356957944*bioverJB_2[5]*hamil[21])-0.6123724356957944*bioverJB_2[1]*hamil[12])*rdx2*rdz2)/q_; 
+  alphaz[14] = ((-(0.6123724356957944*bioverJB_2[0]*hamil[21])-0.6123724356957944*bioverJB_2[3]*hamil[12])*rdx2*rdz2)/q_; 
+  alphaz[16] = ((-(0.6123724356957944*bioverJB_2[1]*hamil[16])-0.6123724356957944*bioverJB_2[5]*hamil[6])*rdx2*rdz2)/q_; 
+  alphaz[18] = (0.5590169943749475*hamil[4]*dualcurlbhatoverB_3[5]*hamil[32]*rdz2)/(m_*q_*vmap2)+(1.118033988749895*vmap[1]*rtg33inv[5]*hamil[32]*rdz2)/(m_*vmap2); 
+  alphaz[21] = ((-(0.6123724356957944*bioverJB_2[1]*hamil[21])-0.6123724356957944*bioverJB_2[5]*hamil[12])*rdx2*rdz2)/q_; 
+  alphaz[32] = (0.5590169943749475*dualcurlbhatoverB_3[0]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
+  alphaz[33] = (0.5590169943749476*dualcurlbhatoverB_3[1]*hamil2[1]*rdz2)/(m_*q_*vmap2); 
+  alphaz[35] = (0.5590169943749476*hamil2[1]*dualcurlbhatoverB_3[3]*rdz2)/(m_*q_*vmap2); 
+  alphaz[38] = (0.5590169943749475*hamil2[1]*dualcurlbhatoverB_3[5]*rdz2)/(m_*q_*vmap2); 
 
 
   out[3] += 0.3061862178478971*(alphaz[38]*fin[38]+alphaz[35]*fin[35]+alphaz[33]*fin[33]+alphaz[32]*fin[32]+alphaz[21]*fin[21]+alphaz[18]*fin[18]+alphaz[16]*fin[16]+alphaz[14]*fin[14]+alphaz[12]*fin[12]+alphaz[11]*fin[11]+alphaz[9]*fin[9]+alphaz[8]*fin[8]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[4]*fin[4]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -198,30 +198,30 @@ GKYL_CU_DH double dg_gyrokinetic_vol_3x2v_ser_p1(const double *w, const double *
   out[47] += (0.19561519910898784*alphaz[35]+0.3061862178478971*alphaz[3])*fin[47]+0.19561519910898784*alphaz[38]*fin[46]+0.3061862178478971*(alphaz[7]*fin[46]+alphaz[8]*fin[45])+0.19561519910898784*alphaz[32]*fin[44]+0.3061862178478971*(alphaz[0]*fin[44]+alphaz[14]*fin[43]+alphaz[16]*fin[42])+0.19561519910898784*alphaz[33]*fin[41]+0.3061862178478971*(alphaz[1]*fin[41]+alphaz[2]*fin[40]+alphaz[21]*fin[39]+fin[22]*alphaz[38]+alphaz[5]*fin[37]+alphaz[6]*fin[36]+fin[27]*alphaz[35]+alphaz[12]*fin[34]+fin[13]*alphaz[33]+fin[20]*alphaz[32])+0.273861278752583*(alphaz[11]*fin[31]+alphaz[18]*fin[30]+alphaz[4]*fin[28]+alphaz[9]*fin[24]); 
 
   double alphavpar[48] = {0.}; 
-  alphavpar[0] = (rdy2*(-((0.125*hamil[4]*dualcurlbhatoverB_y[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_y[3]*hamil[4]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_y[1]*hamil[4]*hamil[6])/vmap2-(0.125*dualcurlbhatoverB_y[0]*hamil[2]*hamil[4])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[3]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_x[0]*hamil[1]*hamil[4])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[1]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_z[0]*hamil[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[7])/vmap2)-(0.5*rtg33inv[0]*hamil[3])/vmap2))/m_; 
-  alphavpar[1] = (rdy2*(-((0.125*dualcurlbhatoverB_y[3]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_y[5]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_y[0]*hamil[4]*hamil[6])/vmap2-(0.125*dualcurlbhatoverB_y[1]*hamil[2]*hamil[4])/vmap2)+rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_x[5]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_x[1]*hamil[1]*hamil[4])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[0]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_z[1]*hamil[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[7])/vmap2)-(0.5*rtg33inv[1]*hamil[3])/vmap2))/m_; 
-  alphavpar[2] = (rdx2*(-((0.125*dualcurlbhatoverB_x[3]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_x[0]*hamil[4]*hamil[6])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[1]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_z[0]*hamil[4]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[16])/vmap2)-(0.5*rtg33inv[0]*hamil[8])/vmap2))/m_; 
-  alphavpar[3] = (rdy2*(-((0.125*dualcurlbhatoverB_y[1]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_y[0]*hamil[4]*hamil[8])/vmap2-(0.125*hamil[4]*dualcurlbhatoverB_y[5]*hamil[6])/vmap2-(0.125*hamil[2]*dualcurlbhatoverB_y[3]*hamil[4])/vmap2)+rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_z[5]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_z[3]*hamil[3]*hamil[4])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[0]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[1]*dualcurlbhatoverB_x[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[7])/vmap2)-(0.5*hamil[3]*rtg33inv[3])/vmap2))/m_; 
-  alphavpar[4] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_y[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_y[3]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[1]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[0]*hamil[2]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[3]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[1]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[3]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[5] = (rdx2*(-((0.125*dualcurlbhatoverB_x[3]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_x[0]*hamil[4]*hamil[12])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[1]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_z[0]*hamil[4]*hamil[14])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[21])/vmap2)-(0.5*rtg33inv[0]*hamil[14])/vmap2))/m_; 
-  alphavpar[6] = (rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_x[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_x[1]*hamil[4]*hamil[6])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_z[1]*hamil[4]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[16])/vmap2)-(0.5*rtg33inv[1]*hamil[8])/vmap2))/m_; 
-  alphavpar[7] = (rdy2*(-((0.125*dualcurlbhatoverB_y[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_y[1]*hamil[4]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_y[3]*hamil[4]*hamil[6])/vmap2-(0.125*hamil[2]*hamil[4]*dualcurlbhatoverB_y[5])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[3]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[3]*hamil[4]*dualcurlbhatoverB_z[5])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[1]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[1]*hamil[4]*dualcurlbhatoverB_x[5])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[7])/vmap2)-(0.5*hamil[3]*rtg33inv[5])/vmap2))/m_; 
-  alphavpar[8] = (rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_z[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_z[3]*hamil[4]*hamil[8])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_x[3]*hamil[4]*hamil[6])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[16])/vmap2)-(0.5*rtg33inv[3]*hamil[8])/vmap2))/m_; 
-  alphavpar[9] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_y[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_y[5]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[0]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[1]*hamil[2]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[5]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[1]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[3]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[10] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[6]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[8]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[11] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_y[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_y[0]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[5]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*hamil[2]*dualcurlbhatoverB_y[3]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[5]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[3]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[1]*dualcurlbhatoverB_x[3]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[12] = (rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_x[5]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_x[1]*hamil[4]*hamil[12])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_z[0]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_z[1]*hamil[4]*hamil[14])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[21])/vmap2)-(0.5*rtg33inv[1]*hamil[14])/vmap2))/m_; 
-  alphavpar[14] = (rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_z[5]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_z[3]*hamil[4]*hamil[14])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[0]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_x[3]*hamil[4]*hamil[12])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[21])/vmap2)-(0.5*rtg33inv[3]*hamil[14])/vmap2))/m_; 
-  alphavpar[15] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[3]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[12]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[14]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[16] = (rdz2*(-((0.125*dualcurlbhatoverB_z[3]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_z[5]*hamil[8])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[1]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_x[5]*hamil[6])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[16])/vmap2)-(0.5*rtg33inv[5]*hamil[8])/vmap2))/m_; 
-  alphavpar[17] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[6]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[8]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[18] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_y[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_y[1]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_y[3]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*hamil[2]*dualcurlbhatoverB_y[5]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[3]*dualcurlbhatoverB_z[5]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[1]*dualcurlbhatoverB_x[5]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[19] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[8]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[3]*hamil[6]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[21] = (rdz2*(-((0.125*dualcurlbhatoverB_z[3]*hamil[4]*hamil[21])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_z[5]*hamil[14])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_x[1]*hamil[4]*hamil[21])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_x[5]*hamil[12])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[21])/vmap2)-(0.5*rtg33inv[5]*hamil[14])/vmap2))/m_; 
-  alphavpar[23] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[5]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[12]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[0]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[1]*hamil[14]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[25] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[5]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[14]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[0]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[3]*hamil[12]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[26] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[5]*hamil[8]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[5]*hamil[6]*hamil[32])/vmap2))/(m_*q_); 
-  alphavpar[29] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_z[3]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_z[5]*hamil[14]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_x[1]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_x[5]*hamil[12]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[0] = (rdy2*(-((0.125*hamil[4]*dualcurlbhatoverB_2[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_2[3]*hamil[4]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_2[1]*hamil[4]*hamil[6])/vmap2-(0.125*dualcurlbhatoverB_2[0]*hamil[2]*hamil[4])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[3]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_1[0]*hamil[1]*hamil[4])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[1]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_3[0]*hamil[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[7])/vmap2)-(0.5*rtg33inv[0]*hamil[3])/vmap2))/m_; 
+  alphavpar[1] = (rdy2*(-((0.125*dualcurlbhatoverB_2[3]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_2[5]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_2[0]*hamil[4]*hamil[6])/vmap2-(0.125*dualcurlbhatoverB_2[1]*hamil[2]*hamil[4])/vmap2)+rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_1[5]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_1[1]*hamil[1]*hamil[4])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[0]*hamil[4]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_3[1]*hamil[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[7])/vmap2)-(0.5*rtg33inv[1]*hamil[3])/vmap2))/m_; 
+  alphavpar[2] = (rdx2*(-((0.125*dualcurlbhatoverB_1[3]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_1[0]*hamil[4]*hamil[6])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[1]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_3[0]*hamil[4]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[16])/vmap2)-(0.5*rtg33inv[0]*hamil[8])/vmap2))/m_; 
+  alphavpar[3] = (rdy2*(-((0.125*dualcurlbhatoverB_2[1]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_2[0]*hamil[4]*hamil[8])/vmap2-(0.125*hamil[4]*dualcurlbhatoverB_2[5]*hamil[6])/vmap2-(0.125*hamil[2]*dualcurlbhatoverB_2[3]*hamil[4])/vmap2)+rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_3[5]*hamil[7])/vmap2)-(0.125*dualcurlbhatoverB_3[3]*hamil[3]*hamil[4])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[0]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[1]*dualcurlbhatoverB_1[3]*hamil[4])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[7])/vmap2)-(0.5*hamil[3]*rtg33inv[3])/vmap2))/m_; 
+  alphavpar[4] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_2[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_2[3]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[1]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[0]*hamil[2]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[3]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[1]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[3]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[5] = (rdx2*(-((0.125*dualcurlbhatoverB_1[3]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_1[0]*hamil[4]*hamil[12])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[1]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_3[0]*hamil[4]*hamil[14])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[1]*hamil[21])/vmap2)-(0.5*rtg33inv[0]*hamil[14])/vmap2))/m_; 
+  alphavpar[6] = (rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_1[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_1[1]*hamil[4]*hamil[6])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_3[1]*hamil[4]*hamil[8])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[16])/vmap2)-(0.5*rtg33inv[1]*hamil[8])/vmap2))/m_; 
+  alphavpar[7] = (rdy2*(-((0.125*dualcurlbhatoverB_2[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_2[1]*hamil[4]*hamil[8])/vmap2-(0.125*dualcurlbhatoverB_2[3]*hamil[4]*hamil[6])/vmap2-(0.125*hamil[2]*hamil[4]*dualcurlbhatoverB_2[5])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[3]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[3]*hamil[4]*dualcurlbhatoverB_3[5])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[1]*hamil[4]*hamil[7])/vmap2)-(0.125*hamil[1]*hamil[4]*dualcurlbhatoverB_1[5])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[7])/vmap2)-(0.5*hamil[3]*rtg33inv[5])/vmap2))/m_; 
+  alphavpar[8] = (rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_3[5]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_3[3]*hamil[4]*hamil[8])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[0]*hamil[4]*hamil[16])/vmap2)-(0.125*dualcurlbhatoverB_1[3]*hamil[4]*hamil[6])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[16])/vmap2)-(0.5*rtg33inv[3]*hamil[8])/vmap2))/m_; 
+  alphavpar[9] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_2[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_2[5]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[0]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[1]*hamil[2]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[5]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[1]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[3]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[10] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[6]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[8]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[11] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_2[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_2[0]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[5]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*hamil[2]*dualcurlbhatoverB_2[3]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[5]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[3]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[1]*dualcurlbhatoverB_1[3]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[12] = (rdx2*(-((0.125*hamil[4]*dualcurlbhatoverB_1[5]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_1[1]*hamil[4]*hamil[12])/vmap2)+rdz2*(-((0.125*dualcurlbhatoverB_3[0]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_3[1]*hamil[4]*hamil[14])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[0]*hamil[21])/vmap2)-(0.5*rtg33inv[1]*hamil[14])/vmap2))/m_; 
+  alphavpar[14] = (rdz2*(-((0.125*hamil[4]*dualcurlbhatoverB_3[5]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_3[3]*hamil[4]*hamil[14])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[0]*hamil[4]*hamil[21])/vmap2)-(0.125*dualcurlbhatoverB_1[3]*hamil[4]*hamil[12])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[5]*hamil[21])/vmap2)-(0.5*rtg33inv[3]*hamil[14])/vmap2))/m_; 
+  alphavpar[15] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[3]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[12]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[14]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[16] = (rdz2*(-((0.125*dualcurlbhatoverB_3[3]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_3[5]*hamil[8])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[1]*hamil[4]*hamil[16])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_1[5]*hamil[6])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[16])/vmap2)-(0.5*rtg33inv[5]*hamil[8])/vmap2))/m_; 
+  alphavpar[17] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[6]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[8]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[18] = (rdy2*(-((0.2795084971874737*dualcurlbhatoverB_2[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_2[1]*hamil[8]*hamil[32])/vmap2-(0.2795084971874737*dualcurlbhatoverB_2[3]*hamil[6]*hamil[32])/vmap2-(0.2795084971874737*hamil[2]*dualcurlbhatoverB_2[5]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[3]*dualcurlbhatoverB_3[5]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[7]*hamil[32])/vmap2)-(0.2795084971874737*hamil[1]*dualcurlbhatoverB_1[5]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[19] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[5]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[8]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[3]*hamil[6]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[21] = (rdz2*(-((0.125*dualcurlbhatoverB_3[3]*hamil[4]*hamil[21])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_3[5]*hamil[14])/vmap2)+rdx2*(-((0.125*dualcurlbhatoverB_1[1]*hamil[4]*hamil[21])/vmap2)-(0.125*hamil[4]*dualcurlbhatoverB_1[5]*hamil[12])/vmap2))/(m_*q_)+(vmap[1]*rdz2*(-((0.5*rtg33inv[3]*hamil[21])/vmap2)-(0.5*rtg33inv[5]*hamil[14])/vmap2))/m_; 
+  alphavpar[23] = (rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[5]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[12]*hamil[32])/vmap2)+rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[0]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[1]*hamil[14]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[25] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[5]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[14]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[0]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[3]*hamil[12]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[26] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[5]*hamil[8]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[16]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[5]*hamil[6]*hamil[32])/vmap2))/(m_*q_); 
+  alphavpar[29] = (rdz2*(-((0.2795084971874737*dualcurlbhatoverB_3[3]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_3[5]*hamil[14]*hamil[32])/vmap2)+rdx2*(-((0.2795084971874737*dualcurlbhatoverB_1[1]*hamil[21]*hamil[32])/vmap2)-(0.2795084971874737*dualcurlbhatoverB_1[5]*hamil[12]*hamil[32])/vmap2))/(m_*q_); 
 
 
   out[4] += 0.3061862178478971*(alphavpar[29]*fin[29]+alphavpar[26]*fin[26]+alphavpar[25]*fin[25]+alphavpar[23]*fin[23]+alphavpar[21]*fin[21]+alphavpar[19]*fin[19]+alphavpar[18]*fin[18]+alphavpar[17]*fin[17]+alphavpar[16]*fin[16]+alphavpar[15]*fin[15]+alphavpar[14]*fin[14]+alphavpar[12]*fin[12]+alphavpar[11]*fin[11]+alphavpar[10]*fin[10]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[7]*fin[7]+alphavpar[6]*fin[6]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[3]*fin[3]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index a266ef3c3e..8f17e490dc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 965fe74fae..98068d61bd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 36ba1fea10..3570650c26 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index e489640137..7222eb7a57 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index c1f4cc7d70..de86af7df4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -81,7 +81,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -117,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -129,7 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -151,7 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -175,7 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -187,7 +187,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -199,7 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -211,7 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 4abf974c5e..31f7efb238 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 64470288c2..9b36f8f09f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -84,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -96,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -120,7 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -154,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -166,7 +166,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -190,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -202,7 +202,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -236,7 +236,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -260,7 +260,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -272,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -284,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -296,7 +296,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -330,7 +330,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -342,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -354,7 +354,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -366,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -378,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
index 2fe98f6682..dce0037dcc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
index e3225f86b7..916687c75f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index 9d319506ed..56209c7c75 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,8 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index 00a7dea761..bea9b242fc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -75,8 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 54b88039ef..27ce6f7d85 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,11 +69,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,11 +163,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index 04aa78d07c..7982c363b4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -77,8 +77,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index a14470b3b9..7f276f9f09 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,11 +72,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,11 +86,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,11 +100,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,11 +114,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,11 +128,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,11 +142,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,11 +166,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,11 +180,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,11 +194,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,11 +208,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,11 +222,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,11 +236,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -260,11 +260,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -274,11 +274,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,11 +288,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,11 +302,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -316,11 +316,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -330,11 +330,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -354,11 +354,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -368,11 +368,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -382,11 +382,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -396,11 +396,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -410,11 +410,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -424,11 +424,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 92b51ca333..79cd22d54d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 21bdc8e646..c155b423f6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 0637f96946..99d773d7b0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 9f40259cff..e360fdd5d5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -101,8 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +115,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +289,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +317,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +331,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +397,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +411,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +425,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +439,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +453,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index c3c0b6acec..08c93c94d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,11 +153,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -247,11 +247,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 0f44d08528..aebf381670 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 83e09311df..8d0e867c43 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,11 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,11 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -126,11 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -140,11 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,11 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,11 +168,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,11 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -220,11 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -234,11 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,11 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,11 +262,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -286,11 +286,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -300,11 +300,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,11 +328,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -342,11 +342,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -356,11 +356,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -380,11 +380,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -394,11 +394,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -408,11 +408,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -422,11 +422,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -436,11 +436,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -450,11 +450,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
index f805246ea4..dbbe32b877 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
index c1c25d1dd4..4c38fac253 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index 519637e5b7..0de5ae40a0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index 7b07cf337b..3bf86e95ff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -101,8 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +115,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +289,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +317,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +331,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +397,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +411,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +425,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +439,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +453,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index c5eba93f40..69148b02e3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,11 +153,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -247,11 +247,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index 9c47c715a0..c47ff307c6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index 8c6726dd8d..224c8572e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,11 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,11 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -126,11 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -140,11 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,11 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,11 +168,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,11 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -220,11 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -234,11 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,11 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,11 +262,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -286,11 +286,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -300,11 +300,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,11 +328,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -342,11 +342,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -356,11 +356,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -380,11 +380,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -394,11 +394,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -408,11 +408,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -422,11 +422,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -436,11 +436,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -450,11 +450,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
index 962754d863..d3de3c252d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
index 07cf133c7d..27dadb2e2a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
index b6d94852fd..43fe0486a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
index 16ae6e6457..d0cc5168ce 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
index 3edfb2bec4..e1849695b1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 3d9224a449..9e4173e417 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index bb102d731a..c8a082b087 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 6db6d85773..f7f890655e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 64ad80ab51..d3836fbe92 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index d9c1650115..5ed6f03f81 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 1898589ca4..f77df04fc1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index fd4cdafb4e..f42d46306e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 7e6c977977..f9a3bacbfa 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index f33afe2ec5..d980d12406 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 1d010f61ff..a250e7b97f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
index bcd43f34a8..2b65302e17 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
index 9a3ed84042..f314188a4a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
index e682671edd..1f81378812 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
index 682135df7a..313d367cff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
index 363a5d4584..8f122b113b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
index 2a8bf51834..352c8063d2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
index 40311e9356..63cea05a52 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
index e59fc9b049..4d73966690 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,8 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index 03670ee55a..b7336aeb63 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -75,8 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index bc24a62da2..5e97e18cb1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,11 +69,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,11 +163,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 23c1a2a136..1e2a656bb8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -77,8 +77,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index e952951819..a038408660 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,11 +72,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,11 +86,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,11 +100,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,11 +114,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,11 +128,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,11 +142,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,11 +166,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,11 +180,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,11 +194,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,11 +208,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,11 +222,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,11 +236,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -260,11 +260,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -274,11 +274,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,11 +288,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,11 +302,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -316,11 +316,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -330,11 +330,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -354,11 +354,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -368,11 +368,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -382,11 +382,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -396,11 +396,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -410,11 +410,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -424,11 +424,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 4c93412b8b..5e10da1a20 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 3cc4606e24..ce9d2de201 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 4b950af060..1a9d96a471 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
index d268ffdc29..fa3c87fdf6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -101,8 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +115,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +289,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +317,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +331,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +397,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +411,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +425,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +439,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +453,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 12a268c27a..2e59d6cb2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,11 +153,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -247,11 +247,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 1633321359..52b0cf84d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
index b29ef01f9e..a9948d4f5b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,11 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,11 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -126,11 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -140,11 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,11 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,11 +168,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,11 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -220,11 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -234,11 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,11 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,11 +262,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -286,11 +286,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -300,11 +300,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,11 +328,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -342,11 +342,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -356,11 +356,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -380,11 +380,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -394,11 +394,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -408,11 +408,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -422,11 +422,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -436,11 +436,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -450,11 +450,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
index 33549ad913..4548f44a98 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
index b8c9fbbc7e..6886a4ac4f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
index b22f64932c..530b1d9c73 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +156,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +250,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
index 434bec1437..beb8fd720e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -101,8 +101,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +115,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +129,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +143,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +157,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +195,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +209,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +223,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +237,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +251,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +289,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +303,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +317,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +331,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +345,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +383,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +397,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +411,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +425,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +439,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +453,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index b64e8dbaec..82e0bbb8f7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,11 +153,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -247,11 +247,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
index fea9f5a7b0..ffefbef949 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
index e32362aca0..1d1f8742d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,11 +98,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,11 +112,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -126,11 +126,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -140,11 +140,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,11 +154,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,11 +168,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,11 +192,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -220,11 +220,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -234,11 +234,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,11 +248,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,11 +262,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -286,11 +286,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -300,11 +300,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,11 +328,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -342,11 +342,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -356,11 +356,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -380,11 +380,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -394,11 +394,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -408,11 +408,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -422,11 +422,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -436,11 +436,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -450,11 +450,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
index 3a6ed49216..c3dbf14331 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
index b36f735aa9..d33a33ebfc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
index 31b515c00b..8b6505e5bc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
index 54a68c611a..bb51b8813c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
index 88c5f19992..0a3c6bd99c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 4d3f035e60..c7c7a6fa51 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index c480062590..f0e15580b6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index c25e95d46a..0583a5c6bf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 8f63f2b2d7..1705edaa2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 505f4c1c0f..71791f4279 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 25a4f401b1..6e303ccf9f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 6ce1635f91..386c36b8ad 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index cc40492811..4e8387df5d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 13b104a97f..a7f63c59a1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index fa420703d2..30f6a9d380 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
index 4947a0b9c3..22311b65a8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
index 9553614b91..7defcfcd29 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
index 9738cec169..0d6a456cca 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
index 5f50fe8ef2..06912e6b9b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
index 9e954c6beb..b0b7af1573 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index 99f17bec3e..95cd1dc2ce 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -80,7 +80,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -117,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -140,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -154,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -177,7 +177,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -191,7 +191,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index d758236228..c210c0e1f1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -71,11 +71,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -89,11 +89,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -116,11 +116,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -134,11 +134,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -161,11 +161,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -179,11 +179,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -206,11 +206,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -224,11 +224,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -251,11 +251,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -269,11 +269,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -296,11 +296,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -314,11 +314,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -341,11 +341,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -359,11 +359,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -386,11 +386,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -404,11 +404,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
index c777f47565..6c5fd72170 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
index b5d6ffc73b..3eeeb5d415 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
index 99a6714615..9e02f71820 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,8 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index e0b82123a7..137c870cd2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -75,8 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index c97c693445..bdf4fffe43 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,11 +69,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,11 +163,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index fbc62eeb89..9c7caab925 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -77,8 +77,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 342bd01612..5be3be215b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,11 +72,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,11 +86,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,11 +100,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,11 +114,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,11 +128,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,11 +142,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,11 +166,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,11 +180,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,11 +194,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,11 +208,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,11 +222,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,11 +236,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -260,11 +260,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -274,11 +274,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,11 +288,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,11 +302,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -316,11 +316,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -330,11 +330,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -354,11 +354,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -368,11 +368,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -382,11 +382,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -396,11 +396,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -410,11 +410,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -424,11 +424,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index ef3f8fd71a..ce84bee8cb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -81,7 +81,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -120,7 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -144,7 +144,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index 4c0363ace2..b7cd11600a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -71,11 +71,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -90,11 +90,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -118,11 +118,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -137,11 +137,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -165,11 +165,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -184,11 +184,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -212,11 +212,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -231,11 +231,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -259,11 +259,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -278,11 +278,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -306,11 +306,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -325,11 +325,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -353,11 +353,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -372,11 +372,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -400,11 +400,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -419,11 +419,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += bioverJB_quad[0]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += bioverJB_quad[1]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += bioverJB_quad[2]/m_ * ((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
index 53c6f1492b..05f7b0adce 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
index a822ec8120..dc07ba9735 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index d3c6c99e8c..3ef9053db6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,8 +72,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +86,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +100,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +114,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +128,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +142,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +166,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +180,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +194,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +208,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +222,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +236,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index 90b48246d7..05b5d2f181 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -75,8 +75,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +89,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +169,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +263,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +277,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +357,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +371,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index 0cb5a8675e..2310237393 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,11 +69,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -83,11 +83,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -97,11 +97,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,11 +111,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,11 +125,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,11 +139,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,11 +163,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -177,11 +177,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -191,11 +191,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,11 +205,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,11 +219,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,11 +233,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * bhat_quad[1]*(0.6123724356957944*apar[1]*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index fad227e7b6..f40fa74407 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -77,8 +77,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +91,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +171,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +185,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +265,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +279,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +359,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +373,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index 018239315a..137d07cefd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,11 +72,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,11 +86,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,11 +100,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,11 +114,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,11 +128,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,11 +142,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,11 +166,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,11 +180,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,11 +194,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,11 +208,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,11 +222,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,11 +236,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -260,11 +260,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -274,11 +274,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,11 +288,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,11 +302,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -316,11 +316,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -330,11 +330,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -354,11 +354,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -368,11 +368,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -382,11 +382,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -396,11 +396,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[0]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -410,11 +410,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[1]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -424,11 +424,11 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad) * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad; 
-  alpha_quad += mvpar_quad[2]/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]); 
+  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index e0d595d3fd..ec0aaed538 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index a0183d2fea..4ec2aa04fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 7aec7c1174..b72fa0bc56 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index ca40ecf294..b8926ad492 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 7ea596b97a..25790c6de8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -95,7 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -107,7 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -131,7 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -143,7 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -165,7 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -177,7 +177,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -201,7 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -213,7 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -225,7 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 7cdf6e59e6..0cd555a507 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 00ba9ae584..126b740838 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -134,7 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -158,7 +158,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -180,7 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -204,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -216,7 +216,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -228,7 +228,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -274,7 +274,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -286,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -298,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -310,7 +310,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -344,7 +344,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -356,7 +356,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -368,7 +368,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -380,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -392,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -404,7 +404,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 9619be16fb..013f2db119 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -48,14 +48,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -67,7 +67,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -78,7 +78,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index af23cd30e1..4beb85d6e5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -49,14 +49,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -68,7 +68,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -90,7 +90,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -101,7 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index e3da94ba96..7173fab4de 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 000b03b922..68e15b6e58 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index f17b4abda2..9e5e1b48fa 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -95,7 +95,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -107,7 +107,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -131,7 +131,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -143,7 +143,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -165,7 +165,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -177,7 +177,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -201,7 +201,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -213,7 +213,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -225,7 +225,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index d84c7f993c..95686206c1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index e202b69597..6c1090ddc4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -134,7 +134,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -158,7 +158,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -180,7 +180,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -204,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -216,7 +216,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -228,7 +228,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -274,7 +274,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -286,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -298,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -310,7 +310,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -344,7 +344,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -356,7 +356,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -368,7 +368,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -380,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -392,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -404,7 +404,7 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 47dd50e920..072bab42e4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index 9b0e361df1..beef88b515 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index c5d012f06a..75019f7489 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index 4da146f811..c4e86d67ff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 1c3d1b577b..21d73e1f3f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index dcec602bad..720e058d01 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index ac1f4606ed..99790bdf4b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index a693a8d3d4..7e96b4cd7c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 7a2c577e54..8a5feaa8de 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 9c84941d6f..8266e5b4b4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 6de9b89901..1b3a1c3259 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 2626cd24da..94fe4931bc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 2253e195ed..8f1a28700e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -64,14 +64,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -83,7 +83,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,7 +113,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,7 +123,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,7 +133,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -153,7 +153,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,7 +173,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,7 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,7 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -203,7 +203,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 83f1f49c29..74969cd7a1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -81,14 +81,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 00805d7452..ab2dea1556 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -79,14 +79,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -98,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,7 +128,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -138,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +148,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,7 +168,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -188,7 +188,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,7 +208,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -218,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -238,7 +238,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -258,7 +258,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -278,7 +278,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -288,7 +288,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +308,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -328,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -338,7 +338,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -358,7 +358,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index f4775e4ff2..74c598c8b5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index 007b8c717a..6311c4e78b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index 08ce32d959..eefb8d3120 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -79,7 +79,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,7 +89,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -109,7 +109,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,7 +119,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,7 +139,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,7 +149,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,7 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,7 +169,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -179,7 +179,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -189,7 +189,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index 44312bc9a4..8514d1f80d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index d6ad3632c6..0c3fcdce96 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -82,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -92,7 +92,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -102,7 +102,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -112,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,7 +122,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,7 +142,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -152,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +162,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -172,7 +172,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -182,7 +182,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,7 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -232,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +242,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -252,7 +252,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -262,7 +262,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -282,7 +282,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -302,7 +302,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -312,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +322,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -332,7 +332,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 9a63687952..5d6b2632d6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -46,14 +46,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  mvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
+  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -65,7 +65,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -76,7 +76,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -87,7 +87,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index 3665094082..61705ec812 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -47,14 +47,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  mvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -66,7 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -88,7 +88,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -99,7 +99,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -110,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
@@ -121,7 +121,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index 2ead917c5f..ee444d7199 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 8e83ab7d4b..9586cf6447 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index 2d6b0df100..ba4fbb65a3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -50,14 +50,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  mvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -69,7 +69,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -81,7 +81,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -93,7 +93,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -105,7 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -117,7 +117,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -129,7 +129,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -151,7 +151,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -163,7 +163,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -175,7 +175,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -187,7 +187,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -199,7 +199,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -211,7 +211,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index f45d49c8ab..33da4fed8c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index eb9fbe0b7a..002ed373e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -53,14 +53,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
-  double mvpar_quad[3] = {0.0}; 
-  mvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  mvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  mvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
+  double dHdvpar_quad[3] = {0.0}; 
+  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
+  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
+  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
   double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = mvpar_quad[0]*mvpar_quad[0]/m_; 
-  mvparsq_quad[1] = mvpar_quad[1]*mvpar_quad[1]/m_; 
-  mvparsq_quad[2] = mvpar_quad[2]*mvpar_quad[2]/m_; 
+  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
+  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
+  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
 
   bmag_quad = gkdgs[0].bmag; 
   Jc_quad = gkdgs[0].Jc; 
@@ -72,7 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[0].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -84,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -96,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -108,7 +108,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -120,7 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -154,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[1].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -166,7 +166,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -178,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -190,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -202,7 +202,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -214,7 +214,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -236,7 +236,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[2].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -248,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -260,7 +260,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -272,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -284,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -296,7 +296,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -318,7 +318,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   area_elem_quad = dgs[3].area_elem; 
 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -330,7 +330,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -342,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -354,7 +354,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -366,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
@@ -378,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
   flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
 
-  alpha_quad = (mvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
+  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 

From a30f152fff3cebfa9a86e345f1542f803f59a10e Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Apr 2026 17:02:14 -0400
Subject: [PATCH 136/181] =?UTF-8?q?this=20commit=20runs=20the=20alfven=203?=
 =?UTF-8?q?x2v=20test=20without=20any=20aliasing=20error=20=F0=9F=8F=86=20?=
 =?UTF-8?q?for=20@JunoRavin?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |   6 +
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |   6 +
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |   6 +
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 124 +++++++++++-------
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 124 +++++++++++-------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 124 +++++++++++-------
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 124 +++++++++++-------
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 124 +++++++++++-------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 124 +++++++++++-------
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c |  38 ++++++
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 124 +++++++++++-------
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 124 +++++++++++-------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 124 +++++++++++-------
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  38 ++++++
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 124 +++++++++++-------
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 124 +++++++++++-------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 124 +++++++++++-------
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  38 ++++++
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |   6 +
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |   6 +
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |   6 +
 21 files changed, 1062 insertions(+), 576 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 7222eb7a57..c7c2a381b6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 31f7efb238..1b35619a58 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 9b36f8f09f..fe54f02a40 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index bea9b242fc..08602d97d4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
+  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
+  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
+  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
+  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
+  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
+  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
+  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index 7982c363b4..580b636042 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
+  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
+  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
+  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
+  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
+  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
+  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
+  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +255,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +443,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +457,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index 7f276f9f09..ae76bf930d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
+  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
+  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
+  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
+  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
+  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
+  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
+  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index b7336aeb63..804467fca4 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
+  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
+  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
+  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
+  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
+  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
+  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
+  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 1e2a656bb8..7ec906e8a0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
+  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
+  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
+  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
+  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
+  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
+  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
+  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +255,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +443,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +457,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index a038408660..3ddd6a8435 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
+  mvpargradA_2[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
+  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
+  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
+  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
+  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
+  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
+  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
+  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index c210c0e1f1..4617954bef 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -45,6 +45,44 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
+  double gradHxgradA_1[48] = {0.}; 
+  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
+  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
+  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
+  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
+  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
+
+  double gradHxgradA_2[48] = {0.}; 
+  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
+  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
+  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
+  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
+  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
+  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
+  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
+  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
+
+  double gradHxgradA_3[48] = {0.}; 
+  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
+  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
+  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
+
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index 137c870cd2..e134febdd5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
+  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
+  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
+  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
+  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
+  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
+  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
+  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
+  mvpargradA_2[2] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
+  mvpargradA_2[7] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index 9c7caab925..19c6e65cbd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -42,6 +42,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
+  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
+  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
+  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
+  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
+  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
+  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
+  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +255,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +443,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +457,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 5be3be215b..8d9c86c30b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
+  mvpargradA_2[1] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
+  mvpargradA_2[6] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
+  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
+  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
+  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
+  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
+  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
+  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
+  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index b7cd11600a..8269c2ebbd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -45,6 +45,44 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
+  double gradHxgradA_1[48] = {0.}; 
+  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
+  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
+  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
+  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
+  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
+
+  double gradHxgradA_2[48] = {0.}; 
+  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
+  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
+  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
+  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
+  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
+  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
+  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
+  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
+
+  double gradHxgradA_3[48] = {0.}; 
+  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
+  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
+  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
+
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index 05b5d2f181..95a9f309f3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
+  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
+  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
+  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
+  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
+  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
+  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
+  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
+  mvpargradA_2[2] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
+  mvpargradA_2[7] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index f40fa74407..81f0ab73ec 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -42,6 +42,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
+  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
+  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
+  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
+  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
+  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
+  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
+  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
+  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
+  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
+  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,8 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -91,8 +119,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -105,8 +133,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -119,8 +147,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -133,8 +161,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -147,8 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +199,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,8 +213,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -199,8 +227,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -213,8 +241,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -227,8 +255,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,8 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +293,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,8 +307,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -293,8 +321,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -307,8 +335,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,8 +349,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,8 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +387,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,8 +401,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -387,8 +415,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -401,8 +429,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -415,8 +443,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -429,8 +457,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index 137d07cefd..d0c3c6c01a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -40,6 +40,34 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
+  double mvpargradA_1[48] = {0.}; 
+  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
+  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
+  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
+  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
+
+  double mvpargradA_2[48] = {0.}; 
+  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
+  mvpargradA_2[1] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
+  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
+  mvpargradA_2[6] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
+
+  double mvpargradA_3[48] = {0.}; 
+  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
+  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
+  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
+  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
+  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
+  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
+  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
+  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,8 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,8 +117,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -103,8 +131,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +145,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +173,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,8 +197,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,8 +211,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +225,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +239,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +253,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +267,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,8 +291,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,8 +305,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +319,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +333,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +347,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +361,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,8 +385,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,8 +399,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +413,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +427,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +441,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +455,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index f328a124fe..d2091dd046 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -45,6 +45,44 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
+  double gradHxgradA_1[48] = {0.}; 
+  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
+  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
+  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
+  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
+  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
+
+  double gradHxgradA_2[48] = {0.}; 
+  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
+  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
+  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
+  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
+  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
+  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
+  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
+  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
+
+  double gradHxgradA_3[48] = {0.}; 
+  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
+  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
+  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
+
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 9586cf6447..9ba73aa959 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 33da4fed8c..aa10c2619c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 002ed373e7..6ee59db3a7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 

From 1c31d531da147538fbab345c32f3fa1776f47bf1 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Apr 2026 17:08:34 -0400
Subject: [PATCH 137/181] =?UTF-8?q?forgot=20a=20line=20in=20the=20kernel?=
 =?UTF-8?q?=20generation,=20everything=20is=20fine=20=F0=9F=90=B6?=
 =?UTF-8?q?=F0=9F=94=A5?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 48 +++++++++----------
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 48 +++++++++----------
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 48 +++++++++----------
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 48 +++++++++----------
 4 files changed, 96 insertions(+), 96 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index 08602d97d4..cd7b1e2efa 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -104,7 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +226,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +254,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +306,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +320,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +334,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +362,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +386,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +400,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +414,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +428,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +442,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +456,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index 804467fca4..dce41b3545 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -104,7 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +226,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +254,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +306,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +320,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +334,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +362,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +386,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +400,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +414,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +428,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +442,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +456,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index e134febdd5..7fbe75d6e9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -104,7 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +226,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +254,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +306,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +320,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +334,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +362,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +386,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +400,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +414,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +428,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +442,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +456,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index 95a9f309f3..c376c8f6ae 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -104,7 +104,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +118,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +132,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +146,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +160,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +174,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +212,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +226,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +240,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +254,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +268,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +292,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +306,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +320,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +334,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +348,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +362,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +386,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +400,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +414,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +428,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +442,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +456,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 

From a12859a70b4762b960987365d7be0fb615d00d2d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 17 Apr 2026 18:40:36 -0400
Subject: [PATCH 138/181] this is the minimal correction to get rid of the
 spurious alfven 3x2v oscillation

---
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |   6 --
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |   6 --
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |   6 --
 ...isionless_flux_em_edge_surfx_1x1v_ser_p1.c |   3 +
 ...isionless_flux_em_edge_surfx_1x2v_ser_p1.c |   3 +
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c |  70 +++++-------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c |  70 +++++-------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c |  70 +++++-------
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c |   3 +
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c |   3 +
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 102 +++++++++---------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 102 +++++++++---------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 102 +++++++++---------
 ...lux_em_multib_boundary_surfx_1x1v_ser_p1.c |   3 +
 ...lux_em_multib_boundary_surfx_1x2v_ser_p1.c |   3 +
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 102 +++++++++---------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 102 +++++++++---------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 102 +++++++++---------
 ...ess_flux_em_no_by_edge_surfx_2x2v_ser_p1.c |   4 +
 ...ess_flux_em_no_by_edge_surfx_3x2v_ser_p1.c |   6 ++
 ...ess_flux_em_no_by_edge_surfy_2x2v_ser_p1.c |   4 +
 ...ess_flux_em_no_by_edge_surfy_3x2v_ser_p1.c |   6 ++
 ...ess_flux_em_no_by_edge_surfz_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |   6 ++
 ...sionless_flux_em_no_by_surfx_2x2v_ser_p1.c |   4 +
 ...sionless_flux_em_no_by_surfx_3x2v_ser_p1.c |   6 ++
 ...sionless_flux_em_no_by_surfy_2x2v_ser_p1.c |   4 +
 ...sionless_flux_em_no_by_surfy_3x2v_ser_p1.c |   6 ++
 ...sionless_flux_em_no_by_surfz_3x2v_ser_p1.c |   6 ++
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c |   3 +
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c |   3 +
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c |  70 +++++-------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c |  70 +++++-------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c |  70 +++++-------
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c |   3 +
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c |   3 +
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 102 +++++++++---------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 102 +++++++++---------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 102 +++++++++---------
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c |   3 +
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c |   3 +
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 102 +++++++++---------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 102 +++++++++---------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 102 +++++++++---------
 ...lux_em_star_no_by_edge_surfx_2x2v_ser_p1.c |   4 +
 ...lux_em_star_no_by_edge_surfx_3x2v_ser_p1.c |   6 ++
 ...lux_em_star_no_by_edge_surfy_2x2v_ser_p1.c |   4 +
 ...lux_em_star_no_by_edge_surfy_3x2v_ser_p1.c |   6 ++
 ...lux_em_star_no_by_edge_surfz_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |   6 ++
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |   6 ++
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |   6 ++
 ...ess_flux_em_star_no_by_surfx_2x2v_ser_p1.c |   4 +
 ...ess_flux_em_star_no_by_surfx_3x2v_ser_p1.c |   6 ++
 ...ess_flux_em_star_no_by_surfy_2x2v_ser_p1.c |   4 +
 ...ess_flux_em_star_no_by_surfy_3x2v_ser_p1.c |   6 ++
 ...ess_flux_em_star_no_by_surfz_3x2v_ser_p1.c |   6 ++
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c |  24 +++--
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c |  38 -------
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c |   3 +
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c |   3 +
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c |  52 ++++-----
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c |  70 +++++-------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c |  52 ++++-----
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c |  70 +++++-------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c |  70 +++++-------
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c |  24 +++--
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c |  38 -------
 ..._collisionless_flux_em_surfx_1x1v_ser_p1.c |   3 +
 ..._collisionless_flux_em_surfx_1x2v_ser_p1.c |   3 +
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c |  52 ++++-----
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c |  70 +++++-------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c |  52 ++++-----
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c |  70 +++++-------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c |  70 +++++-------
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c |  38 -------
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |   6 --
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |   6 --
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |   6 --
 107 files changed, 1672 insertions(+), 1678 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index c7c2a381b6..7222eb7a57 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -40,12 +40,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 1b35619a58..31f7efb238 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -42,12 +42,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index fe54f02a40..9b36f8f09f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -40,12 +40,6 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
index dce0037dcc..5bb6b0a75a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
index 916687c75f..5adfce3283 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
   hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
index 56209c7c75..e8896c6d4b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
index cd7b1e2efa..87af2dae39 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
-  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
-  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
-  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
-  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
-  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
-  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
-  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
index 27ce6f7d85..73ee4404df 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
index 580b636042..e681b9589f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
@@ -48,28 +48,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
-  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
-  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
-  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
-  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
-  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
-  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
-  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -106,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +126,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -176,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -200,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,7 +206,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +220,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -256,7 +234,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -270,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -294,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +300,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -336,7 +314,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -350,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -364,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -388,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -402,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -416,7 +394,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -430,7 +408,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -444,7 +422,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -458,7 +436,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
index ae76bf930d..31a7ccd890 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
-  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
-  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
-  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
-  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
-  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
-  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
-  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 79cd22d54d..ae20218be5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p
 
   double JRatfR[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
index c155b423f6..b7a042a1fe 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p
 
   double JRatfR[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 99d773d7b0..6a867658a9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
index e360fdd5d5..3735fbdf54 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 08c93c94d6..7441ae3793 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
index aebf381670..97b2d0679d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,8 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 8d0e867c43..077c9205dd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
index dbbe32b877..1e42e613b9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
 
   double JRatfL[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
index 4c38fac253..ec14fa1571 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
 
   double JRatfL[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
index 0de5ae40a0..68ab1cb353 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
index 3bf86e95ff..9fff406b73 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
index 69148b02e3..64dbe2da91 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
index c47ff307c6..536e6c34d8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,8 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
index 224c8572e7..bc1cb3ba1e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
index d3de3c252d..ba90f5a442 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
index 27dadb2e2a..a3b36fbf3f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
index 43fe0486a3..e082865dc9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
index d0cc5168ce..adbfed0e0a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
index e1849695b1..00b7d70fe6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 9e4173e417..7d0f83ae5f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index c8a082b087..8899b591f9 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index f7f890655e..1d1911e717 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index d3836fbe92..4023c31e6e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 5ed6f03f81..939c66a928 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index f77df04fc1..bd65d6e496 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index f42d46306e..a68f391f0e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index f9a3bacbfa..f460213950 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index d980d12406..352a5f8155 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index a250e7b97f..c1e212a51e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
index 2b65302e17..0fc1866a80 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
index f314188a4a..a7e78831e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
index 1f81378812..b73446db49 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
index 313d367cff..0d0c2981ff 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
index 8f122b113b..53d8775015 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
index 352c8063d2..898f51cea6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
index 63cea05a52..1cac10f2af 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
   hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
index 4d73966690..e1db697a7a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
index dce41b3545..74499dc569 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
-  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
-  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
-  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
-  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
-  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
-  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
-  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[6])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
index 5e97e18cb1..b034de3f86 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
index 7ec906e8a0..373f4cd523 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
@@ -48,28 +48,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(3.0*apar[4]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
-  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
-  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
-  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
-  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
-  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
-  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
-  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[3])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[5])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -106,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +126,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -176,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -200,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,7 +206,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +220,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -256,7 +234,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -270,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -294,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +300,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -336,7 +314,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -350,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -364,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -388,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -402,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -416,7 +394,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -430,7 +408,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -444,7 +422,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -458,7 +436,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
index 3ddd6a8435..b9ffb09703 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
   apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(3.0*apar[5]+1.7320508075688772*apar[1])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[1] = vmap[0]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(3.0*apar[6]+1.7320508075688772*apar[2])*m_*rdy2; 
-  mvpargradA_2[6] = vmap[1]*(3.0*apar[7]+1.7320508075688772*apar[4])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
-  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
-  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
-  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
-  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
-  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
-  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
-  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
index 5e10da1a20..b6234d654d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_
 
   double JRatfR[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
index ce9d2de201..2794ea343b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_
 
   double JRatfR[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 1a9d96a471..ec2773a9be 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
index fa3c87fdf6..801cfd794d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 2e59d6cb2c..4b0279bad1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 52b0cf84d4..8d590940f2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,8 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
index a9948d4f5b..de6e8f5375 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
index 4548f44a98..94941234a0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p
 
   double JRatfL[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
index 6886a4ac4f..98e5834ab7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p
 
   double JRatfL[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
index 530b1d9c73..5b9a29e4d3 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
index beb8fd720e..18e9c75f3c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
index 82e0bbb8f7..6eb39e2e81 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -156,8 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -250,8 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
index ffefbef949..f67ec48d4d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,8 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -117,8 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -131,8 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -145,8 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,8 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -173,8 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,8 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -211,8 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -225,8 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,8 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,8 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,8 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,8 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -305,8 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -319,8 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,8 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,8 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,8 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,8 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -399,8 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -413,8 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -427,8 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -441,8 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -455,8 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
index 1d1f8742d4..86a4032c6c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,8 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,8 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -129,8 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -143,8 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,8 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,8 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]-0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,8 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,8 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -223,8 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -237,8 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,8 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,8 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])+0.25*apar[2]-0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[2]-0.4330127018922193*apar[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,8 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,8 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -317,8 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -331,8 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,8 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,8 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar[5])-0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[1]-0.4330127018922193*apar[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,8 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,8 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -411,8 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -425,8 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -439,8 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -453,8 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar[5]+0.25*apar[2]+0.25*apar[1]+0.25*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar[5]+0.4330127018922193*apar[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar[5]+0.4330127018922193*apar[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
index c3dbf14331..16107a4bfd 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
index d33a33ebfc..e348146b19 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
index 8b6505e5bc..c08a9acce7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
index bb51b8813c..d96fbc8007 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
index 0a3c6bd99c..5b80440dcb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index c7c7a6fa51..c92a1ac2c5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index f0e15580b6..2707c88374 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 0583a5c6bf..be05533432 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 1705edaa2c..16a921c788 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 71791f4279..fe114feeb1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 6e303ccf9f..2ac072efa7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 386c36b8ad..484c74eea5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 4e8387df5d..717ef56760 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index a7f63c59a1..dc082abd14 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index 30f6a9d380..0191a5c18f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
index 22311b65a8..021c3b4c0f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
index 7defcfcd29..16322da7ec 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
index 0d6a456cca..6df6055c88 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
index 06912e6b9b..5a717ab448 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
index b0b7af1573..c143d2e516 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
index 95cd1dc2ce..6f884a9f3a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -80,7 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -103,7 +105,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -117,7 +120,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -140,7 +144,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -154,7 +159,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -177,7 +183,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -191,7 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
index 4617954bef..c210c0e1f1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
@@ -45,44 +45,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
-  double gradHxgradA_1[48] = {0.}; 
-  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
-  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
-  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
-  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
-  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
-
-  double gradHxgradA_2[48] = {0.}; 
-  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
-  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
-  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
-  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
-  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
-  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
-  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
-  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
-
-  double gradHxgradA_3[48] = {0.}; 
-  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
-  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
-  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
-
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
index 6c5fd72170..37cbe773dc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
index 3eeeb5d415..06aa03bcf5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
   hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
index 9e02f71820..83fbd9d73a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
index 7fbe75d6e9..8c775e0b8e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
   apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
-  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
-  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
-  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
-  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
-  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
-  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
-  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
-  mvpargradA_2[2] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
-  mvpargradA_2[7] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
index bdf4fffe43..e617ddb95c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
index 19c6e65cbd..3e950f1ca2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
@@ -48,28 +48,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
   apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
-  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
-  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
-  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
-  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
-  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
-  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
-  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -106,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +126,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -176,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -200,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,7 +206,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +220,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -256,7 +234,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -270,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -294,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +300,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -336,7 +314,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -350,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -364,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -388,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -402,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -416,7 +394,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -430,7 +408,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -444,7 +422,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -458,7 +436,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
index 8d9c86c30b..927f268fc5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
   apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
-  mvpargradA_2[1] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
-  mvpargradA_2[6] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
-  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
-  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
-  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
-  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
-  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
-  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
-  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
index ce84bee8cb..b577e243d0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
@@ -66,7 +66,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -81,7 +82,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -105,7 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -120,7 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -144,7 +148,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -159,7 +164,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -183,7 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -198,7 +205,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
index 8269c2ebbd..b7cd11600a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
@@ -45,44 +45,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
-  double gradHxgradA_1[48] = {0.}; 
-  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
-  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
-  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
-  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
-  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
-
-  double gradHxgradA_2[48] = {0.}; 
-  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
-  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
-  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
-  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
-  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
-  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
-  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
-  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
-
-  double gradHxgradA_3[48] = {0.}; 
-  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
-  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
-  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
-
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
index 05f7b0adce..7240774398 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
index dc07ba9735..c0917aa28c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
   hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
index 3ef9053db6..256d3fa931 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
index c376c8f6ae..670244e151 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
   apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = 1.7320508075688772*vmap[0]*apar[1]*m_*rdx2; 
-  mvpargradA_1[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdx2; 
-  mvpargradA_1[2] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdx2; 
-  mvpargradA_1[3] = 1.7320508075688772*apar[1]*vmap[1]*m_*rdx2; 
-  mvpargradA_1[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdx2; 
-  mvpargradA_1[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdx2; 
-  mvpargradA_1[7] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdx2; 
-  mvpargradA_1[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
-  mvpargradA_2[2] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[4])*m_*rdy2; 
-  mvpargradA_2[7] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[5])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[6]-3.0*apar[7])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[0]-0.25*mvpargradA_2[2]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_2[7])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_2[7]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[2]+0.25*mvpargradA_2[0]) * bhat_quad[2] - (0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[1]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
index 2310237393..496e3bc191 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,8 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -86,8 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -100,8 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -114,8 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -128,8 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -142,8 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[0]-0.3535533905932737*apar[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,8 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,8 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -194,8 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -208,8 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -222,8 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -236,8 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar[1]+0.3535533905932737*apar[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
index 81f0ab73ec..3b0af0a204 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
@@ -48,28 +48,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
   apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[4])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = 1.7320508075688772*vmap[0]*apar[2]*m_*rdy2; 
-  mvpargradA_2[1] = 1.7320508075688772*vmap[0]*apar[4]*m_*rdy2; 
-  mvpargradA_2[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdy2; 
-  mvpargradA_2[3] = 1.7320508075688772*vmap[1]*apar[2]*m_*rdy2; 
-  mvpargradA_2[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdy2; 
-  mvpargradA_2[6] = 1.7320508075688772*vmap[1]*apar[4]*m_*rdy2; 
-  mvpargradA_2[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdy2; 
-  mvpargradA_2[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = vmap[0]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
-  mvpargradA_3[1] = vmap[0]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
-  mvpargradA_3[3] = vmap[1]*(1.7320508075688772*apar[3]-3.0*apar[6])*m_*rdz2; 
-  mvpargradA_3[6] = vmap[1]*(1.7320508075688772*apar[5]-3.0*apar[7])*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -106,7 +84,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,7 +98,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,7 +112,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -148,7 +126,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -162,7 +140,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -176,7 +154,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -200,7 +178,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,7 +192,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,7 +206,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -242,7 +220,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]-0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -256,7 +234,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[0]-0.25*mvpargradA_3[1]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -270,7 +248,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])+0.33541019662496846*mvpargradA_3[3]-0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -294,7 +272,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -308,7 +286,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -322,7 +300,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -336,7 +314,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -350,7 +328,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -364,7 +342,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -388,7 +366,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -402,7 +380,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -416,7 +394,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -430,7 +408,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_3[6])-0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -444,7 +422,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -458,7 +436,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_3[6]+0.33541019662496846*mvpargradA_3[3]+0.25*mvpargradA_3[1]+0.25*mvpargradA_3[0]) * bhat_quad[0] - (0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[2]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
index d0c3c6c01a..ee0ef2c9bf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
@@ -46,28 +46,6 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
   apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
 
-  double mvpargradA_1[48] = {0.}; 
-  mvpargradA_1[0] = vmap[0]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
-  mvpargradA_1[2] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
-  mvpargradA_1[3] = vmap[1]*(1.7320508075688772*apar[1]-3.0*apar[5])*m_*rdx2; 
-  mvpargradA_1[7] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdx2; 
-
-  double mvpargradA_2[48] = {0.}; 
-  mvpargradA_2[0] = vmap[0]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
-  mvpargradA_2[1] = vmap[0]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
-  mvpargradA_2[3] = vmap[1]*(1.7320508075688772*apar[2]-3.0*apar[6])*m_*rdy2; 
-  mvpargradA_2[6] = vmap[1]*(1.7320508075688772*apar[4]-3.0*apar[7])*m_*rdy2; 
-
-  double mvpargradA_3[48] = {0.}; 
-  mvpargradA_3[0] = 1.7320508075688772*vmap[0]*apar[3]*m_*rdz2; 
-  mvpargradA_3[1] = 1.7320508075688772*vmap[0]*apar[5]*m_*rdz2; 
-  mvpargradA_3[2] = 1.7320508075688772*vmap[0]*apar[6]*m_*rdz2; 
-  mvpargradA_3[3] = 1.7320508075688772*vmap[1]*apar[3]*m_*rdz2; 
-  mvpargradA_3[5] = 1.7320508075688772*vmap[0]*apar[7]*m_*rdz2; 
-  mvpargradA_3[6] = 1.7320508075688772*vmap[1]*apar[5]*m_*rdz2; 
-  mvpargradA_3[7] = 1.7320508075688772*vmap[1]*apar[6]*m_*rdz2; 
-  mvpargradA_3[11] = 1.7320508075688772*vmap[1]*apar[7]*m_*rdz2; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -104,7 +82,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -118,7 +96,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,7 +110,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,7 +124,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -160,7 +138,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -174,7 +152,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -198,7 +176,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -212,7 +190,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -226,7 +204,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -240,7 +218,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]-0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -254,7 +232,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[0]-0.25*mvpargradA_2[1]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -268,7 +246,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])+0.33541019662496846*mvpargradA_2[3]-0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -292,7 +270,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -306,7 +284,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -320,7 +298,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -334,7 +312,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]-0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -348,7 +326,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[0]-0.25*mvpargradA_1[2]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -362,7 +340,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])+0.33541019662496846*mvpargradA_1[3]-0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -386,7 +364,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -400,7 +378,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -414,7 +392,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -428,7 +406,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((-(0.33541019662496846*mvpargradA_1[7])-0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (-(0.33541019662496846*mvpargradA_2[6])-0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -442,7 +420,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -456,7 +434,7 @@ GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
   alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * ((0.33541019662496846*mvpargradA_1[7]+0.33541019662496846*mvpargradA_1[3]+0.25*mvpargradA_1[2]+0.25*mvpargradA_1[0]) * bhat_quad[1] - (0.33541019662496846*mvpargradA_2[6]+0.33541019662496846*mvpargradA_2[3]+0.25*mvpargradA_2[1]+0.25*mvpargradA_2[0]) * bhat_quad[0]); 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index d2091dd046..f328a124fe 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -45,44 +45,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
-  double gradHxgradA_1[48] = {0.}; 
-  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
-  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
-  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
-  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
-  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
-  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
-  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
-
-  double gradHxgradA_2[48] = {0.}; 
-  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
-  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
-  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
-  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
-  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
-  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
-  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
-  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
-  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
-
-  double gradHxgradA_3[48] = {0.}; 
-  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
-  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
-  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
-  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
-  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
-  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
-
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 9ba73aa959..9586cf6447 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -40,12 +40,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index aa10c2619c..33da4fed8c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -42,12 +42,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 6ee59db3a7..002ed373e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -40,12 +40,6 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 

From 24ef656cc25d85fea7e1ab4183a3f31f4cb9db7a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 20 Apr 2026 05:52:34 -0700
Subject: [PATCH 139/181] remove unused variable

---
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 1 -
 1 file changed, 1 deletion(-)

diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 58183d6c43..42295acaea 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1251,7 +1251,6 @@ struct gk_field {
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
   bool is_em; // Whether we solve the EM field equations.
-  bool freeze_apar; // Whether we set Apardot=0. 
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density

From 3ee4437c2e072e5454e2def5b3d3036139267071 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 20 Apr 2026 09:08:05 -0400
Subject: [PATCH 140/181] add tool to potentially smooth Apar if required

---
 gyrokinetic/apps/gk_field.c              | 4 ++++
 gyrokinetic/apps/gk_field_2x3x.c         | 6 ++++++
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 1 +
 3 files changed, 11 insertions(+)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 73e387cf21..8175022d97 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -224,6 +224,10 @@ gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, st
 {
   // Apar^{n+1} = Apar^{n} + dt*dApar/dt
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
+
+  // Smooth along z.
+  // gk_field_fem_projection_par(app, field, field->apar, field->apar_smooth_aux);
+  // gkyl_array_copy_range(field->apar, field->apar_smooth_aux, &app->local_ext);
 }
 
 static void
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 9d8d3c1b51..7150c10614 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -246,6 +246,10 @@ gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field)
   gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
   gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
 
+  // Smooth along z.
+  // gk_field_fem_projection_par(app, field, field->apar, field->apar_smooth_aux);
+  // gkyl_array_copy_range(field->apar, field->apar_smooth_aux, &app->local_ext);
+
   field->invert_flr(app, field, field->apar);
 
   field->enforce_parallel_bc_em_func(app, field, field->apar);
@@ -287,6 +291,7 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->aparnew);
 
   if (f->is_em) {
+    gkyl_array_release(f->apar_smooth_aux);
     gkyl_array_release(f->currentDens);
     gkyl_array_release(f->currentDensdot);
     gkyl_array_release(f->lapWeightAmpere);
@@ -364,6 +369,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
     }
 
+    f->apar_smooth_aux = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->currentDensdot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     f->lapWeightAmpere = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 58183d6c43..0bcba75e7e 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1278,6 +1278,7 @@ struct gk_field {
     struct {
       struct gkyl_array *apar, *apar1, *aparnew; // Array for A_parallel and RK stages.
       struct gkyl_array *apar_curr; // A_parallel at current RK stage.
+      struct gkyl_array *apar_smooth_aux; // Auxiliary array for smoothing A_parallel in z.
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
       struct gkyl_array *apardot_host; // Host copy for use IO.

From 75a22165ce56f5c322b70b70907f39edad19ec48 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 20 Apr 2026 11:45:39 -0400
Subject: [PATCH 141/181] Apar is now computed from the initial state when
 starting from a frame

---
 gyrokinetic/apps/gyrokinetic.c | 25 +++++++++++++++++--------
 1 file changed, 17 insertions(+), 8 deletions(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index b5fedbf060..a89f01872f 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -677,10 +677,8 @@ gkyl_gyrokinetic_app_new_solver(struct gkyl_gk *gk, gkyl_gyrokinetic_app *app)
   app->field = gk_field_new(gk, app); // Initialize field, even if we are  skipping field updates.
 
   // Choose the function that updates the fields in time.
-  if (app->field->update_field)
-    app->calc_field_func = gyrokinetic_calc_field_enabled;
-  else
-    app->calc_field_func = gyrokinetic_calc_field_disabled;
+  app->calc_field_func = app->field->update_field? 
+    gyrokinetic_calc_field_enabled : gyrokinetic_calc_field_disabled;
 
   // Initialize the post-positivity quasineutrality enforcement.
   app->post_positivity_quasineut = false;
@@ -3014,10 +3012,12 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
   if (rstat.io_status == GKYL_ARRAY_RIO_SUCCESS) {
     // Compute the fields and apply BCs.
     struct gkyl_array *distf[app->num_species];
+    struct gkyl_array *distfdot[app->num_species];
     struct gkyl_array **bflux[app->num_species];
     struct gkyl_array *distf_neut[app->num_neut_species];
     for (int i=0; i<app->num_species; ++i) {
       distf[i] = app->species[i].f;
+      distfdot[i] = app->species[i].f1;
       bflux[i] = app->species[i].bflux.f;
     }
     for (int i=0; i<app->num_neut_species; ++i) {
@@ -3042,6 +3042,16 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
       // MF 2024/09/27/: Need the cast here for consistency. Fixing
       // this may require removing 'const' from a lot of places.
       gyrokinetic_calc_field(app, rstat.stime, (const struct gkyl_array **) distf, bflux);
+
+      if (app->field->is_em) {
+        gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
+        gk_field_calc_apar_ic(app, app->field);
+        for (int i=0; i<app->num_species; ++i) {
+          struct gk_species *gk_s = &app->species[i];
+          gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+        }
+        gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
+      }      
     }
     else {
       // Read the t=0 field.
@@ -3186,8 +3196,7 @@ gkyl_gyrokinetic_app_reset_field(gkyl_gyrokinetic_app* app, double tm,
 {
   app->field->info.is_static = field_inp.is_static;
   app->field->update_field = !field_inp.is_static;
-  if (app->field->update_field)
-    app->calc_field_func = gyrokinetic_calc_field_enabled;
-  else
-    app->calc_field_func = gyrokinetic_calc_field_disabled;
+
+  app->calc_field_func = app->field->update_field? 
+    gyrokinetic_calc_field_enabled : gyrokinetic_calc_field_disabled;
 }

From a6c6bbffaa63f053d3cf218e2b1676c903d9a5a3 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 09:00:25 -0400
Subject: [PATCH 142/181] Add a new field info parameter that we can use to
 force an Ampere computation of the initial Apar. Otherwise, restarting from a
 frame will look for the Apar frame and load it instead of solving Ampere. We
 implement this because we see a discrepancy between solving Ampere from the
 species restart frame or loading the corresponding last Ampere frame.

---
 gyrokinetic/apps/gk_field.c              |  1 +
 gyrokinetic/apps/gkyl_gyrokinetic.h      |  1 +
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  1 +
 gyrokinetic/apps/gyrokinetic.c           | 60 +++++++++++++++++++++---
 4 files changed, 56 insertions(+), 7 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 8175022d97..0cff93bc3a 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -405,6 +405,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
     f->em_combine_func = gk_field_combine_disabled;
     f->em_copy_func = gk_field_copy_range_disabled;
   }
+  f->calc_init_apar = f->info.calc_init_apar;
 
   f->calc_init_field = !f->info.zero_init_field;
   f->update_field = !f->info.is_static;
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index c00bbbaa98..a68ab9eeed 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -489,6 +489,7 @@ struct gkyl_gyrokinetic_field {
   bool is_static; // =true field does not change in time.
   bool is_apar_static; // =true Apar at initial time is used for all time steps.
   bool zero_init_field; // =true doesn't compute the initial field.
+  bool calc_init_apar; // Whether to calculate the initial Apar from the initial condition of the distribution function.
 
   double polarization_bmag; 
   double kperpSq; // kperp^2 parameter for 1D field equations
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 0417c7016a..abdd062504 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1251,6 +1251,7 @@ struct gk_field {
   bool update_field; // Are we updating the field?.
   bool calc_init_field; // Whether to compute the t=0 field.
   bool is_em; // Whether we solve the EM field equations.
+  bool calc_init_apar; // Whether to initialize A_parallel with Ampere's law solve.
 
   struct gkyl_job_pool *job_pool; // Job pool  
   // arrays for local charge density, global charge density, and global smoothed (in z) charge density
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index a89f01872f..f4e719b18e 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -2873,6 +2873,31 @@ gkyl_gyrokinetic_app_from_file_field(gkyl_gyrokinetic_app *app, const char *fnam
   return rstat;
 }
 
+struct gkyl_app_restart_status
+gkyl_gyrokinetic_app_from_file_em(gkyl_gyrokinetic_app *app, const char *fname_apar, const char *fname_apardot)
+{
+  struct gkyl_app_restart_status rstat;
+
+  rstat = header_from_file(app, fname_apar);
+
+  if (rstat.io_status == GKYL_ARRAY_RIO_SUCCESS) {
+    rstat.io_status =
+      gkyl_comm_array_read(app->comm, &app->grid, &app->local, app->field->apar_host, fname_apar);
+    if (app->use_gpu)
+      gkyl_array_copy(app->field->apar, app->field->apar_host);
+  }
+
+  rstat = header_from_file(app, fname_apardot);
+  if (rstat.io_status == GKYL_ARRAY_RIO_SUCCESS) {
+    rstat.io_status =
+      gkyl_comm_array_read(app->comm, &app->grid, &app->local, app->field->apardot_host, fname_apardot);
+    if (app->use_gpu)
+      gkyl_array_copy(app->field->apardot, app->field->apardot_host);
+  }
+  
+  return rstat;
+}
+
 struct gkyl_app_restart_status 
 gkyl_gyrokinetic_app_from_file_species(gkyl_gyrokinetic_app *app, int sidx,
   const char *fname)
@@ -2931,6 +2956,20 @@ gkyl_gyrokinetic_app_from_frame_field(gkyl_gyrokinetic_app *app, int frame)
   return rstat;
 }
 
+struct gkyl_app_restart_status
+gkyl_gyrokinetic_app_from_frame_em(gkyl_gyrokinetic_app *app, int frame)
+{
+  cstr fileNm_apar = cstr_from_fmt("%s-%s_%d.gkyl", app->name, "apar", frame);
+  cstr fileNm_apardot = cstr_from_fmt("%s-%s_%d.gkyl", app->name, "apardot", frame);
+  struct gkyl_app_restart_status rstat = gkyl_gyrokinetic_app_from_file_em(app, fileNm_apar.str, fileNm_apardot.str);
+  app->field->is_first_energy_write_call = false; // Append to existing diagnostic.
+  app->field->is_first_energy_dot_write_call = false; // Append to existing diagnostic.
+  cstr_drop(&fileNm_apar);
+  cstr_drop(&fileNm_apardot);
+  
+  return rstat;
+}
+
 struct gkyl_app_restart_status
 gkyl_gyrokinetic_app_from_frame_species(gkyl_gyrokinetic_app *app, int sidx, int frame)
 {
@@ -3044,14 +3083,21 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
       gyrokinetic_calc_field(app, rstat.stime, (const struct gkyl_array **) distf, bflux);
 
       if (app->field->is_em) {
-        gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
-        gk_field_calc_apar_ic(app, app->field);
-        for (int i=0; i<app->num_species; ++i) {
-          struct gk_species *gk_s = &app->species[i];
-          gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+        if (app->field->calc_init_apar) {
+          // Compute Apar.
+          gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
+          gk_field_calc_apar_ic(app, app->field);
+          // We also compute Apardot here to output the first frame.
+          for (int i=0; i<app->num_species; ++i) {
+            struct gk_species *gk_s = &app->species[i];
+            gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+          }
+          gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
+        } else {
+          // Load Apar and Apardot from last frame.
+          gkyl_gyrokinetic_app_from_frame_em(app, frame);
         }
-        gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
-      }      
+      }
     }
     else {
       // Read the t=0 field.

From 9ce537c14d5673c4eed63719887e0b2b34bc09e7 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 14:58:48 -0400
Subject: [PATCH 143/181] change the structure of the EM GK solver to avoid
 redundant computation while keeping a correct upwinding. - There are no
 em_star or rhs_star naming anymore. - The base rhs function is either ES as
 usual or a partial RHS computation which include the ES + Apar vol and conf
 surf terms only  (no vpar surf contribution). - This partial RHS is what is
 necessary to compute Apardot with Ohms law since we do not need vpar surf
 term there. - After that we call a new GK rhs updater that will only add
 Apardot volume term and the ES+Apar+Apardot vpar surf term.

---
 gyrokinetic/apps/gk_species.c                 |  48 +-----
 gyrokinetic/apps/gk_species_collisionless.c   |  39 +++--
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  19 +--
 gyrokinetic/apps/gyrokinetic.c                |  19 ++-
 gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c          |   2 +-
 .../creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c |   4 +
 ... => gk_collisionless_flux_surfconf_none.c} |   2 +-
 ..._collisionless_flux_surfconf_return_zero.c |  11 ++
 .../gk_collisionless_flux_surfvpar_none.c     |  11 ++
 ..._collisionless_flux_surfvpar_return_zero.c |  11 ++
 .../gkyl_gk_collisionless_flux_kernels.h      |  12 +-
 gyrokinetic/zero/dg_gyrokinetic.c             |  23 ++-
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         |  25 +--
 gyrokinetic/zero/dg_updater_gyrokinetic.c     |   4 +-
 gyrokinetic/zero/gk_collisionless_flux.c      |   6 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  |   8 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic.h        |   4 +-
 gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h   |  26 +++-
 .../zero/gkyl_dg_updater_gyrokinetic.h        |   4 +-
 gyrokinetic/zero/gkyl_gk_collisionless_flux.h |   4 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 146 +++++++++---------
 21 files changed, 237 insertions(+), 191 deletions(-)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surf_return_zero.c => gk_collisionless_flux_surfconf_none.c} (89%)
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
 create mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index de66da911f..3f8a95d16e 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -162,45 +162,11 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 static void
-gk_species_rhs_star_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_em_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  // Gyroaverage the potential if needed.
-  species->gyroaverage(app, species, app->field->phi_smooth, species->gyro_phi);
-
-  gkyl_array_clear(species->cflrate, 0.0);
-  gkyl_array_clear(rhs, 0.0);
-
   // Collisionless terms.
-  gk_species_collisionless_rhs_star(app, species, &species->collisionless, fin, rhs);
-
-  // Damping term.
-  gk_species_damping_advance(app, species, &species->damping, app->field->phi_smooth, fin,
-    species->lte.f_lte, rhs, species->cflrate);
-
-  // LBO Collisions.
-  gk_species_lbo_rhs(app, species, &species->lbo, fin, rhs);
-
-  // BGK collisions.
-  gk_species_bgk_rhs(app, species, &species->bgk, fin, rhs);
-  
-  // Anomalous diffusion.
-  gk_species_anomalous_diff_rhs(app, species, &species->anom_diff, fin, rhs);
-
-  // Line radiation.
-  gk_species_radiation_rhs(app, species, &species->rad, fin, rhs);
-
-  // Reactions with charged species.
-  gk_species_react_rhs(app, species, &species->react, fin, rhs);
-
-  // Reactions with neutral species.
-  gk_species_react_rhs(app, species, &species->react_neut, fin, rhs);
-
-  // Heating source.
-  gk_species_heating_rhs(app, species, &species->heat_src, fin, rhs);
-
-  // Particle + heat source terms.
-  gk_species_source_rhs(app, species, &species->src, fin, rhs);
+  gk_species_collisionless_rhs_em(app, species, &species->collisionless, fin, rhs);
 }
 
 static double
@@ -1013,9 +979,9 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
   if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
-    gks->rhs_star_func = gk_species_rhs_star_dynamic;
+    gks->rhs_em_func = gk_species_rhs_em_dynamic;
   } else {
-    gks->rhs_star_func = gk_species_rhs_static;
+    gks->rhs_em_func = gk_species_rhs_static;
   }
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
   gks->bflux_update = gk_species_update_bflux_dynamic;
@@ -1053,7 +1019,7 @@ gk_species_init_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
   
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
-  gks->rhs_star_func = gk_species_rhs_static;
+  gks->rhs_em_func = gk_species_rhs_static;
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
   gks->bflux_update = gk_species_rhs_static;
   gks->get_cfl = gk_species_get_cfl_static;  
@@ -1874,10 +1840,10 @@ gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 void
-gk_species_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  species->rhs_star_func(app, species, fin, rhs, bflux_moms);
+  species->rhs_em_func(app, species, fin, rhs, bflux_moms);
 }
 
 void 
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index a90773e655..e5ecc20460 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -24,7 +24,7 @@ gk_species_collisionless_flux_enabled(gkyl_gyrokinetic_app *app, struct gk_speci
 }
 
 static void
-gk_species_collisionless_flux_star_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_collisionless_flux_em_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin)
 {
   // Compute the surface expansion of the phase space flux for ES + Apar contributions.
@@ -57,14 +57,17 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
 }
 
 static void
-gk_species_collisionless_rhs_star_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_collisionless_rhs_em_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
   struct timespec wst = gkyl_wall_clock();
 
-  gkcls->flux_func_star(app, species, gkcls, fin);
+  // It is importnat to clear the flux_surf array since we already pushed the RHS once.
+  gkyl_array_clear(gkcls->flux_surf, 0.0);
 
-  gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_em_star, &species->local, 
+  gkcls->flux_func_em_complete(app, species, gkcls, fin);
+
+  gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_em_complete, &species->local, 
     fin, species->cflrate, rhs);
 
   // AH Note: I'm not sure we need this here.
@@ -125,7 +128,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
-  gkcls->rhs_star_func = gk_species_collisionless_rhs_disabled;
+  gkcls->rhs_em_func = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -169,10 +172,10 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       bctype_conf[GKYL_MAX_CDIM+d] = gks->upper_bc[d].type;
     }
 
-    bool em_star = false;
+    bool complete_em = false;
     gkcls->surf_flux_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
       gks->info.charge, gks->info.mass,
-      gkcls->collisionless_id,  gkcls->no_by, em_star, app->gk_geom, 
+      gkcls->collisionless_id,  gkcls->no_by, complete_em, app->gk_geom, 
       app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
 
     struct gkyl_dg_gyrokinetic_auxfields aux_inp = { .flux_surf = gkcls->flux_surf, 
@@ -180,7 +183,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     // Create solver.
     gkcls->slvr = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
       &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-      gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
+      gkcls->collisionless_id, gkcls->no_by, complete_em, app->gk_geom, gks->vel_map, 
       &aux_inp, app->use_gpu);
 
     gkcls->scale_fac = -1.0; // Not used if scale_factor in input file is not given.
@@ -197,20 +200,21 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
       gkcls->flux_surf_ho = mkarr(false, gkcls->flux_surf->ncomp, gkcls->flux_surf->size);
       gkcls->write_diags_func = gk_species_collisionless_write_diags_enabled;
     }
+
     // Electromagnetic set up.
     if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
       // Set up ES + Apar contributions to flux and solver.
-      em_star = true;
+      complete_em = true;
       gkcls->surf_flux_em_star_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
-        gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, 
+        gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, complete_em, app->gk_geom, 
         app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
-      gkcls->slvr_em_star = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
+      gkcls->slvr_em_complete = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
         &app->local, &gks->local, is_zero_flux, gks->info.charge, gks->info.mass,
-        gkcls->collisionless_id, gkcls->no_by, em_star, app->gk_geom, gks->vel_map, 
+        gkcls->collisionless_id, gkcls->no_by, complete_em, app->gk_geom, gks->vel_map, 
         &aux_inp, app->use_gpu);
       // Methods chosen at runtime.
-      gkcls->flux_func_star = gk_species_collisionless_flux_star_enabled; // ES + Apar.
-      gkcls->rhs_star_func = gk_species_collisionless_rhs_star_enabled; // ES + Apar.
+      gkcls->flux_func_em_complete = gk_species_collisionless_flux_em_enabled;
+      gkcls->rhs_em_func = gk_species_collisionless_rhs_em_enabled;
     }
   }
 }
@@ -226,14 +230,15 @@ void
 gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
+  // gkyl_array_clear(gkcls->flux_surf, 0.0);
   gkcls->rhs_func(app, species, gkcls, fin, rhs);
 }
 
 void
-gk_species_collisionless_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_collisionless_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
-  gkcls->rhs_star_func(app, species, gkcls, fin, rhs);
+  gkcls->rhs_em_func(app, species, gkcls, fin, rhs);
 }
 
 void
@@ -254,7 +259,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
 
     if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
       gkyl_gk_collisionless_flux_release(gkcls->surf_flux_em_star_op);
-      gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_em_star);
+      gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_em_complete);
     }
 
     if (gkcls->write_diagnostics) {
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index abdd062504..565d3fac9a 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -287,12 +287,12 @@ struct gk_collisionless {
       struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
       struct gkyl_gk_collisionless_flux *surf_flux_em_star_op; // EM collisionless fluxes without Apardot contribution.
       gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.
-      gkyl_dg_updater_gyrokinetic *slvr_em_star; // EM without Apardot contribution.
+      gkyl_dg_updater_gyrokinetic *slvr_em_complete; // EM without Apardot contribution.
 
       // Methods chosen at runtime.
       void (*flux_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
         struct gk_collisionless *gkcls, const struct gkyl_array *fin);
-      void (*flux_func_star)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+      void (*flux_func_em_complete)(gkyl_gyrokinetic_app *app, struct gk_species *species,
         struct gk_collisionless *gkcls, const struct gkyl_array *fin);
     };
     // Neutral (Vlasov) species ............................................ //
@@ -312,7 +312,7 @@ struct gk_collisionless {
   };
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
-  void (*rhs_star_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+  void (*rhs_em_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
   void (*fdot_scaling)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, struct gkyl_array *rhs, struct gkyl_array *cflrate, struct gkyl_range *rng);
@@ -1066,7 +1066,7 @@ struct gk_species {
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
   // Pointer to RHS star function (ES + [Apar]).
-  void (*rhs_star_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*rhs_em_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
   void (*bflux_update)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
@@ -1846,7 +1846,7 @@ void gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *
  * @param fin Input distribution function.
  * @param rhs collisionless contribution to df/dt.
  */
-void gk_species_collisionless_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+void gk_species_collisionless_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *gks,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
@@ -3092,7 +3092,8 @@ void gk_species_apply_ic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 void gk_species_apply_ic_cross(gkyl_gyrokinetic_app *app, struct gk_species *species, double t0);
 
 /**
- * Compute RHS from species distribution function
+ * Compute RHS from species distribution function. 
+ * In EM simulation, this does not include contribution from Apardot and vpar surface flux.
  *
  * @param app gyrokinetic app object.
  * @param species Pointer to species.
@@ -3104,15 +3105,15 @@ void gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
- * Compute RHS star (ES + Apar) from species distribution function.
- *
+ * Complete the EM RHS by adding the contribution from Apardot and vpar surface flux.
+ * 
  * @param app gyrokinetic app object.
  * @param species Pointer to species.
  * @param fin Input distribution function.
  * @param rhs On output, the RHS from the species object.
  * @param bflux_moms Output boundary flux moments.
  */
-void gk_species_rhs_star(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index f4e719b18e..ed5e160a72 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -915,7 +915,7 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
         gk_field_calc_apar_ic(app, app->field);
         for (int i=0; i<app->num_species; ++i) {
           struct gk_species *gk_s = &app->species[i];
-          gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+          gk_species_rhs_em(app, gk_s, distf[i], distfdot[i], bflux[i]);
         }
         gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
       }
@@ -1928,23 +1928,26 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
     gk_neut_species_scaling_cross_moms(app, gk_ns, &gk_ns->sca, fin, fin_neut);
   }
 
-  // Compute Apardot (solves Ohm's law using the previously built df/dt^*).
-  // Compute df/dt^* (ES + Apar)
+  // Build the GK RHS in two steps.
+  // 1. Configuration space surface fluxes and ES (+ Apar) volume terms. 
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
-    gk_species_rhs_star(app, gk_s, fin[i], fout[i], bflux_out[i]);
-    gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    // I don't think this is necessary.
+    // gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
   }
+  // Compute Apardot (solves Ohm's law using the current state of the RHS).
   gk_field_em_rhs(app, app->field, fin, fout);
   // Update aparout.
   gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
 
-  // Compute the total RHS.
+  // 2. Finish building the GK RHS (vpar surface flux and Apardot volume term).
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
-    gk_species_rhs(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_rhs_em(app, gk_s, fin[i], fout[i], bflux_out[i]);
     gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
   }
+
   for (int i=0; i<app->num_neut_species; ++i) {
     struct gk_neut_species *gk_ns = &app->neut_species[i];
     double dt1 = gk_neut_species_rhs(app, gk_ns, fin_neut[i], fout_neut[i], bflux_out_neut[i]);
@@ -3090,7 +3093,7 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
           // We also compute Apardot here to output the first frame.
           for (int i=0; i<app->num_species; ++i) {
             struct gk_species *gk_s = &app->species[i];
-            gk_species_rhs_star(app, gk_s, distf[i], distfdot[i], bflux[i]);
+            gk_species_rhs_em(app, gk_s, distf[i], distfdot[i], bflux[i]);
           }
           gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
         } else {
diff --git a/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c b/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c
index f77f672128..9053beaf62 100644
--- a/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_kbm_3x2v_p1.c
@@ -138,7 +138,7 @@ void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *c
   double x = xc[0], y = xc[1], z = xc[2];
   fout[0] = 0.0;
   fout[1] = 0.0;
-  fout[2] = app->B*app->R/(app->R + x);
+  fout[2] = app->B*app->R/(app->R + x); // this may be wrong!
 }
 
 void mapc2p_vel_elc(double t, const double *vc, double* GKYL_RESTRICT vp, void *ctx)
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index 6e22d63067..0906b72ec2 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -819,6 +819,10 @@ main(int argc, char **argv)
       .restart_frame = app_args.restart_frame,
       .num_steps = app_args.num_steps,
     },
+    .print_verbosity = {
+      .enabled = true,
+      .frequency = 0.01,
+    }
   };
 
   gkyl_gyrokinetic_run_simulation(&run_inp);
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
similarity index 89%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
index abf19ca158..341b6e2c2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surf_return_zero.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
+GKYL_CU_DH double gk_collisionless_flux_surfconf_none(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c
new file mode 100644
index 0000000000..b8e1844650
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c
@@ -0,0 +1,11 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_surfconf_return_zero(
+    const double *w, const double *dxv,
+    const double *vmap, const double *vmapSq, const double q_, const double m_,
+    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
+    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
+    const double *phi, const double *apar, const double *apardot, 
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  return 0.0; 
+}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
new file mode 100644
index 0000000000..8be40ca284
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
@@ -0,0 +1,11 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_none(
+    const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+    const double *bmag, const double *phi, const double *apar, const double *apardot, 
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  return 0.0; 
+}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
new file mode 100644
index 0000000000..6ebfb94492
--- /dev/null
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
@@ -0,0 +1,11 @@
+#include <gkyl_gk_collisionless_flux_kernels.h> 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
+    const double *w, const double *dxv,
+    const double *vmap_prime_l, const double *vmap_prime_r,
+    const double *vmap, const double *vmapSq, const double q_, const double m_, 
+    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+    const double *bmag, const double *phi, const double *apar, const double *apardot, 
+    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
+{ 
+  return 0.0; 
+}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index c908ee160b..7f6ddefc61 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -1159,12 +1159,20 @@ GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
   const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_surf_return_zero(
+GKYL_CU_DH double gk_collisionless_flux_surfconf_none(
   const double *w, const double *dxv,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
+  const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR, 
   double* GKYL_RESTRICT flux_surf);
 
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_none(
+  const double *w, const double *dxv,
+  const double *vmap_prime_l, const double *vmap_prime_r,
+  const double *vmap, const double *vmapSq, const double q_, const double m_, 
+  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
+  const double *bmag, const double *phi, const double *apar, const double *apardot, 
+  const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf);
+
 EXTERN_C_END
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 3ffffef5dd..141e9357db 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -48,14 +48,14 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool complete_em,
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, bool use_gpu)
 {
 
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_dg_gyrokinetic_cu_dev_new(cbasis, pbasis, conf_range, phase_range,
-      charge, mass, collless_type, no_by, em_star, gk_geom, vel_map);
+      charge, mass, collless_type, no_by, complete_em, gk_geom, vel_map);
 #endif
 
   struct dg_gyrokinetic *gyrokinetic = gkyl_malloc(sizeof(struct dg_gyrokinetic));
@@ -119,13 +119,20 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
 
   // Setup electromagnetic terms if needed.
   bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
-  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_return_zero;
-  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_return_zero;
+  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
+  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
   if (is_em) {
-    gyrokinetic->vol_add_apar_kernel = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
-    // Apardot is removed if we want to compute RHS star (ES + Apardot).
-    gyrokinetic->vol_add_apardot_kernel = em_star ? 
-      dg_gyrokinetic_add_apardot_vol_return_zero : CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+    if (complete_em) {
+      // We complete with Apardot contribution to get the full GK RHS.
+      gyrokinetic->vol_es_kernel = dg_gyrokinetic_vol_none;
+      gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
+      gyrokinetic->vol_add_apardot_kernel = CK(vol_add_apardot_kernels,cdim,vdim,poly_order);
+    } else {
+      // We build for Ohm's law RHS (no Apardot contribution).
+      gyrokinetic->vol_es_kernel = gyrokinetic->vol_es_kernel; // no change to ES kernel
+      gyrokinetic->vol_add_apar_kernel = CK(vol_add_apar_kernels,cdim,vdim,poly_order);
+      gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
+    }
   }
 
   gyrokinetic->surf[0] = CK(surf_x_kernels,cdim,vdim,poly_order);
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 13857c3658..9ef0548f9f 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -39,7 +39,7 @@ gkyl_gyrokinetic_set_auxfields_cu(const struct gkyl_dg_eqn *eqn, struct gkyl_dg_
 __global__ static void 
 dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_basis_type b_type,
   int cv_index, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type collless_type, 
-  bool no_by, bool em_star)
+  bool no_by, bool complete_em)
 {
   gyrokinetic->auxfields.flux_surf = 0; 
   gyrokinetic->auxfields.phi = 0; 
@@ -96,13 +96,20 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
 
   // Setup electromagnetic terms if needed.
   bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
-  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_return_zero;
-  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_return_zero;
+  gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
+  gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
   if (is_em) {
-    gyrokinetic->vol_add_apar_kernel = vol_add_apar_kernels[cv_index].kernels[poly_order];
-    // Apardot is removed if we want to compute RHS star (ES + Apardot).
-    gyrokinetic->vol_add_apardot_kernel = em_star ?
-      dg_gyrokinetic_add_apardot_vol_return_zero : vol_add_apardot_kernels[cv_index].kernels[poly_order];
+    if (complete_em) {
+      // We build Ohm's law RHS (no Apardot contribution).
+      gyrokinetic->vol_es_kernel = gyrokinetic->vol_es_kernel; // no change to ES kernel
+      gyrokinetic->vol_add_apar_kernel = vol_add_apar_kernels[cv_index].kernels[poly_order];
+      gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
+    } else {
+      // We complete the Ohm's law RHS with Apardot contribution to get the full GK RHS.
+      gyrokinetic->vol_es_kernel = dg_gyrokinetic_vol_none;
+      gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
+      gyrokinetic->vol_add_apardot_kernel = vol_add_apardot_kernels[cv_index].kernels[poly_order];
+    }
   }
 
   gyrokinetic->surf[0] = surf_x_kernels[cv_index].kernels[poly_order];
@@ -125,7 +132,7 @@ struct gkyl_dg_eqn*
 gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis,
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
+  const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map)
 {
   struct dg_gyrokinetic *gyrokinetic = (struct dg_gyrokinetic*) gkyl_malloc(sizeof(*gyrokinetic));
 
@@ -159,7 +166,7 @@ gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gky
   gkyl_cu_memcpy(gyrokinetic_cu, gyrokinetic, sizeof(struct dg_gyrokinetic), GKYL_CU_MEMCPY_H2D);
 
   dg_gyrokinetic_set_cu_dev_ptrs<<<1,1>>>(gyrokinetic_cu, cbasis->b_type, cv_index[cdim].vdim[vdim],
-    cdim, vdim, poly_order, collless_type, no_by, em_star);
+    cdim, vdim, poly_order, collless_type, no_by, complete_em);
 
   // set parent on_dev pointer
   gyrokinetic->eqn.on_dev = &gyrokinetic_cu->eqn;
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 2965355c82..9661bd05ca 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -22,7 +22,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, 
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom, 
   const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu)
 {
   struct gkyl_dg_updater_gyrokinetic *up = gkyl_malloc(sizeof(struct gkyl_dg_updater_gyrokinetic));
@@ -30,7 +30,7 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
   up->use_gpu = use_gpu;
 
   up->eqn_gyrokinetic = gkyl_dg_gyrokinetic_new(cbasis, pbasis, conf_range, phase_range, 
-    charge, mass, collless_type, no_by, em_star, gk_geom, vel_map, up->use_gpu);
+    charge, mass, collless_type, no_by, complete_em, gk_geom, vel_map, up->use_gpu);
 
   struct gkyl_dg_gyrokinetic_auxfields *gk_inp = aux_inp;
   gkyl_gyrokinetic_set_auxfields(up->eqn_gyrokinetic, *gk_inp);
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index 5342fed2a7..af46dd313c 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -15,14 +15,14 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass,
   enum gkyl_gk_collisionless_type type,
-  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
+  const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu)
 {
 #ifdef GKYL_HAVE_CUDA
   if (use_gpu)
     return gkyl_gk_collisionless_flux_cu_dev_new(phase_grid, conf_basis, phase_basis,
-      charge, mass, type, no_by, em_star, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
+      charge, mass, type, no_by, complete_em, gk_geom, dg_geom, gk_dg_geom, vel_map, bctype_conf);
 #endif     
 
   gkyl_gk_collisionless_flux *up = gkyl_malloc(sizeof(gkyl_gk_collisionless_flux));
@@ -45,7 +45,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
 
   // Choose appropriate kernels.
   int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
-  em = em_star ? 2 : em; // If em_star is true, use EM kernels without Apardot contribution.
+  em = complete_em ? 2 : em; // If complete_em is true, use EM kernels without Apardot contribution.
   if (no_by) {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 06494d9d4b..1ed5946f85 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -206,11 +206,11 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
   bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, 
-  bool no_by, bool em_star,
+  bool no_by, bool complete_em,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
   // Choose appropriate kernels.
-  em = em_star ? 2 : em; // If em_star is true, use EM kernels without Apardot contribution.
+  em = complete_em ? 2 : em; // If complete_em is true, use EM kernels without Apardot contribution.
   if (no_by) {
     for (int d=0; d<cdim; ++d) {
       // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
@@ -239,7 +239,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass,
   enum gkyl_gk_collisionless_type type, 
-  const bool no_by, const bool em_star,
+  const bool no_by, const bool complete_em,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
@@ -279,7 +279,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
   struct gkyl_gk_collisionless_flux *up_cu = (struct gkyl_gk_collisionless_flux*) gkyl_cu_malloc(sizeof(*up_cu));
   gkyl_cu_memcpy(up_cu, up, sizeof(gkyl_gk_collisionless_flux), GKYL_CU_MEMCPY_H2D);
 
-  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, no_by, em_star, bctype_conf_dev);
+  gk_collisionless_flux_set_cu_dev_ptrs<<<1,1>>>(up_cu, em, cdim, vdim, poly_order, type, no_by, complete_em, bctype_conf_dev);
 
   gkyl_cu_free(bctype_conf_dev);
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
index df3f339de3..b230a71330 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic.h
@@ -28,7 +28,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
  * @param mass Species mass
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param em_star Whether to compute RHS star (i.e. ES + Apardot) RHS for electromagnetic simulations.
+ * @param complete_em Whether to compute RHS star (i.e. ES + Apardot) RHS for electromagnetic simulations.
  * @param gk_geom Geometry struct
  * @param vel_map Velocity space mapping object.
  * @param use_gpu Boolean to determine if gyrokinetic equation object is on device
@@ -37,7 +37,7 @@ struct gkyl_dg_gyrokinetic_auxfields {
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, 
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, const struct gk_geometry *gk_geom,
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom,
   const struct gkyl_velocity_map *vel_map, bool use_gpu);
 
 
diff --git a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
index 39ceb764fa..af3131daec 100644
--- a/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
+++ b/gyrokinetic/zero/gkyl_dg_gyrokinetic_priv.h
@@ -107,7 +107,7 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
   const double *bioverJB = (const double*) gkyl_array_cfetch(gyrokinetic->gk_geom->geo_int.bioverJB, cidx);
   
   // Electrostatic contribution to volume term.
-  cfl = gyrokinetic->vol_es_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
+  cfl += gyrokinetic->vol_es_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
     bmag, phi, dualcurlbhatoverB, rtg33inv, bioverJB, qIn, qRhsOut);
   // Add Apar contribution to volume term if needed.
   cfl += gyrokinetic->vol_add_apar_kernel(xc, dx, vm, vm_sq, gyrokinetic->charge, gyrokinetic->mass, 
@@ -118,19 +118,31 @@ kernel_dg_gyrokinetic_vol(const struct gkyl_dg_eqn *eqn, const double* xc, const
   return cfl;
 }
 
-// To turn off EM effects:
+// To turn off terms (used in EM).
+
+GKYL_CU_DH 
+static double 
+dg_gyrokinetic_vol_none(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *phi,
+    const double *dualcurlbhatoverB, const double *rtg33inv, const double *bioverJB,
+    const double *fin, double* GKYL_RESTRICT out)
+{ 
+  return 0.; 
+}
+
 GKYL_CU_DH 
 static double 
-dg_gyrokinetic_add_apar_vol_return_zero(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
-    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, const double *dualcurlbhatoverB, const double *bioverJB,
-    const double *b_i, const double *phi, const double *apar, const double *fin, double* GKYL_RESTRICT out) 
+dg_gyrokinetic_add_apar_vol_none(const double *w, const double *dxv, const double *vmap, const double *vmapSq,
+    const double q_, const double m_, const double *bmag, const double *jacobtot_inv, 
+    const double *dualcurlbhatoverB, const double *bioverJB, const double *b_i, const double *phi, 
+    const double *apar, const double *fin, double* GKYL_RESTRICT out) 
 { 
   return 0.; 
 }
 
 GKYL_CU_DH 
 static double 
-dg_gyrokinetic_add_apardot_vol_return_zero(const double *vmap, const double q_, const double m_,
+dg_gyrokinetic_add_apardot_vol_none(const double *vmap, const double q_, const double m_,
             const double *apardot, const double *fin, double* GKYL_RESTRICT out)
 { 
   return 0.; 
@@ -390,7 +402,7 @@ boundary_diag(const struct gkyl_dg_eqn *eqn,
 struct gkyl_dg_eqn* gkyl_dg_gyrokinetic_cu_dev_new(const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range, 
   const double charge, const double mass, enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
+  const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map);
 
 /**
  * CUDA device function to set the auxiliary fields (e.g. geometry & EM fields)
diff --git a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
index 9e3cd36dec..d2d454ba23 100644
--- a/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
+++ b/gyrokinetic/zero/gkyl_dg_updater_gyrokinetic.h
@@ -30,7 +30,7 @@ struct gkyl_dg_updater_gyrokinetic_tm {
  * @param mass Species mass
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param em_star Whether it computes (ES + [Apar]) or [ES + [Apar + Apardot]).
+ * @param complete_em Whether it is meant to complete the RHS after partial EM update.
  * @param gk_geom Geometry struct 
  * @param vel_map Velocity space mapping object.
  * @param aux_inp Void pointer to auxiliary fields. Void to be flexible to different auxfields structs
@@ -41,7 +41,7 @@ gkyl_dg_updater_gyrokinetic* gkyl_dg_updater_gyrokinetic_new(const struct gkyl_r
   const struct gkyl_basis *cbasis, const struct gkyl_basis *pbasis, 
   const struct gkyl_range *conf_range, const struct gkyl_range *phase_range,
   const bool *is_zero_flux_bc, double charge, double mass,
-  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool em_star, 
+  enum gkyl_gk_collisionless_type collless_type, const bool no_by, const bool complete_em, 
   const struct gk_geometry *gk_geom, const struct gkyl_velocity_map *vel_map, void *aux_inp, bool use_gpu);
 
 /**
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
index 30ae5d541c..445433b980 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux.h
@@ -25,7 +25,7 @@ typedef struct gkyl_gk_collisionless_flux gkyl_gk_collisionless_flux;
  * @param mass Species mass
  * @param collless_type Type of collisionless terms.
  * @param no_by Whether to neglect the toroidal field (set b_y=0).
- * @param em_star Whether to compute fstar for Ohm's law.
+ * @param complete_em Whether it is meant to complete the RHS after partial EM update.
  * @param gk_geom Gyrokinetic geometry object.
  * @param gk_dg_geom DG geometry object.
  * @param vel_map Velocity space mapping object.
@@ -38,7 +38,7 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   const double charge, const double mass,
   enum gkyl_gk_collisionless_type collless_type,
-  const bool no_by, const bool em_star, const struct gk_geometry *gk_geom, 
+  const bool no_by, const bool complete_em, const struct gk_geometry *gk_geom, 
   const struct gkyl_dg_geom *dg_geom, const struct gkyl_gk_dg_geom *gk_dg_geom, 
   const struct gkyl_velocity_map *vel_map, const enum gkyl_gyrokinetic_bc_type *bctype_conf, bool use_gpu);
 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 07e73a6594..8eaa13efbf 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -86,10 +86,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -115,10 +115,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -146,8 +146,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -175,8 +175,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -205,7 +205,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -234,7 +234,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -252,18 +252,18 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 3
     },
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -292,10 +292,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -321,10 +321,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list= {
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -352,8 +352,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -381,8 +381,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -411,7 +411,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -440,7 +440,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -470,10 +470,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -499,10 +499,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -530,8 +530,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -559,8 +559,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -589,7 +589,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -618,7 +618,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -636,18 +636,18 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 3
     },
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
+      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
+      { NULL, gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+      { NULL, gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
     },
   }
 };
@@ -676,10 +676,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -705,10 +705,10 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
   },
   {
     .kernels_list = {
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -736,8 +736,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -765,8 +765,8 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
     .kernels_list = {
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -795,7 +795,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -824,7 +824,7 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
       { NULL, NULL, NULL }, // 0
       { NULL, NULL, NULL }, // 1
       { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
+      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
     },
   }
 };
@@ -956,7 +956,7 @@ struct gkyl_gk_collisionless_flux*
 gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid, 
   const struct gkyl_basis *conf_basis, const struct gkyl_basis *phase_basis, 
   double charge, double mass,
-  enum gkyl_gk_collisionless_type type, const bool no_by, const bool em_star,
+  enum gkyl_gk_collisionless_type type, const bool no_by, const bool complete_em,
   const struct gk_geometry *gk_geom, const struct gkyl_dg_geom *dg_geom, 
   const struct gkyl_gk_dg_geom *gk_dg_geom, const struct gkyl_velocity_map *vel_map,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf);

From 445820ca820baf5cb081d8d3a7bab1b5c9a1ef9d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 15:31:42 -0400
Subject: [PATCH 144/181] additional optimization of EM: the two hyper DG
 updaters defined in EM case are now split, one for conf space surface flux,
 the other for vpar surface flux. We refactor the em specialized RHS function
 to `em_complete` instead of only `em` to be more specific. Works fine on CPU,
 test on GPU soon. Note: the single CPU alfven 3x2v went from 30s to 18s with
 the last commit, now it is closer to 15s.

---
 gyrokinetic/apps/gk_species.c               | 17 +++++++++--------
 gyrokinetic/apps/gk_species_collisionless.c | 13 +++++--------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h    |  8 ++++----
 gyrokinetic/apps/gyrokinetic.c              |  8 ++++----
 gyrokinetic/zero/dg_updater_gyrokinetic.c   | 19 +++++++++++++++++--
 5 files changed, 39 insertions(+), 26 deletions(-)

diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 3f8a95d16e..a8057db600 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -162,11 +162,11 @@ gk_species_rhs_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 static void
-gk_species_rhs_em_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_em_complete_dynamic(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
   // Collisionless terms.
-  gk_species_collisionless_rhs_em(app, species, &species->collisionless, fin, rhs);
+  gk_species_collisionless_rhs_em_complete(app, species, &species->collisionless, fin, rhs);
 }
 
 static double
@@ -978,10 +978,11 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
 
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
-  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
-    gks->rhs_em_func = gk_species_rhs_em_dynamic;
+  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) 
+   || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
+    gks->rhs_em_complete_func = gk_species_rhs_em_complete_dynamic;
   } else {
-    gks->rhs_em_func = gk_species_rhs_static;
+    gks->rhs_em_complete_func = gk_species_rhs_static;
   }
   gks->rhs_implicit_func = gk_species_rhs_implicit_dynamic;
   gks->bflux_update = gk_species_update_bflux_dynamic;
@@ -1019,7 +1020,7 @@ gk_species_init_static(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *
   
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_static;
-  gks->rhs_em_func = gk_species_rhs_static;
+  gks->rhs_em_complete_func = gk_species_rhs_static;
   gks->rhs_implicit_func = gk_species_rhs_implicit_static;
   gks->bflux_update = gk_species_rhs_static;
   gks->get_cfl = gk_species_get_cfl_static;  
@@ -1840,10 +1841,10 @@ gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
 }
 
 void
-gk_species_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_rhs_em_complete(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms)
 {
-  species->rhs_em_func(app, species, fin, rhs, bflux_moms);
+  species->rhs_em_complete_func(app, species, fin, rhs, bflux_moms);
 }
 
 void 
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index e5ecc20460..5202d5499d 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -57,14 +57,11 @@ gk_species_collisionless_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_specie
 }
 
 static void
-gk_species_collisionless_rhs_em_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_collisionless_rhs_em_complete_enabled(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
   struct timespec wst = gkyl_wall_clock();
 
-  // It is importnat to clear the flux_surf array since we already pushed the RHS once.
-  gkyl_array_clear(gkcls->flux_surf, 0.0);
-
   gkcls->flux_func_em_complete(app, species, gkcls, fin);
 
   gkyl_dg_updater_gyrokinetic_advance(gkcls->slvr_em_complete, &species->local, 
@@ -128,7 +125,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
   gkcls->write_diags_func = gk_species_collisionless_write_diags_disabled;
   gkcls->flux_func = gk_species_collisionless_flux_disabled;
   gkcls->rhs_func = gk_species_collisionless_rhs_disabled;
-  gkcls->rhs_em_func = gk_species_collisionless_rhs_disabled;
+  gkcls->rhs_em_complete_func = gk_species_collisionless_rhs_disabled;
 
   if (gkcls->collisionless_id) {
 
@@ -214,7 +211,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
         &aux_inp, app->use_gpu);
       // Methods chosen at runtime.
       gkcls->flux_func_em_complete = gk_species_collisionless_flux_em_enabled;
-      gkcls->rhs_em_func = gk_species_collisionless_rhs_em_enabled;
+      gkcls->rhs_em_complete_func = gk_species_collisionless_rhs_em_complete_enabled;
     }
   }
 }
@@ -235,10 +232,10 @@ gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *speci
 }
 
 void
-gk_species_collisionless_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
+gk_species_collisionless_rhs_em_complete(gkyl_gyrokinetic_app *app, struct gk_species *species,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs)
 {
-  gkcls->rhs_em_func(app, species, gkcls, fin, rhs);
+  gkcls->rhs_em_complete_func(app, species, gkcls, fin, rhs);
 }
 
 void
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 565d3fac9a..36d16ed49b 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -312,7 +312,7 @@ struct gk_collisionless {
   };
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
-  void (*rhs_em_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+  void (*rhs_em_complete_func)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
   void (*fdot_scaling)(gkyl_gyrokinetic_app *app, struct gk_species *gks,
     struct gk_collisionless *gkcls, struct gkyl_array *rhs, struct gkyl_array *cflrate, struct gkyl_range *rng);
@@ -1066,7 +1066,7 @@ struct gk_species {
   void (*rhs_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
   // Pointer to RHS star function (ES + [Apar]).
-  void (*rhs_em_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
+  void (*rhs_em_complete_func)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
   void (*bflux_update)(gkyl_gyrokinetic_app *app, struct gk_species *species,
     const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
@@ -1846,7 +1846,7 @@ void gk_species_collisionless_rhs(gkyl_gyrokinetic_app *app, struct gk_species *
  * @param fin Input distribution function.
  * @param rhs collisionless contribution to df/dt.
  */
-void gk_species_collisionless_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *gks,
+void gk_species_collisionless_rhs_em_complete(gkyl_gyrokinetic_app *app, struct gk_species *gks,
   struct gk_collisionless *gkcls, const struct gkyl_array *fin, struct gkyl_array *rhs);
 
 /**
@@ -3113,7 +3113,7 @@ void gk_species_rhs(gkyl_gyrokinetic_app *app, struct gk_species *species,
  * @param rhs On output, the RHS from the species object.
  * @param bflux_moms Output boundary flux moments.
  */
-void gk_species_rhs_em(gkyl_gyrokinetic_app *app, struct gk_species *species,
+void gk_species_rhs_em_complete(gkyl_gyrokinetic_app *app, struct gk_species *species,
   const struct gkyl_array *fin, struct gkyl_array *rhs, struct gkyl_array **bflux_moms);
 
 /**
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index ed5e160a72..c527ec97be 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -915,7 +915,7 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
         gk_field_calc_apar_ic(app, app->field);
         for (int i=0; i<app->num_species; ++i) {
           struct gk_species *gk_s = &app->species[i];
-          gk_species_rhs_em(app, gk_s, distf[i], distfdot[i], bflux[i]);
+          gk_species_rhs_em_complete(app, gk_s, distf[i], distfdot[i], bflux[i]);
         }
         gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
       }
@@ -1941,10 +1941,10 @@ gyrokinetic_rhs(gkyl_gyrokinetic_app* app, double tcurr, double dt,
   // Update aparout.
   gk_field_em_copy_range(app->field, aparout, app->field->apardot, &app->local_ext);
 
-  // 2. Finish building the GK RHS (vpar surface flux and Apardot volume term).
+  // 2. Finish building the EM GK RHS (vpar surface flux and Apardot volume term).
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *gk_s = &app->species[i];
-    gk_species_rhs_em(app, gk_s, fin[i], fout[i], bflux_out[i]);
+    gk_species_rhs_em_complete(app, gk_s, fin[i], fout[i], bflux_out[i]);
     gk_species_update_bflux(app, gk_s, fin[i], fout[i], bflux_out[i]);
   }
 
@@ -3093,7 +3093,7 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
           // We also compute Apardot here to output the first frame.
           for (int i=0; i<app->num_species; ++i) {
             struct gk_species *gk_s = &app->species[i];
-            gk_species_rhs_em(app, gk_s, distf[i], distfdot[i], bflux[i]);
+            gk_species_rhs_em_complete(app, gk_s, distf[i], distfdot[i], bflux[i]);
           }
           gk_field_em_rhs(app, app->field, (const struct gkyl_array **) distf, distfdot);
         } else {
diff --git a/gyrokinetic/zero/dg_updater_gyrokinetic.c b/gyrokinetic/zero/dg_updater_gyrokinetic.c
index 9661bd05ca..8cdf75a9e0 100644
--- a/gyrokinetic/zero/dg_updater_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_updater_gyrokinetic.c
@@ -37,9 +37,24 @@ gkyl_dg_updater_gyrokinetic_new(const struct gkyl_rect_grid *grid,
 
   int cdim = cbasis->ndim, pdim = pbasis->ndim;
   int vdim = pdim-cdim;
+
   int up_dirs[GKYL_MAX_DIM] = {0};
-  int num_up_dirs = cdim+1;
-  for (int d=0; d<num_up_dirs; ++d) up_dirs[d] = d;
+  int num_up_dirs;
+  if (collless_type == GKYL_GK_COLLISIONLESS_ES) {
+    // For ES, we always update all surface fluxes.
+    num_up_dirs = cdim+1;
+    for (int d=0; d<num_up_dirs; ++d) up_dirs[d] = d;
+  } else {
+    // For EM, we split the conf. space and vpar surface fluxes for the partial RHS computation.
+    if (complete_em) {
+      num_up_dirs = 1;
+      up_dirs[0] = cdim; // Only surface flux in vpar direction.
+
+    } else {
+      num_up_dirs = cdim; // Only surface fluxes in configuration space.
+      for (int d=0; d<num_up_dirs; ++d) up_dirs[d] = d;
+    }
+  }
 
   int zero_flux_flags[2*GKYL_MAX_DIM] = {0};
   for (int d=0; d<cdim; ++d) {

From 7e43419fe9b9bb9190a3ad5b2abeacff4b298419 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 13:49:02 -0700
Subject: [PATCH 145/181] logic error in the GPU code, something is still wrong
 in the GPU code since commit 9ce537c14d5673c4eed63719887e0b2b34bc09e7

---
 gyrokinetic/zero/dg_gyrokinetic_cu.cu | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 9ef0548f9f..7da89ba3a0 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -100,15 +100,15 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
   if (is_em) {
     if (complete_em) {
-      // We build Ohm's law RHS (no Apardot contribution).
-      gyrokinetic->vol_es_kernel = gyrokinetic->vol_es_kernel; // no change to ES kernel
-      gyrokinetic->vol_add_apar_kernel = vol_add_apar_kernels[cv_index].kernels[poly_order];
-      gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
-    } else {
       // We complete the Ohm's law RHS with Apardot contribution to get the full GK RHS.
       gyrokinetic->vol_es_kernel = dg_gyrokinetic_vol_none;
       gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
       gyrokinetic->vol_add_apardot_kernel = vol_add_apardot_kernels[cv_index].kernels[poly_order];
+    } else {
+      // We build Ohm's law RHS (no Apardot contribution).
+      gyrokinetic->vol_es_kernel = gyrokinetic->vol_es_kernel; // no change to ES kernel
+      gyrokinetic->vol_add_apar_kernel = vol_add_apar_kernels[cv_index].kernels[poly_order];
+      gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
     }
   }
 

From ec00993d1be0d73ac874823eb2ee5e9fa7616596 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 14:03:20 -0700
Subject: [PATCH 146/181] fix a boolean that should have been an int. This
 error was present since at least two months :o there. The GPU helical turb
 restarted nicely and we see a gain of speed from ~2.2 steps/s to ~2.8
 steps/s. The Hemlhotlz solver is the next beast we have to optimize. the
 commit related to the weird boolean error is this:
 https://github.com/ammarhakim/gkeyll/blame/a6c6bbffaa63f053d3cf218e2b1676c903d9a5a3/gyrokinetic/zero/gk_collisionless_flux_cu.cu#:~:text=2%20months%20ago-,finish%20GPU%20implementation%20of%20full%20upwind%20em%20scheme.%20Tested%20in%20all%20alf%E2%80%A6,-212

---
 gyrokinetic/zero/gk_collisionless_flux_cu.cu | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index 1ed5946f85..e21e34ee05 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -205,7 +205,7 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
 // Doing function pointer stuff in here avoids troublesome cudaMemcpyFromSymbol
 __global__ static void 
 gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up, 
-  bool em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, 
+  int em, int cdim, int vdim, int poly_order, enum gkyl_gk_collisionless_type type, 
   bool no_by, bool complete_em,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {

From 08fafab13d5b282fc4197223bb362e9fdb4c6a63 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 23 Apr 2026 14:10:29 -0700
Subject: [PATCH 147/181] update the helical sol regression test with the fixed
 geometry. The geometry used in Mandell et al. 2020 does not pass the geometry
 right hand check.

---
 .../creg/rt_gk_em_helical_sol_3x2v_p1.c       | 143 ++++++++++++------
 1 file changed, 100 insertions(+), 43 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
index 884967d33b..805f710e08 100644
--- a/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_helical_sol_3x2v_p1.c
@@ -18,12 +18,9 @@ struct gk_app_ctx {
   
   // Geometry and magnetic field.
   double B_axis;
-  double R_axis;
-  double a_center;
-  double R_center;
-  double B_center;
-  double Lp; // Poloidal length (used to get the field line pitch).
-  double Lt; // Toroidal length (used to get the field line pitch).
+  double R0;
+  double Rc;
+  double Bv0;
 
   // Plasma parameters.
   double me; double qe;
@@ -159,14 +156,66 @@ double driftSpeed(const double * GKYL_RESTRICT xn, void *ctx){
   }
 }
 
-// Magnetic field strength.
-double bmag(const double *xc, void *ctx)
+// Radial coordinate mapping.
+double Rx(const double *xc, void *ctx)
+{
+  return xc[0];
+}
+
+// Toroidal magnetic field.
+double Bphi(const double *xc, void *ctx)
 {
   double x = xc[0];
   struct gk_app_ctx *app = ctx;
   double B_axis = app->B_axis;
-  double R_axis = app->R_axis;
-  return B_axis * R_axis/x;
+  double R0 = app->R0;
+  double R = Rx(xc, ctx);
+  return B_axis*R0/R;
+}
+
+// Vertical magnetic field.
+double Bvert(const double *xc, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double Bv0 = app->Bv0;
+  return Bv0;
+}
+
+// Magnetic field magnitude.
+double bmag(const double *xc, void *ctx)
+{
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  return sqrt(pow(Bt,2) + pow(Bv,2));
+}
+
+// Field line pitch.
+double thetax(const double *xc, void *ctx)
+{
+  return asin(Bvert(xc, ctx)/bmag(xc, ctx));
+}
+
+// Parallel coordinate mapping.
+double Zx(const double *xc, void *ctx)
+{
+  double theta = thetax(xc, ctx);
+  return xc[2]*sin(theta);
+}
+
+double phix(const double *xc, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+  struct gk_app_ctx *app = ctx;
+  double Rc = app->Rc;
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+
+  // double theta = asin(Lp/Lt);
+  // return (y/sin(theta) + z*cos(theta))/Rc; // Original Shi mapping.
+
+  double theta = thetax(xc, ctx);
+  return (y/sin(theta) + z*cos(theta))/x;
+  // return y/Rc + (Bt * z*sin(theta))/(Bv * x); // Helical sheared mapping.
 }
 
 // Interface function calls.
@@ -181,7 +230,15 @@ void temp_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT
 void upar_ion_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
 { fout[0] = driftSpeed(xn, ctx); }
 void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
-{ fout[0] = bmag(xc, ctx); }
+{ 
+  // Cartesian formulation of the magnetic field.
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  double phi = phix(xc, ctx);
+  fout[0] = -Bt*sin(phi);
+  fout[1] = Bt*cos(phi);
+  fout[2] = Bv;
+}
 void zero_func(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
 { fout[0] = 0.0; }
 
@@ -189,19 +246,13 @@ void zero_func(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT
 void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
 {
   double x = xc[0], y = xc[1], z = xc[2];
-
-  struct gk_app_ctx *app = ctx;
-  double R_center = app->R_center;
-  double Lp = app->Lp;
-  double Lt = app->Lt;
-
-  double theta = asin(Lp/Lt);
+  
+  double theta = thetax(xc, ctx);
 
   // Map to cylindrical (R, Z, phi) coordinates.
   double R   = x;
   double Z   = z*sin(theta);
-  double phi = (y/sin(theta) + z*cos(theta))/R_center;
-
+  double phi = phix(xc, ctx);
   // Map to Cartesian (X, Y, Z) coordinates.
   double X = R*cos(phi);
   double Y = R*sin(phi);
@@ -231,17 +282,20 @@ create_ctx(void)
 
   // Geometry and magnetic field.
   double B_axis = 0.5;
-  double R_axis = 0.85;
-  double a_center = 0.5; // Minor radius of the center of the domain.
-  double R_center = R_axis + a_center; // Major radius of the center of the domain.
-  double B_center = B_axis*R_axis/R_center; // Magnetic field strength at the center of the domain.
-  double Lp = 2.4; // Poloidal length (used to get the field line pitch).
-  double Lt = 8.0; // Toroidal length (used to get the field line pitch).
+  double R0 = 0.85;
+  double a0 = 0.5;
+  double Lp = 2.4; // Poloidal length at x0.
+  double Lt = 8.0; // Toroidal length at x0.
+  double Rc = R0 + a0;
+  double B0 = B_axis*R0/Rc;
+
+  double sintheta = Lp/Lt;
+  double Bv0 = B0*sintheta;
 
   // Source parameters.
   double P_SOL = 8.1e5;
-  double S0 = 5.7691e23*10;
-  double xSource = R_center - 0.05;
+  double S0 = 5.7691e23*10; // Multiplied by 10 to increase beta
+  double xSource = Rc - 0.05;
   double lambdaSource = 0.005;
 
   // Collisions;
@@ -250,7 +304,7 @@ create_ctx(void)
   // Derived parameters.
   double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
   double c_s = sqrt(Te0/mi); // Sound speed.
-  double omega_ci = fabs(qi*B_center/mi); // Ion cyclotron frequency.
+  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
   double rho_s = c_s/omega_ci; // Ion sound gyroradius.
 
   // Box size.
@@ -258,27 +312,27 @@ create_ctx(void)
   double Ly = 100*rho_s;
   double Lz = Lt; // [m]
 
-  double x_min = R_center - Lx/2;
-  double x_max = R_center + Lx/2;
+  double x_min = Rc - Lx/2;
+  double x_max = Rc + Lx/2;
   double y_min = -Ly/2;
   double y_max = Ly/2;
   double z_min = -Lz/2;
   double z_max = Lz/2;
 
   // Grid parameters
-  int Nx = 2;
-  int Ny = 2;
+  int Nx = 4;
+  int Ny = 4;
   int Nz = 4;
   int Nvpar = 4;
   int Nmu = 4;
   int poly_order = 1;
 
   double vpar_max_elc = 4.*vte;
-  double mu_max_elc = 12*me*pow(vte,2)/(2*B_center);
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
   double vpar_max_ion = 4.*vti;
-  double mu_max_ion = 12*mi*pow(vti,2)/(2*B_center);
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
 
-  double t_end = 1.e-6; // End time, should terminate in 43 steps.
+  double t_end = 2.e-7; // End time, should terminate in 43 steps.
   int num_frames = 1;
   double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
   int int_diag_calc_num = num_frames*100;
@@ -289,12 +343,9 @@ create_ctx(void)
     .cdim = cdim,
     .vdim = vdim,
     .B_axis = B_axis,
-    .R_axis = R_axis,
-    .a_center = a_center,
-    .Lp = Lp,
-    .Lt = Lt,
-    .R_center = R_center,
-    .B_center = B_center,
+    .R0 = R0,
+    .Rc = Rc,
+    .Bv0 = Bv0,
     .Lx = Lx,
     .Ly = Ly,
     .Lz = Lz,
@@ -506,6 +557,8 @@ main(int argc, char **argv)
       .num_integrated_diag_moments = 1,
       .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
     },
+
+    .time_rate_diagnostics = true,
   };
 
   // field
@@ -557,7 +610,6 @@ main(int argc, char **argv)
     }
   };
 
-  // Set app output name from the executable name (argv[0]).
   snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
@@ -572,6 +624,11 @@ main(int argc, char **argv)
       .restart_frame = app_args.restart_frame,
       .num_steps = app_args.num_steps,
     },
+    .print_verbosity = {
+      .enabled = true,
+      .frequency = 1.0,
+      .disable_timings = true,
+    }
   };
 
   gkyl_gyrokinetic_run_simulation(&run_inp);

From b60c82d89582f2a560c86a3735cca48576c72cbd Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 24 Apr 2026 14:11:44 -0400
Subject: [PATCH 148/181] rename the helmholtz unit test

---
 ...tz_perp.c => ctest_fem_poisson_perp_kSq.c} | 311 +++++++-----------
 1 file changed, 113 insertions(+), 198 deletions(-)
 rename gyrokinetic/unit/{ctest_fem_helmholtz_perp.c => ctest_fem_poisson_perp_kSq.c} (70%)

diff --git a/gyrokinetic/unit/ctest_fem_helmholtz_perp.c b/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
similarity index 70%
rename from gyrokinetic/unit/ctest_fem_helmholtz_perp.c
rename to gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
index bfbf4d7149..e7234c7a85 100644
--- a/gyrokinetic/unit/ctest_fem_helmholtz_perp.c
+++ b/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
@@ -39,6 +39,24 @@ static double error_L2norm(struct gkyl_rect_grid grid, struct gkyl_range range,
   return sqrt(l2[0]);
 }
 
+static double field_L2norm(struct gkyl_rect_grid grid, struct gkyl_range range,
+  struct gkyl_basis basis, struct gkyl_array *field)
+{
+  // Compute the L2 norm of a single field.
+  struct gkyl_array *l2_cell = gkyl_array_new(GKYL_DOUBLE, 1, field->size);
+  gkyl_dg_calc_l2_range(basis, 0, l2_cell, 0, field, range);
+  gkyl_array_scale_range(l2_cell, grid.cellVolume, &range);
+  double l2[1];
+  gkyl_array_reduce_range(l2, l2_cell, GKYL_SUM, &range);
+  gkyl_array_release(l2_cell);
+  return sqrt(l2[0]);
+}
+
+// Return true when the HELMHOLTZ_OUTPUT env var is set (enables results file writing).
+static bool helmholtz_write_output(void) { return getenv("HELMHOLTZ_OUTPUT") != NULL; }
+// Return true when the HELMHOLTZ_VERBOSE env var is set (enables extra printf output).
+static bool helmholtz_verbose(void) { return getenv("HELMHOLTZ_VERBOSE") != NULL; }
+
 static struct gkyl_array*
 mkarr(bool use_gpu, long nc, long size)
 {
@@ -68,7 +86,7 @@ static void evalFunc_ksquare(double t, const double *xn, double* restrict fout,
   fout[0] = ksquare();
   // fout[0] *= cos(2*M_PI*x); 
   fout[0] *= exp(4*M_PI*y); 
-  // fout[0] *= sin(z)+2;  
+  fout[0] *= sin(z)+2;
 }
 
 // RHS: rho(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m sin(2*pi*m*x)
@@ -148,42 +166,6 @@ void evalFunc_sol_periodicx_2x(double t, const double *xn, double* restrict fout
   fout[0] *= (1.+kz*z);
 }
 
-// 3x cases
-// RHS: rho(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m sin(2*pi*m*x)
-void evalFunc_rhs_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
-{
-  double x = xn[0], y = xn[1], z = xn[2];
-  // These values have to match those in the test below.
-  double bmn[] = {0.2, 0.5, -0.5};
-  fout[0] = 0.;
-  for (int m=1; m<3; m++) {
-    double b = bmn[m-1];
-    double kx = 2*M_PI*m;
-    double ky = 2*M_PI;
-    double t2 = b*sin(kx*x) * sin(ky*y);
-    fout[0] += t2;
-  }
-  double kz = 1.;
- fout[0] *= (1.+kz*z+0.5*pow(z,2));
-}
-// Solution: phi(x,z) = (1.+kz*z+0.5*pow(z,2)) * sum_{m=1}^2 b_m*sin(2*pi*m*x)/( (2*pi*m)^2 - kSq )
-void evalFunc_sol_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
-{
-  double x = xn[0], y = xn[1], z = xn[2];
-  // These values have to match those in the test below.
-  double bmn[] = {0.2, 0.5, -0.5};
-  fout[0] = 0.;
-  for (int m=1; m<3; m++) {
-    double b = bmn[m-1];
-    double kx = 2*M_PI*m;
-    double ky = 2*M_PI;
-    double t2 = b*sin(kx*x) * sin(ky*y)/(kx*kx + ky*ky - ksquare());
-    fout[0] += t2;
-  }
-  double kz = 1.;
- fout[0] *= (1.+kz*z+0.5*pow(z,2));
-}
-
 double trig_func(double x, double y, bool laplacian)
 {
   double amn[] = {0.0, -1., 0., -0.0};
@@ -210,6 +192,27 @@ double z_envelope(double z)
   return 1.0;
 }
 
+// 3x Dirichlet-Dirichlet cases — manufactured solution approach.
+// Choose phi = sin(kx*x)*sin(ky*y)*z_envelope(z), which vanishes at x=0,1 and y=0,1.
+// Derive rho from: -nabla_perp^2 phi + kSq(x,y)*phi = rho
+//   => rho = (kx^2 + ky^2)*phi + kSq(x,y)*phi
+// This is consistent with any kSq(x,y), including the spatially varying evalFunc_ksquare.
+void evalFunc_sol_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  double kx = M_PI, ky = M_PI;
+  fout[0] = sin(kx*x) * sin(ky*y) * z_envelope(z);
+}
+void evalFunc_rhs_dirichletx_dirichlety_3x(double t, const double *xn, double* restrict fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  double kx = M_PI, ky = M_PI;
+  double kSq_val[1];
+  evalFunc_ksquare(t, xn, kSq_val, ctx);
+  double phi_val = sin(kx*x) * sin(ky*y) * z_envelope(z);
+  fout[0] = (kx*kx + ky*ky - kSq_val[0]) * phi_val;
+}
+
 void evalFunc_sol_dirichletx_periodicy_3x(double t, const double *xn, double* restrict fout, void *ctx)
 {
   double x = xn[0], y = xn[1], z = xn[2];
@@ -228,6 +231,39 @@ void evalFunc_rhs_dirichletx_periodicy_3x(double t, const double *xn, double* re
   fout[0] = -trig_func(x,y,true)*z_envelope(z) - kSq[0]*fsol[0];
 }
 
+// Check that the relative L2 error between numerical and analytical solutions is < 1%.
+static void check_solution(struct gkyl_rect_grid grid, struct gkyl_range range,
+  struct gkyl_basis basis, struct gkyl_array *phi, struct gkyl_array *phisol)
+{
+  double err_L2 = error_L2norm(grid, range, basis, phi, phisol);
+  double sol_L2 = field_L2norm(grid, range, basis, phisol);
+  double rel_err = (sol_L2 > 0.0) ? err_L2 / sol_L2 : err_L2;
+  TEST_CHECK( rel_err < 0.01 );
+  TEST_MSG("Relative L2 error = %.6e (threshold 1%%)", rel_err);
+
+  if (helmholtz_verbose())
+    printf("L2 error = %.6e, relative L2 error = %.6e\n", err_L2, rel_err);
+}
+
+// Read 2x grid resolution from environment variables (or defaults).
+static void get_2x_cells(int *cells) {
+  int nx = 32, nz = 48;
+  char *env;
+  if ((env = getenv("TEST_NX"))) nx = atoi(env);
+  if ((env = getenv("TEST_NZ"))) nz = atoi(env);
+  cells[0] = nx; cells[1] = nz;
+}
+
+// Read 3x grid resolution from environment variables (or defaults).
+static void get_3x_cells(int *cells) {
+  int nx = 32, ny = 24, nz = 8;
+  char *env;
+  if ((env = getenv("TEST_NX"))) nx = atoi(env);
+  if ((env = getenv("TEST_NY"))) ny = atoi(env);
+  if ((env = getenv("TEST_NZ"))) nz = atoi(env);
+  cells[0] = nx; cells[1] = ny; cells[2] = nz;
+}
+
 void
 test_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson_bc bcs, bool use_gpu)
 {
@@ -315,7 +351,7 @@ test_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson
 #endif
 
   // Write data to text file for visualization (Python notebook can read this)
-  FILE *fp = fopen("helmholtz_2x_results.txt", "w");
+  FILE *fp = helmholtz_write_output() ? fopen("helmholtz_2x_results.txt", "w") : NULL;
   if (fp) {
     fprintf(fp, "# x z phi_numerical phi_analytical\n");
     struct gkyl_range_iter iter;
@@ -332,46 +368,8 @@ test_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson
     fclose(fp);
   }
 
-  // // Write parameters file for visualization.
-  // fp = fopen("helmholtz_2x_params.txt", "w");
-  // if (fp) {
-  //   fprintf(fp, "lower: %.16e %.16e\n", lower[0], lower[1]);
-  //   fprintf(fp, "upper: %.16e %.16e\n", upper[0], upper[1]);
-  //   fprintf(fp, "cells: %d %d\n", cells[0], cells[1]);
-  //   fprintf(fp, "poly_order: %d\n", poly_order);
-  //   fprintf(fp, "kSq: %.16e\n", kSq);
-  //   fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
-  //   fclose(fp);
-  // }
-
-  // // Write parameters file for visualization.
-  // fp = fopen("helmholtz_2x_params.txt", "w");
-  // if (fp) {
-  //   fprintf(fp, "lower: %.16e %.16e\n", lower[0], lower[1]);
-  //   fprintf(fp, "upper: %.16e %.16e\n", upper[0], upper[1]);
-  //   fprintf(fp, "cells: %d %d\n", cells[0], cells[1]);
-  //   fprintf(fp, "poly_order: %d\n", poly_order);
-  //   fprintf(fp, "kSq: %.16e\n", kSq);
-  //   fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
-  //   fclose(fp);
-  // }
-
-  // double errL2 = error_L2norm(grid, localRange, basis, phi_ho, phisol_ho);
-  // printf("\nerror L2 norm = %g\n",errL2);
-
   // Compare solution to analytic result.
-  struct gkyl_range_iter iter;
-  gkyl_range_iter_init(&iter, &localRange);
-  while (gkyl_range_iter_next(&iter)) {
-    long loc = gkyl_range_idx(&localRange, iter.idx);
-    const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
-    const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
-    for (int m = 0; m < basis.num_basis; m++) {
-      // TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
-      // TEST_MSG("Expected: %.13e in cell (%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1]);
-      // TEST_MSG("Produced: %.13e", phi_p[m]);
-    }
-  }
+  check_solution(grid, localRange, basis, phi_ho, phisol_ho);
 
   gkyl_fem_poisson_perp_release(poisson);
   gkyl_proj_on_basis_release(projob);
@@ -479,69 +477,31 @@ test_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisson
 #endif
 
   // Write data to text file for visualization (Python notebook can read this)
-  // FILE *fp = fopen("helmholtz_3x_results.txt", "w");
-  // if (fp) {
-  //   fprintf(fp, "# x y z phi_numerical phi_analytical\n");
-  //   struct gkyl_range_iter iter;
-  //   gkyl_range_iter_init(&iter, &localRange);
-  //   while (gkyl_range_iter_next(&iter)) {
-  //     double xc[3];
-  //     gkyl_rect_grid_cell_center(&grid, iter.idx, xc);
-  //     long loc = gkyl_range_idx(&localRange, iter.idx);
-  //     const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
-  //     const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
-  //     // Write cell center coordinates and the 0th basis coefficient (cell average)
-  //     fprintf(fp, "%.16e %.16e %.16e %.16e %.16e\n", xc[0], xc[1], xc[2], phi_p[0]/dg0norm, phisol_p[0]/dg0norm);
-  //   }
-  //   fclose(fp);
-  // }
-
-  // // Write parameters file for visualization.
-  // fp = fopen("helmholtz_3x_params.txt", "w");
-  // if (fp) {
-  //   fprintf(fp, "lower: %.16e %.16e %.16e\n", lower[0], lower[1], lower[2]);
-  //   fprintf(fp, "upper: %.16e %.16e %.16e\n", upper[0], upper[1], upper[2]);
-  //   fprintf(fp, "cells: %d %d %d\n", cells[0], cells[1], cells[2]);
-  //   fprintf(fp, "poly_order: %d\n", poly_order);
-  //   fprintf(fp, "kSq: %.16e\n", kSq);
-  //   fprintf(fp, "epsilon_0: %.16e\n", epsilon_0);
-  //   fclose(fp);
-  // }
-
-  // double errL2 = error_L2norm(grid, localRange, basis, phi_ho, phisol_ho);
-  // printf("\nerror L2 norm = %g\n",errL2);
+  FILE *fp = helmholtz_write_output() ? fopen("helmholtz_3x_results.txt", "w") : NULL;
+  if (fp) {
+    fprintf(fp, "# x y z phi_numerical phi_analytical\n");
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &localRange);
+    while (gkyl_range_iter_next(&iter)) {
+      double xc[3];
+      gkyl_rect_grid_cell_center(&grid, iter.idx, xc);
+      long loc = gkyl_range_idx(&localRange, iter.idx);
+      const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
+      const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
+      // Write cell center coordinates and the 0th basis coefficient (cell average)
+      fprintf(fp, "%.16e %.16e %.16e %.16e %.16e\n", xc[0], xc[1], xc[2], phi_p[0]/dg0norm, phisol_p[0]/dg0norm);
+    }
+    fclose(fp);
+  }
 
   // Compare solution to analytic result.
   if (poly_order == 1) {
-    if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
-        (bcs.lo_type[1] == GKYL_POISSON_DIRICHLET && bcs.up_type[1] == GKYL_POISSON_DIRICHLET)) {
-      struct gkyl_range_iter iter;
-      gkyl_range_iter_init(&iter, &localRange);
-      while (gkyl_range_iter_next(&iter)) {
-        long loc = gkyl_range_idx(&localRange, iter.idx);
-        const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
-        const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
-        for (int m = 0; m < basis.num_basis; m++) {
-          TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
-          TEST_MSG("Expected: %.13e in cell (%d,%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1], iter.idx[2]);
-          TEST_MSG("Produced: %.13e", phi_p[m]);
-        }
-      }
-    } else if ((bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET) &&
-               (bcs.lo_type[1] == GKYL_POISSON_PERIODIC && bcs.up_type[1] == GKYL_POISSON_PERIODIC)) {
-      struct gkyl_range_iter iter;
-      gkyl_range_iter_init(&iter, &localRange);
-      while (gkyl_range_iter_next(&iter)) {
-        long loc = gkyl_range_idx(&localRange, iter.idx);
-        const double *phi_p = gkyl_array_cfetch(phi_ho, loc);
-        const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
-        for (int m = 0; m < basis.num_basis; m++) {
-          TEST_CHECK( gkyl_compare(phisol_p[m], phi_p[m], 1e-10) );
-          TEST_MSG("Expected: %.13e in cell (%d,%d,%d)", phisol_p[m], iter.idx[0], iter.idx[1], iter.idx[2]);
-          TEST_MSG("Produced: %.13e", phi_p[m]);
-        }
-      }
-    } else {
+    bool dd = (bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET);
+    bool ydir_ok = (bcs.lo_type[1] == GKYL_POISSON_DIRICHLET && bcs.up_type[1] == GKYL_POISSON_DIRICHLET) ||
+                   (bcs.lo_type[1] == GKYL_POISSON_PERIODIC  && bcs.up_type[1] == GKYL_POISSON_PERIODIC);
+    if (dd && ydir_ok)
+      check_solution(grid, localRange, basis, phi_ho, phisol_ho);
+    else {
       TEST_CHECK( gkyl_compare(1., 2., 1e-10) );
       TEST_MSG("This BC combination is not available");
     }
@@ -565,84 +525,39 @@ test_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisson
 
 // 2x test wrappers
 void test_2x_p1_dirichletx() {
-  // Read grid resolution from environment variables, or use defaults
-  int nx = 32, nz = 48;
-  char *env_nx = getenv("TEST_NX");
-  char *env_nz = getenv("TEST_NZ");
-  if (env_nx) nx = atoi(env_nx);
-  if (env_nz) nz = atoi(env_nz);
-  
-  int cells[] = {nx, nz};
+  int cells[2]; get_2x_cells(cells);
   struct gkyl_poisson_bc bc_tv;
-  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.lo_value[0].v[0] = x_dirichletbc_lo();
-  bc_tv.up_value[0].v[0] = x_dirichletbc_up();
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET; bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = x_dirichletbc_lo(); bc_tv.up_value[0].v[0] = x_dirichletbc_up();
   test_fem_helmholtz_perp_2x(1, cells, bc_tv, false);
 }
 
 void test_2x_p1_periodicx() {
-  // Read grid resolution from environment variables, or use defaults
-  int nx = 32, nz = 48;
-  char *env_nx = getenv("TEST_NX");
-  char *env_nz = getenv("TEST_NZ");
-  if (env_nx) nx = atoi(env_nx);
-  if (env_nz) nz = atoi(env_nz);
-  
-  int cells[] = {nx, nz};
+  int cells[2]; get_2x_cells(cells);
   struct gkyl_poisson_bc bc_tv;
-  bc_tv.lo_type[0] = GKYL_POISSON_PERIODIC;
-  bc_tv.up_type[0] = GKYL_POISSON_PERIODIC;
-  bc_tv.lo_value[0].v[0] = 0.;
-  bc_tv.up_value[0].v[0] = 0.;
+  bc_tv.lo_type[0] = GKYL_POISSON_PERIODIC; bc_tv.up_type[0] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.; bc_tv.up_value[0].v[0] = 0.;
   test_fem_helmholtz_perp_2x(1, cells, bc_tv, false);
 }
 
-
 // 3x test wrappers
 void test_3x_p1_dirichletx_dirichlety() {
-  // Read grid resolution from environment variables, or use defaults
-  int nx = 32, ny = 16, nz = 2;
-  char *env_nx = getenv("TEST_NX");
-  char *env_ny = getenv("TEST_NY");
-  char *env_nz = getenv("TEST_NZ");
-  if (env_nx) nx = atoi(env_nx);
-  if (env_ny) ny = atoi(env_ny);
-  if (env_nz) nz = atoi(env_nz);
-  
-  int cells[] = {nx, ny, nz};
+  int cells[3]; get_3x_cells(cells);
   struct gkyl_poisson_bc bc_tv;
-  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.lo_type[1] = GKYL_POISSON_DIRICHLET;
-  bc_tv.up_type[1] = GKYL_POISSON_DIRICHLET;
-  bc_tv.lo_value[0].v[0] = 0.0;
-  bc_tv.up_value[0].v[0] = 0.0;
-  bc_tv.lo_value[1].v[0] = 0.0;
-  bc_tv.up_value[1].v[0] = 0.0;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET; bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_DIRICHLET; bc_tv.up_type[1] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_value[0].v[0] = 0.; bc_tv.up_value[0].v[0] = 0.;
+  bc_tv.lo_value[1].v[0] = 0.; bc_tv.up_value[1].v[0] = 0.;
   test_fem_helmholtz_perp_3x(1, cells, bc_tv, false);
 }
 
 void test_3x_p1_dirichletx_periodicy() {
-  // Read grid resolution from environment variables, or use defaults
-  int nx = 32, ny = 16, nz = 2;
-  char *env_nx = getenv("TEST_NX");
-  char *env_ny = getenv("TEST_NY");
-  char *env_nz = getenv("TEST_NZ");
-  if (env_nx) nx = atoi(env_nx);
-  if (env_ny) ny = atoi(env_ny);
-  if (env_nz) nz = atoi(env_nz);
-  
-  int cells[] = {nx, ny, nz};
+  int cells[3]; get_3x_cells(cells);
   struct gkyl_poisson_bc bc_tv;
-  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
-  bc_tv.lo_type[1] = GKYL_POISSON_PERIODIC;
-  bc_tv.up_type[1] = GKYL_POISSON_PERIODIC;
-  bc_tv.lo_value[0].v[0] = 0.0;
-  bc_tv.up_value[0].v[0] = 0.0;
-  bc_tv.lo_value[1].v[0] = 0.;
-  bc_tv.up_value[1].v[0] = 0.;
+  bc_tv.lo_type[0] = GKYL_POISSON_DIRICHLET; bc_tv.up_type[0] = GKYL_POISSON_DIRICHLET;
+  bc_tv.lo_type[1] = GKYL_POISSON_PERIODIC;  bc_tv.up_type[1] = GKYL_POISSON_PERIODIC;
+  bc_tv.lo_value[0].v[0] = 0.; bc_tv.up_value[0].v[0] = 0.;
+  bc_tv.lo_value[1].v[0] = 0.; bc_tv.up_value[1].v[0] = 0.;
   test_fem_helmholtz_perp_3x(1, cells, bc_tv, false);
 }
 

From 8ab0a7f2a6fff956c3b47d79dc3c3924051bd743 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 25 Apr 2026 10:00:31 -0400
Subject: [PATCH 149/181] the merge between EM and poisson_perp compiles now,
 unit test passes, alfven looks ok but the tcv 3x2v reg test shows time step
 drop that should not occur.

---
 gyrokinetic/apps/gk_field_2x3x.c              | 168 ++++--------------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |   1 -
 gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c |  67 +------
 gyrokinetic/zero/fem_poisson_perp.c           |  54 ++----
 gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h |   5 -
 5 files changed, 55 insertions(+), 240 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 2b45a179b2..0bfe30d489 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -189,64 +189,18 @@ gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       .shift_func_ctx = par_lower_bc->aux_ctx,
       .use_gpu = app->use_gpu,
     };
-    // Add the forward TS updater to f
-    f->bc_ts_lo = gkyl_bc_twistshift_new(&ts_lo);
-  }
-
-  // Add the SSFG updater for lower and upper application.
-  f->ssfg_z_lo = gkyl_skin_surf_from_ghost_new(par_dir,  GKYL_LOWER_EDGE,
-    app->basis, &app->lower_skin_par_core,  &app->lower_ghost_par_core, app->use_gpu);
-
-  // Write the discrete shift to file.
-  if (app->cdim == 3)
-    gk_field_2x3x_write_twistshift(app, f);
-}
-
-static void 
-gk_field_twistshift_enabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
-  gkyl_bc_twistshift_advance(up, fdo, ftar);
-}
-
-static void
-gk_field_twistshift_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar){
-  // Do nothing
-}
-
-static void
-gk_field_enforce_parallel_bc_enabled(const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
-{
-  // Apply the periodicity along the field to fill ghost cells.
-  int num_periodic_dir = 1;
-  int par_dir = app->cdim - 1;
-  int periodic_dirs[] = {par_dir};
-  gkyl_comm_array_per_sync(app->comm, &app->local, &app->local_ext,
-    num_periodic_dir, periodic_dirs, finout); 
-  
-  // Update the lower z ghosts with twist-and-shift if we are in 3x2v
-   field->twistshift_func(field->bc_ts_lo, finout, finout);
+    f->bc_ts_lo = gkyl_bc_twistshift_new(&T_LU_lo);
 
-  // Sync ghost cells between MPI processes.
-  gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);
+    long buff_sz = GKYL_MAX2(app->global_lower_ghost_par_sol.volume, app->global_lower_ghost_par_core.volume);
+    f->bc_buffer = mkarr(app->use_gpu, app->basis.num_basis, buff_sz);
 
-  // Force the lower skin surface value to match the ghost cell at the node position.
-  gkyl_skin_surf_from_ghost_advance(field->ssfg_z_lo, finout);
-}
+    f->gfss_bc_op_core_up = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_UPPER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
+      app->basis_on_dev, &app->global_upper_skin_par_core, &app->global_upper_ghost_par_core,
+      app->basis.num_basis, app->cdim, app->use_gpu);
 
-static void
-gk_field_enforce_parallel_bc_em_enabled(const struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
-{
-  // Apply the periodicity along the field to fill ghost cells.
-  int num_periodic_dir = 1;
-  int par_dir = app->cdim - 1;
-  int periodic_dirs[] = {par_dir};
-  gkyl_comm_array_per_sync(app->comm, &app->local, &app->local_ext,
-    num_periodic_dir, periodic_dirs, finout); 
-  
-  // Update the lower z ghosts with twist-and-shift if we are in 3x2v
-  field->twistshift_func(field->bc_ts_lo, finout, finout);
-
-  // Sync ghost cells between MPI processes.
-  gkyl_comm_array_sync(app->comm, &app->local, &app->local_ext, finout);
+    // Write the discrete shift to file.
+    gk_field_3x_write_twistshift(app, f);
+  }
 }
 
 static void
@@ -260,37 +214,10 @@ gk_field_rhs_poisson_perp_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field
   gkyl_fem_poisson_perp_solve(field->fem_poisson_perp, field->phi_smooth);
 
   // Smooth the potential along z.
-  gk_field_fem_projection_par(app, field, field->phi_smooth, field->phi_smooth);
+  field->fem_projection_par_phi_func(app, field, field->phi_smooth, field->phi_smooth);
 
   // Finish the Poisson solve with FLR effects.
   field->invert_flr(app, field, field->phi_smooth);
-
-  // Enforce a BC of the field in the parallel direction.
-  field->enforce_parallel_bc_func(app, field, field->phi_smooth);
-}
-
-static void
-gk_field_rhs_deflate_poisson_es_iwl(struct gkyl_gyrokinetic_app *app, struct gk_field *field)
-{
-  // Gather charge density into global array.
-  gkyl_comm_array_allgather(app->comm, &app->local, &app->global, field->rho_c, field->rho_c_global_dg);
-
-  // Smooth the charge density. Input is rho_c_global_dg, globally smoothed in z,
-  // and then output should be in *local* phi_smooth.
-  gkyl_fem_parproj_set_rhs(field->fem_parproj_core, field->rho_c_global_dg, field->rho_c_global_dg);
-  gkyl_fem_parproj_solve(field->fem_parproj_core, field->rho_c_global_smooth);
-  gkyl_fem_parproj_set_rhs(field->fem_parproj_sol, field->rho_c_global_dg, field->rho_c_global_dg);
-  gkyl_fem_parproj_solve(field->fem_parproj_sol, field->rho_c_global_smooth);
-
-  // Solve the Poisson equation.
-  gkyl_deflated_fem_poisson_advance(field->fem_poisson_deflated, field->rho_c_global_smooth,
-    field->phi_bc, field->phi_smooth);
-
-  // Finish the Poisson solve with FLR effects.
-  field->invert_flr(app, field, field->phi_smooth);
-
-  // Enforce a BC of the field in the parallel direction.
-  field->enforce_parallel_bc_func(app, field, field->phi_smooth);
 }
 
 static void 
@@ -303,7 +230,7 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   // Temporary solution to avoid superLU leak when updating kSq: we release and re-create the solver
   gkyl_fem_poisson_perp_release(field->fem_apardot_solver);
   field->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-    &field->ampere_bcs, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
+    &field->ampere_bcs, field->info.bias_line_list, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
 
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
   gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
@@ -326,7 +253,6 @@ gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field)
 
   field->invert_flr(app, field, field->apar);
 
-  field->enforce_parallel_bc_em_func(app, field, field->apar);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -341,7 +267,6 @@ gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const
   gk_field_accumulate_current_dens_dot(app, field, rhs_in);
   gk_field_accumulate_ohms_kSq(app, field, f_in);
   gk_field_ohm_solve(app, field);
-  field->enforce_parallel_bc_em_func(app, field, field->apardot);
 }
 
 static void
@@ -395,18 +320,10 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_integrate_release(f->calc_em_energy);
 
   // Release IWL updaters.
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     gkyl_fem_parproj_release(f->fem_parproj_core);
     gkyl_fem_parproj_release(f->fem_parproj_sol);
-  }
-  if (f->is_em || !(f->gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
-    gkyl_fem_parproj_release(f->fem_parproj);
-  }
 
-  gkyl_array_integrate_release(f->calc_em_energy);
-
-  // Release TS BC and SSFG updater
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     if (app->cdim == 3) {
       gkyl_bc_twistshift_release(f->bc_ts_lo);
       gkyl_bc_basic_gyrokinetic_release(f->gfss_bc_op_core_up);
@@ -491,9 +408,6 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_set(f->apar_energy_fac, -0.5, f->lapWeightAmpere);
   }
 
-  // Translate input file BCs into Poisson BCs.
-  struct gkyl_poisson_bc poisson_bcs = { };
-
   bool bc_is_np[GKYL_MAX_CDIM]; // Is the BC in this direction non-periodic?
   for (int d=0; d<app->cdim; ++d) bc_is_np[d] = true;
   for (int d=0; d<app->num_periodic_dir; ++d) {
@@ -566,39 +480,20 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     gkyl_array_release(phi_bc_ho);
   }
 
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
-    f->rhs_phi_func = gk_field_rhs_deflate_poisson_es_iwl;
-    enum gkyl_fem_parproj_bc_type fem_parproj_bc_core, fem_parproj_bc_sol;
-    if (app->cdim == 2) {
-      fem_parproj_bc_core = GKYL_FEM_PARPROJ_PERIODIC;
-      fem_parproj_bc_sol = GKYL_FEM_PARPROJ_NONE;
-    } else {
-      fem_parproj_bc_core = GKYL_FEM_PARPROJ_NONE;
-      fem_parproj_bc_sol = GKYL_FEM_PARPROJ_NONE;
-    }
-
-    f->fem_parproj_core = gkyl_fem_parproj_new(&app->global_core, &app->basis,
-      fem_parproj_bc_core, 0, 0, app->use_gpu);
-    f->fem_parproj_sol = gkyl_fem_parproj_new(&app->global_sol, &app->basis,
-      fem_parproj_bc_sol, 0, 0, app->use_gpu);
-  } else {
-    f->rhs_phi_func = gk_field_rhs_poisson_perp_2x3x;
-  }
-
-  if (f->is_em || !(f->gkfield_id == GKYL_GK_FIELD_ES_IWL)) {
+  // Potential smoothing (in z) updater
     enum gkyl_fem_parproj_bc_type fem_parproj_bc = GKYL_FEM_PARPROJ_NONE;
-    for (int d=0; d<app->num_periodic_dir; ++d) {
-      if (app->periodic_dirs[d] == app->cdim-1) {
-        fem_parproj_bc = GKYL_FEM_PARPROJ_PERIODIC;
-      }
-    }
+    for (int d=0; d<app->num_periodic_dir; ++d)
+      if (app->periodic_dirs[d] == app->cdim-1) fem_parproj_bc = GKYL_FEM_PARPROJ_PERIODIC;
+
     f->fem_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
       fem_parproj_bc, 0, 0, app->use_gpu);
-  }
 
+  f->fem_projection_par_rho_func = gk_field_fem_projection_par;
+  f->fem_projection_par_phi_func = gk_field_fem_projection_par;
+
+  // Setup EM solvers.
   f->ampere_solve = gk_field_ampere_solve_none;
   f->em_rhs_func = gk_field_em_rhs_none;
-  // Setup EM solvers.
   if (f->is_em) {
     // Translate input file BCs into Ampere BCs.
     for (int d=0; d<app->cdim-1; d++) {
@@ -623,10 +518,10 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     }
     // FEM solver for Ampere equation (solved at IC only).
     f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-        &f->ampere_bcs, f->lapWeightAmpere, NULL, app->use_gpu);
+        &f->ampere_bcs, f->info.bias_line_list, f->lapWeightAmpere, NULL, app->use_gpu);
     // FEM solver for Ohm's law (evolves d(Apart)/dt).
     f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-      &f->ampere_bcs, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+      &f->ampere_bcs, f->info.bias_line_list, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
     // FEM smoother for Aparallel.
     f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
     f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
@@ -636,6 +531,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
   }
 
+  // Updater for field energy calculation.
   gkyl_array_set(f->es_energy_fac, 0.5, f->epsilon);
   f->calc_em_energy = gkyl_array_integrate_new(&app->grid, &app->basis, 
     1, GKYL_ARRAY_INTEGRATE_OP_EPS_GRADPERP_SQ, app->use_gpu);
@@ -654,17 +550,13 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   }
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
-  f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_disabled;
-  f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_disabled;
-  f->twistshift_func = gk_field_twistshift_disabled;
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
-    gk_field_2x3x_add_TSBC_and_SSFG_updaters(app,f);
-    if (app->cdim == 3)
-      f->twistshift_func = gk_field_twistshift_enabled;
-    f->enforce_parallel_bc_func = gk_field_enforce_parallel_bc_enabled;
-    if (f->is_em)
-      f->enforce_parallel_bc_em_func = gk_field_enforce_parallel_bc_em_enabled;
+  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+    gk_field_2x3x_add_IWL_updaters(app, f);
   }
 
-  f->solver_release_func = gk_field_fem_release_2x3x;
+  // Set the pointer to the function that computes phi.
+  f->rhs_phi_func = gk_field_rhs_poisson_perp_2x3x;
+
+  // Set pointer to function that releases memory.
+  f->release_func = gk_field_fem_release_2x3x;
 }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index b6cdd1fe0f..9054507dca 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1359,7 +1359,6 @@ struct gk_field {
     struct gkyl_array *arr_dg, struct gkyl_array *arr_fem);
   void (*fem_projection_par_phi_func)(gkyl_gyrokinetic_app *app, struct gk_field *field,
     struct gkyl_array *arr_dg, struct gkyl_array *arr_fem);
-  void (*enforce_parallel_bc_em_func) (const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout);
   void (*twistshift_func) (struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
 
   // Pointer to function for electromagnetic field solve.
diff --git a/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c b/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
index c8fe56a2a7..6a0ee473ae 100644
--- a/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
+++ b/gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
@@ -233,23 +233,6 @@ void evalFunc_rhs_dirichletx_periodicy_3x(double t, const double *xn, double* re
   fout[0] = -trig_func(x,y,true)*z_envelope(z) - kSq[0]*fsol[0];
 }
 
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-// Check that the relative L2 error between numerical and analytical solutions is < 1%.
-static void check_solution(struct gkyl_rect_grid grid, struct gkyl_range range,
-  struct gkyl_basis basis, struct gkyl_array *phi, struct gkyl_array *phisol)
-{
-  double err_L2 = error_L2norm(grid, range, basis, phi, phisol);
-  double sol_L2 = field_L2norm(grid, range, basis, phisol);
-  double rel_err = (sol_L2 > 0.0) ? err_L2 / sol_L2 : err_L2;
-  TEST_CHECK( rel_err < 0.01 );
-  TEST_MSG("Relative L2 error = %.6e (threshold 1%%)", rel_err);
-
-  if (helmholtz_verbose())
-    printf("L2 error = %.6e, relative L2 error = %.6e\n", err_L2, rel_err);
-}
-
-========
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
 // Read 2x grid resolution from environment variables (or defaults).
 static void get_2x_cells(int *cells) {
   int nx = 32, nz = 48;
@@ -261,7 +244,7 @@ static void get_2x_cells(int *cells) {
 
 // Read 3x grid resolution from environment variables (or defaults).
 static void get_3x_cells(int *cells) {
-  int nx = 32, ny = 24, nz = 8;
+  int nx = 8, ny = 8, nz = 4;
   char *env;
   if ((env = getenv("TEST_NX"))) nx = atoi(env);
   if ((env = getenv("TEST_NY"))) ny = atoi(env);
@@ -269,10 +252,6 @@ static void get_3x_cells(int *cells) {
   cells[0] = nx; cells[1] = ny; cells[2] = nz;
 }
 
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-void
-test_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson_bc bcs, bool use_gpu)
-========
 // Introduce eps and ksq factors.
 static void introduce_factors(struct gkyl_array *eps, struct gkyl_array *kSqFld) {
   gkyl_array_scale(eps, eps_factor());
@@ -287,7 +266,6 @@ static void remove_factors(struct gkyl_array *eps, struct gkyl_array *kSqFld) {
 static double
 solve_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisson_bc bcs, bool use_gpu,
   double *sol_L2_out)
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
 {
   double epsilon_0 = 1.0;
   double kSq = ksquare();  // Helmholtz wave number squared.
@@ -367,7 +345,7 @@ solve_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisso
   // Set the RHS source.
   gkyl_fem_poisson_perp_set_rhs(poisson, rho);
 
-  // Solve the problem.
+  // Solve the problem once, to allow kSq and epsilon modification.
   gkyl_fem_poisson_perp_solve(poisson, phi);
 
   // Remove the factor and correct the solver's internal kSq and epsilon field accordingly.
@@ -386,11 +364,7 @@ solve_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisso
 #endif
 
   // Write data to text file for visualization (Python notebook can read this)
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-  FILE *fp = helmholtz_write_output() ? fopen("helmholtz_2x_results.txt", "w") : NULL;
-========
   FILE *fp = helmholtz_write_output() ? fopen("ctest_fem_poisson_perp_ksq_results.txt", "w") : NULL;
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
   if (fp) {
     fprintf(fp, "# x z phi_numerical phi_analytical\n");
     struct gkyl_range_iter iter;
@@ -407,14 +381,9 @@ solve_fem_helmholtz_perp_2x(int poly_order, const int *cells, struct gkyl_poisso
     fclose(fp);
   }
 
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-  // Compare solution to analytic result.
-  check_solution(grid, localRange, basis, phi_ho, phisol_ho);
-========
   double err_L2 = error_L2norm(grid, localRange, basis, phi_ho, phisol_ho);
   if (sol_L2_out)
     *sol_L2_out = field_L2norm(grid, localRange, basis, phisol_ho);
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
 
   gkyl_fem_poisson_perp_release(poisson);
   gkyl_proj_on_basis_release(projob);
@@ -508,13 +477,15 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
   // Analytic solution.
   struct gkyl_array *phisol_ho = mkarr(false, basis.num_basis, localRange_ext.volume);
   // Device copies:
-  struct gkyl_array *rho_ho, *phi_ho;
+  struct gkyl_array *rho_ho, *phi_ho, *kSq_ho;
   if (use_gpu) {
     rho_ho = mkarr(false, rho->ncomp, rho->size);
     phi_ho = mkarr(false, phi->ncomp, phi->size);
+    kSq_ho = mkarr(false, kSqFld->ncomp, kSqFld->size);
   } else {
     rho_ho = gkyl_array_acquire(rho);
     phi_ho = gkyl_array_acquire(phi);
+    kSq_ho = gkyl_array_acquire(kSqFld);
   }
 
   // Project RHS charge density on basis.
@@ -528,8 +499,8 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
   gkyl_array_shiftc(eps, epsilon_0 * dg0norm, 2 * basis.num_basis);
 
   // Project kSq onto the basis.
-  // gkyl_array_shiftc(kSqFld, kSq * dg0norm, 0);
-  gkyl_proj_on_basis_advance(projob_kSq, 0.0, &localRange, kSqFld);
+  gkyl_proj_on_basis_advance(projob_kSq, 0.0, &localRange, kSq_ho);
+  gkyl_array_copy(kSqFld, kSq_ho);
 
   // Project the analytic solution.
   gkyl_proj_on_basis_advance(projob_sol, 0.0, &localRange, phisol_ho);
@@ -544,7 +515,7 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
   // Set the RHS source.
   gkyl_fem_poisson_perp_set_rhs(poisson, rho);
 
-  // Solve the problem.
+  // Solve the problem once, to allow kSq and epsilon modification.
   gkyl_fem_poisson_perp_solve(poisson, phi);
 
   // Remove the factor and correct the solver's internal kSq and epsilon field accordingly.
@@ -563,11 +534,7 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
 #endif
 
   // Write data to text file for visualization (Python notebook can read this)
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-  FILE *fp = helmholtz_write_output() ? fopen("helmholtz_3x_results.txt", "w") : NULL;
-========
   FILE *fp = helmholtz_write_output() ? fopen("ctest_fem_poisson_perp_ksq_results.txt", "w") : NULL;
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
   if (fp) {
     fprintf(fp, "# x y z phi_numerical phi_analytical\n");
     struct gkyl_range_iter iter;
@@ -580,23 +547,6 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
       const double *phisol_p = gkyl_array_cfetch(phisol_ho, loc);
       // Write cell center coordinates and the 0th basis coefficient (cell average)
       fprintf(fp, "%.16e %.16e %.16e %.16e %.16e\n", xc[0], xc[1], xc[2], phi_p[0]/dg0norm, phisol_p[0]/dg0norm);
-<<<<<<<< HEAD:gyrokinetic/unit/ctest_fem_poisson_perp_kSq.c
-    }
-    fclose(fp);
-  }
-
-  // Compare solution to analytic result.
-  if (poly_order == 1) {
-    bool dd = (bcs.lo_type[0] == GKYL_POISSON_DIRICHLET && bcs.up_type[0] == GKYL_POISSON_DIRICHLET);
-    bool ydir_ok = (bcs.lo_type[1] == GKYL_POISSON_DIRICHLET && bcs.up_type[1] == GKYL_POISSON_DIRICHLET) ||
-                   (bcs.lo_type[1] == GKYL_POISSON_PERIODIC  && bcs.up_type[1] == GKYL_POISSON_PERIODIC);
-    if (dd && ydir_ok)
-      check_solution(grid, localRange, basis, phi_ho, phisol_ho);
-    else {
-      TEST_CHECK( gkyl_compare(1., 2., 1e-10) );
-      TEST_MSG("This BC combination is not available");
-========
->>>>>>>> origin/ctest_helmholtz_perp:gyrokinetic/unit/ctest_fem_poisson_perp_ksq.c
     }
     fclose(fp);
   }
@@ -616,6 +566,7 @@ solve_fem_helmholtz_perp_3x(int poly_order, const int *cells, struct gkyl_poisso
   gkyl_array_release(phisol_ho);
   gkyl_array_release(rho_ho);
   gkyl_array_release(phi_ho);
+  gkyl_array_release(kSq_ho);
   return err_L2;
 }
 
diff --git a/gyrokinetic/zero/fem_poisson_perp.c b/gyrokinetic/zero/fem_poisson_perp.c
index 0bffd65571..23247c5dfc 100644
--- a/gyrokinetic/zero/fem_poisson_perp.c
+++ b/gyrokinetic/zero/fem_poisson_perp.c
@@ -92,13 +92,13 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
 
   // We assume epsilon and kSq live on the device, and we create a host-side
   // copies temporarily to compute the LHS matrix. This also works for CPU solves.
-  up->epsilon_ho = gkyl_array_new(GKYL_DOUBLE, up->epsilon->ncomp, up->epsilon->size);
-  gkyl_array_copy(up->epsilon_ho, up->epsilon);
+  struct gkyl_array *epsilon_ho = gkyl_array_new(GKYL_DOUBLE, up->epsilon->ncomp, up->epsilon->size);
+  gkyl_array_copy(epsilon_ho, up->epsilon);
+  struct gkyl_array *kSq_ho;
   if (kSq) {
     up->ishelmholtz = true;
-    up->kSq = gkyl_array_acquire(kSq);
-    up->kSq_ho = gkyl_array_new(GKYL_DOUBLE, up->kSq->ncomp, up->kSq->size);
-    gkyl_array_copy(up->kSq_ho, up->kSq);
+    kSq_ho = gkyl_array_new(GKYL_DOUBLE, kSq->ncomp, kSq->size);
+    gkyl_array_copy(kSq_ho, kSq);
   } else {
     up->ishelmholtz = false;
     kSq_ho = gkyl_array_new(GKYL_DOUBLE, up->num_basis, 1);
@@ -327,14 +327,6 @@ gkyl_fem_poisson_perp_new(const struct gkyl_range *solve_range, const struct gky
 #endif
   }
 
-  gkyl_fem_poisson_perp_build_stiffness_matrix(up);
-
-  return up;
-}
-
-void
-gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up)
-{
   // Assign non-zero elements in A.
   int idx0[GKYL_MAX_CDIM],  idx1[GKYL_MAX_CDIM];
   gkyl_range_iter_init(&up->par_iter1d, &up->par_range1d);
@@ -343,14 +335,15 @@ gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up)
 
     gkyl_range_iter_init(&up->perp_iter2d, &up->perp_range2d);
     while (gkyl_range_iter_next(&up->perp_iter2d)) {
+      long perpidx = gkyl_range_idx(&up->perp_range2d, up->perp_iter2d.idx);
 
       for (size_t d=0; d<up->ndim_perp; d++) idx1[d] = up->perp_iter2d.idx[d];
       idx1[up->pardir] = up->par_iter1d.idx[0];
 
       long linidx = gkyl_range_idx(up->solve_range, idx1);
 
-      double *eps_p = gkyl_array_fetch(up->epsilon_ho, linidx);
-      double *kSq_p = up->ishelmholtz? gkyl_array_fetch(up->kSq_ho, linidx) : gkyl_array_fetch(up->kSq_ho,0);
+      double *eps_p = gkyl_array_fetch(epsilon_ho, linidx);
+      double *kSq_p = up->ishelmholtz? gkyl_array_fetch(kSq_ho, linidx) : gkyl_array_fetch(kSq_ho,0);
 
       int keri = idx_to_inup_ker(up->ndim_perp, up->num_cells, up->perp_iter2d.idx);
       for (size_t d=0; d<up->ndim; d++) idx0[d] = idx1[d] - 1;
@@ -449,23 +442,22 @@ gkyl_fem_poisson_perp_build_stiffness_matrix(struct gkyl_fem_poisson_perp *up)
         for (size_t d=0; d<up->ndim; d++) idx0[d] = idx1[d] - 1;
         up->kernels->l2g[keri](up->num_cells, idx0, up->globalidx);
 
-	for (int k=0; k<up->basis.num_basis; k++) {
-	  for (int l=0; l<up->basis.num_basis; l++) {
+        for (int k=0; k<up->basis.num_basis; k++) {
+          for (int l=0; l<up->basis.num_basis; l++) {
             size_t nnz = gkyl_mat_triples_size(up->tri[paridx]); // Number of nonzero elements.
             // Given the global i,j (row-col) place in the LHS matrix, find the linear index into the mat_triples list. 
             // Here we do a brute-force search as we are unsure of the order, and this is done only once at t=0.
-	    long off = -1;
-            gkyl_mat_triples_iter *mtt_iter = gkyl_mat_triples_iter_new(up->tri[k]);
+            long off = -1;
+            gkyl_mat_triples_iter *mtt_iter = gkyl_mat_triples_iter_new(up->tri[paridx]);
             for (size_t m=0; m<nnz; ++m) {
               gkyl_mat_triples_iter_next(mtt_iter); // bump iterator.
               struct gkyl_mtriple mt = gkyl_mat_triples_iter_at(mtt_iter);
               if ((up->globalidx[k] == mt.row) && (up->globalidx[l] == mt.col)) {
                 off = m;
-		break;
-	      }
-	    }
-
-	    csr_val_idx_p[k*up->basis.num_basis+l] = paridx*nnz + off;
+                break;
+              }
+            }
+	          csr_val_idx_p[k*up->basis.num_basis+l] = paridx*nnz + off;
           }
         }
       }
@@ -571,13 +563,6 @@ gkyl_fem_poisson_perp_set_rhs(gkyl_fem_poisson_perp *up, struct gkyl_array *rhsi
 
 void
 gkyl_fem_poisson_perp_solve(gkyl_fem_poisson_perp *up, struct gkyl_array *phiout) {
-
-  // Check if we need to rebuild the stiffness matrix (if epsilon or kSq got updated).
-  if (up->make_stiff) {
-    assert(false); // AH Oct 15, 2025: This call is not valgrind clean. It seems that we cannot rebuild the matrix that easily.
-    gkyl_fem_poisson_perp_build_stiffness_matrix(up);
-  }
-
 #ifdef GKYL_HAVE_CUDA
   if (up->use_gpu) {
     assert(gkyl_array_is_cu_dev(phiout));
@@ -706,12 +691,5 @@ void gkyl_fem_poisson_perp_release(struct gkyl_fem_poisson_perp *up)
   gkyl_free(up->perp_range);
   gkyl_free(up->globalidx);
   gkyl_array_release(up->epsilon);
-  gkyl_array_release(up->epsilon_ho);
-  if (up->ishelmholtz)
-    gkyl_array_release(up->kSq);
-  gkyl_array_release(up->kSq_ho);
-  for (size_t i=0; i<up->par_range.volume; i++)
-    gkyl_mat_triples_release(up->tri[i]);
-  gkyl_free(up->tri);
   gkyl_free(up);
 }
diff --git a/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h b/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
index 12b6096157..ef2c7dd19f 100644
--- a/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
+++ b/gyrokinetic/zero/gkyl_fem_poisson_perp_priv.h
@@ -576,12 +576,7 @@ struct gkyl_fem_poisson_perp {
   bool isdirperiodic[GKYL_MAX_CDIM]; // =true if direction is periodic.
 
   struct gkyl_array *epsilon; // Permittivity.
-  struct gkyl_array *epsilon_ho; // Permittivity on host.
-  struct gkyl_array *kSq; // k squared (Helmholtz term).
-  struct gkyl_array *kSq_ho; // k square on host.
   bool ishelmholtz; // If solving Helmholtz equation (kSq is not zero/NULL).
-  bool make_stiff; // Flag to indicate if we need to remake the stiffness matrix.
-  struct gkyl_mat_triples **tri; // Matrix triples for building stiffness matrices.
 
   bool isdomperiodic; // =true if all directions are periodic.
   struct gkyl_array *rhs_cellavg;

From e36d84eccc463be0b98d10928d05ad88a726fc1d Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 25 Apr 2026 10:17:14 -0400
Subject: [PATCH 150/181] set IWL updater for EM too

---
 gyrokinetic/apps/gk_field_2x3x.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 0bfe30d489..3ad7b35493 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -550,7 +550,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   }
 
   // Twist-and-shift boundary condition for phi and skin surface from ghost to impose phi periodicity at z=-pi.
-  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL) {
+  if (f->gkfield_id == GKYL_GK_FIELD_ES_IWL || f->gkfield_id == GKYL_GK_FIELD_EM_IWL) {
     gk_field_2x3x_add_IWL_updaters(app, f);
   }
 

From 2225a385d311c2ecd5a33355847e4e77ef1cc5cc Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 25 Apr 2026 11:20:46 -0400
Subject: [PATCH 151/181] put back the PT q profile as the NT one makes the
 regression test unstable

---
 gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 4f7a4686e8..80ddb2f5af 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -50,10 +50,10 @@ double r_x(double x, double a_mid, double x_inner)
   return x+a_mid-x_inner;
 }
 
-// cubic polynomial fit to TCV NT q profile (discharge #65130)
+// cubic polynomial fit to TCV PT q profile (more stable for reg test than NT one).
 double qprofile(double R) {
   double qfit[4] = {
-    484.0615913225881, -1378.25993228584, 1309.3099150729233, -414.13270311478726
+    497.3420166252413, -1408.736172826569, 1331.4134861681464, -419.00692601227627
   };
   return qfit[0]*pow(R,3) + qfit[1]*pow(R,2) + qfit[2]*R + qfit[3];
 }

From 0bb65ce7e964e620081d2e6f0b969cd9b3f49136 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 25 Apr 2026 12:07:56 -0700
Subject: [PATCH 152/181] The code is valgrind and compute sanitizer clean
 except some NCCL error cudaErrorNoKernelImageForDevice.We see a great
 performance improvement on GPU thanks to the LHS update routine in the Ohm's
 solve. The TSBC is not implemented for Apar yet.

---
 gyrokinetic/apps/gk_field_2x3x.c         | 14 ++++++--------
 gyrokinetic/zero/gkyl_fem_poisson_perp.h | 22 ----------------------
 2 files changed, 6 insertions(+), 30 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 3ad7b35493..add22c2090 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -224,14 +224,7 @@ static void
 gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
   
-  // The update of kSq is causing issues with leaks and valgrind.
-  // gkyl_fem_poisson_perp_update_kSq(field->fem_apardot_solver, field->dApartdtSlvr_kSq);
-
-  // Temporary solution to avoid superLU leak when updating kSq: we release and re-create the solver
-  gkyl_fem_poisson_perp_release(field->fem_apardot_solver);
-  field->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-    &field->ampere_bcs, field->info.bias_line_list, field->lapWeightAmpere, field->dApartdtSlvr_kSq, app->use_gpu);
-
+  gkyl_fem_poisson_perp_update_lhs(field->fem_apardot_solver, field->lapWeightAmpere, field->dApartdtSlvr_kSq);
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
   gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
 
@@ -522,6 +515,11 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     // FEM solver for Ohm's law (evolves d(Apart)/dt).
     f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
       &f->ampere_bcs, f->info.bias_line_list, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+
+    // We have to advance the updater once to be able to update the kSq later.
+    gkyl_fem_poisson_perp_set_rhs(f->fem_apardot_solver, f->currentDensdot);
+    gkyl_fem_poisson_perp_solve(f->fem_apardot_solver, f->apardot);
+    
     // FEM smoother for Aparallel.
     f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
     f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
diff --git a/gyrokinetic/zero/gkyl_fem_poisson_perp.h b/gyrokinetic/zero/gkyl_fem_poisson_perp.h
index 968827c29d..d68db9e9f8 100644
--- a/gyrokinetic/zero/gkyl_fem_poisson_perp.h
+++ b/gyrokinetic/zero/gkyl_fem_poisson_perp.h
@@ -41,28 +41,6 @@ struct gkyl_fem_poisson_perp* gkyl_fem_poisson_perp_new(
   const struct gkyl_basis basis, struct gkyl_poisson_bc *bcs, struct gkyl_poisson_bias_line_list* bias_line_list,
   struct gkyl_array *epsilon, struct gkyl_array *kSq, bool use_gpu);
 
-/**
- * Update the epsilon array and set the make_stiff flag to true to recompute stiffness
- * matrix at the next solve call.
- * 
- * @param up updater to solver.
- * @param epsilon new epsilon array.
- */
-void
-gkyl_fem_poisson_perp_update_epsilon(struct gkyl_fem_poisson_perp *up, struct gkyl_array *epsilon);
-
-/**
- * Update the kSq array and set the make_stiff flag to true to recompute stiffness
- * matrix at the next solve call. The kSq must be passed as a non Null pointer to array
- * in the gkyl_fem_poisson_perp_new call.
- * 
- * @param up updater to solver.
- * @param kSq new kSq array.
- */
-void
-gkyl_fem_poisson_perp_update_kSq(struct gkyl_fem_poisson_perp *up, struct gkyl_array *kSq);
-
-
 /**
  * Assign the right-side vector with the discontinuous (DG) source field.
  *

From ee5f6d79968a7e253b878bdec830fe302da8155d Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 27 Apr 2026 11:22:18 -0400
Subject: [PATCH 153/181] remove unnecessary cleanup of 'wk' files in the
 Makefile

---
 Makefile_for_ext_C_input | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Makefile_for_ext_C_input b/Makefile_for_ext_C_input
index cf44bb3df3..7f6c00f8a4 100644
--- a/Makefile_for_ext_C_input
+++ b/Makefile_for_ext_C_input
@@ -154,4 +154,4 @@ $(BINS): %: %.c
 	${CC} ${CFLAGS} ${INCLUDES} $< -o $@ -L${G0_LIB_DIR} ${G0_RPATH} ${G0_LIBS} ${LIB_DIRS} ${EXT_LIBS}
 
 clean:
-	rm -rf $(BINS) *.d wk
+	rm -rf $(BINS) *.d

From c2a0e04376bf654354ceb3cbf5da813c1c15915a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 27 Apr 2026 13:58:11 -0400
Subject: [PATCH 154/181] Merge of EM and ES kernels to simplify the code.

---
 core/zero/gkyl_eqn_type.h                     |   2 -
 gyrokinetic/apps/gk_field.c                   |   4 +-
 gyrokinetic/apps/gk_species.c                 |   3 +-
 gyrokinetic/apps/gk_species_collisionless.c   |   4 +-
 gyrokinetic/apps/gyrokinetic_lw.c             |   2 -
 ...ollisionless_flux_edge_surfx_1x1v_ser_p1.c |   3 +
 ...ollisionless_flux_edge_surfx_1x2v_ser_p1.c |   3 +
 ...ollisionless_flux_edge_surfx_2x2v_ser_p1.c |  28 +
 ...ollisionless_flux_edge_surfx_3x2v_ser_p1.c |  54 ++
 ...ollisionless_flux_edge_surfy_2x2v_ser_p1.c |  28 +
 ...ollisionless_flux_edge_surfy_3x2v_ser_p1.c |  54 ++
 ...ollisionless_flux_edge_surfz_3x2v_ser_p1.c |  54 ++
 ...isionless_flux_em_edge_surfx_1x1v_ser_p1.c | 107 ---
 ...isionless_flux_em_edge_surfx_1x2v_ser_p1.c | 141 ---
 ...isionless_flux_em_edge_surfx_2x2v_ser_p1.c | 257 ------
 ...isionless_flux_em_edge_surfx_3x2v_ser_p1.c | 450 ----------
 ...isionless_flux_em_edge_surfy_2x2v_ser_p1.c | 257 ------
 ...isionless_flux_em_edge_surfy_3x2v_ser_p1.c | 452 ----------
 ...isionless_flux_em_edge_surfz_3x2v_ser_p1.c | 450 ----------
 ...m_multib_boundary_edge_surfx_1x1v_ser_p1.c | 109 ---
 ...m_multib_boundary_edge_surfx_1x2v_ser_p1.c | 143 ---
 ...m_multib_boundary_edge_surfx_2x2v_ser_p1.c | 271 ------
 ...m_multib_boundary_edge_surfx_3x2v_ser_p1.c | 476 ----------
 ...m_multib_boundary_edge_surfy_2x2v_ser_p1.c | 271 ------
 ...m_multib_boundary_edge_surfy_3x2v_ser_p1.c | 478 ----------
 ...m_multib_boundary_edge_surfz_3x2v_ser_p1.c | 476 ----------
 ...lux_em_multib_boundary_surfx_1x1v_ser_p1.c | 109 ---
 ...lux_em_multib_boundary_surfx_1x2v_ser_p1.c | 143 ---
 ...lux_em_multib_boundary_surfx_2x2v_ser_p1.c | 271 ------
 ...lux_em_multib_boundary_surfx_3x2v_ser_p1.c | 476 ----------
 ...lux_em_multib_boundary_surfy_2x2v_ser_p1.c | 271 ------
 ...lux_em_multib_boundary_surfy_3x2v_ser_p1.c | 478 ----------
 ...lux_em_multib_boundary_surfz_3x2v_ser_p1.c | 476 ----------
 ...ess_flux_em_no_by_edge_surfx_2x2v_ser_p1.c | 209 -----
 ...ess_flux_em_no_by_edge_surfx_3x2v_ser_p1.c | 354 --------
 ...ess_flux_em_no_by_edge_surfy_2x2v_ser_p1.c | 209 -----
 ...ess_flux_em_no_by_edge_surfy_3x2v_ser_p1.c | 356 --------
 ...ess_flux_em_no_by_edge_surfz_3x2v_ser_p1.c | 354 --------
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c | 223 -----
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c | 380 --------
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c | 223 -----
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c | 382 --------
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c | 380 --------
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c | 223 -----
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c | 380 --------
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c | 223 -----
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c | 382 --------
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c | 380 --------
 ...nless_flux_em_no_by_surfvpar_2x2v_ser_p1.c | 176 ----
 ...nless_flux_em_no_by_surfvpar_3x2v_ser_p1.c | 297 ------
 ...sionless_flux_em_no_by_surfx_2x2v_ser_p1.c | 209 -----
 ...sionless_flux_em_no_by_surfx_3x2v_ser_p1.c | 354 --------
 ...sionless_flux_em_no_by_surfy_2x2v_ser_p1.c | 209 -----
 ...sionless_flux_em_no_by_surfy_3x2v_ser_p1.c | 356 --------
 ...sionless_flux_em_no_by_surfz_3x2v_ser_p1.c | 354 --------
 ...less_flux_em_star_edge_surfx_1x1v_ser_p1.c | 107 ---
 ...less_flux_em_star_edge_surfx_1x2v_ser_p1.c | 141 ---
 ...less_flux_em_star_edge_surfx_2x2v_ser_p1.c | 257 ------
 ...less_flux_em_star_edge_surfx_3x2v_ser_p1.c | 450 ----------
 ...less_flux_em_star_edge_surfy_2x2v_ser_p1.c | 257 ------
 ...less_flux_em_star_edge_surfy_3x2v_ser_p1.c | 452 ----------
 ...less_flux_em_star_edge_surfz_3x2v_ser_p1.c | 450 ----------
 ...r_multib_boundary_edge_surfx_1x1v_ser_p1.c | 109 ---
 ...r_multib_boundary_edge_surfx_1x2v_ser_p1.c | 143 ---
 ...r_multib_boundary_edge_surfx_2x2v_ser_p1.c | 271 ------
 ...r_multib_boundary_edge_surfx_3x2v_ser_p1.c | 476 ----------
 ...r_multib_boundary_edge_surfy_2x2v_ser_p1.c | 271 ------
 ...r_multib_boundary_edge_surfy_3x2v_ser_p1.c | 478 ----------
 ...r_multib_boundary_edge_surfz_3x2v_ser_p1.c | 476 ----------
 ...m_star_multib_boundary_surfx_1x1v_ser_p1.c | 109 ---
 ...m_star_multib_boundary_surfx_1x2v_ser_p1.c | 143 ---
 ...m_star_multib_boundary_surfx_2x2v_ser_p1.c | 271 ------
 ...m_star_multib_boundary_surfx_3x2v_ser_p1.c | 476 ----------
 ...m_star_multib_boundary_surfy_2x2v_ser_p1.c | 271 ------
 ...m_star_multib_boundary_surfy_3x2v_ser_p1.c | 478 ----------
 ...m_star_multib_boundary_surfz_3x2v_ser_p1.c | 476 ----------
 ...lux_em_star_no_by_edge_surfx_2x2v_ser_p1.c | 209 -----
 ...lux_em_star_no_by_edge_surfx_3x2v_ser_p1.c | 354 --------
 ...lux_em_star_no_by_edge_surfy_2x2v_ser_p1.c | 209 -----
 ...lux_em_star_no_by_edge_surfy_3x2v_ser_p1.c | 356 --------
 ...lux_em_star_no_by_edge_surfz_3x2v_ser_p1.c | 354 --------
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c | 223 -----
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c | 380 --------
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c | 223 -----
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c | 382 --------
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c | 380 --------
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c | 223 -----
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c | 380 --------
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c | 223 -----
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c | 382 --------
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c | 380 --------
 ..._flux_em_star_no_by_surfvpar_2x2v_ser_p1.c | 168 ----
 ..._flux_em_star_no_by_surfvpar_3x2v_ser_p1.c | 281 ------
 ...ess_flux_em_star_no_by_surfx_2x2v_ser_p1.c | 209 -----
 ...ess_flux_em_star_no_by_surfx_3x2v_ser_p1.c | 354 --------
 ...ess_flux_em_star_no_by_surfy_2x2v_ser_p1.c | 209 -----
 ...ess_flux_em_star_no_by_surfy_3x2v_ser_p1.c | 356 --------
 ...ess_flux_em_star_no_by_surfz_3x2v_ser_p1.c | 354 --------
 ...onless_flux_em_star_surfvpar_1x1v_ser_p1.c |  93 --
 ...onless_flux_em_star_surfvpar_1x2v_ser_p1.c | 117 ---
 ...onless_flux_em_star_surfvpar_2x2v_ser_p1.c | 216 -----
 ...onless_flux_em_star_surfvpar_3x2v_ser_p1.c | 425 ---------
 ...isionless_flux_em_star_surfx_1x1v_ser_p1.c | 107 ---
 ...isionless_flux_em_star_surfx_1x2v_ser_p1.c | 141 ---
 ...isionless_flux_em_star_surfx_2x2v_ser_p1.c | 257 ------
 ...isionless_flux_em_star_surfx_3x2v_ser_p1.c | 450 ----------
 ...isionless_flux_em_star_surfy_2x2v_ser_p1.c | 257 ------
 ...isionless_flux_em_star_surfy_3x2v_ser_p1.c | 452 ----------
 ...isionless_flux_em_star_surfz_3x2v_ser_p1.c | 450 ----------
 ...llisionless_flux_em_surfvpar_1x1v_ser_p1.c |  95 --
 ...llisionless_flux_em_surfvpar_1x2v_ser_p1.c | 121 ---
 ...llisionless_flux_em_surfvpar_2x2v_ser_p1.c | 224 -----
 ...llisionless_flux_em_surfvpar_3x2v_ser_p1.c | 441 ---------
 ..._collisionless_flux_em_surfx_1x1v_ser_p1.c | 107 ---
 ..._collisionless_flux_em_surfx_1x2v_ser_p1.c | 141 ---
 ..._collisionless_flux_em_surfx_2x2v_ser_p1.c | 257 ------
 ..._collisionless_flux_em_surfx_3x2v_ser_p1.c | 450 ----------
 ..._collisionless_flux_em_surfy_2x2v_ser_p1.c | 257 ------
 ..._collisionless_flux_em_surfy_3x2v_ser_p1.c | 452 ----------
 ..._collisionless_flux_em_surfz_3x2v_ser_p1.c | 450 ----------
 ...x_multib_boundary_edge_surfx_1x1v_ser_p1.c |   3 +
 ...x_multib_boundary_edge_surfx_1x2v_ser_p1.c |   3 +
 ...x_multib_boundary_edge_surfx_2x2v_ser_p1.c |  28 +
 ...x_multib_boundary_edge_surfx_3x2v_ser_p1.c |  54 ++
 ...x_multib_boundary_edge_surfy_2x2v_ser_p1.c |  28 +
 ...x_multib_boundary_edge_surfy_3x2v_ser_p1.c |  54 ++
 ...x_multib_boundary_edge_surfz_3x2v_ser_p1.c |  54 ++
 ...s_flux_multib_boundary_surfx_1x1v_ser_p1.c |   3 +
 ...s_flux_multib_boundary_surfx_1x2v_ser_p1.c |   3 +
 ...s_flux_multib_boundary_surfx_2x2v_ser_p1.c |  28 +
 ...s_flux_multib_boundary_surfx_3x2v_ser_p1.c |  54 ++
 ...s_flux_multib_boundary_surfy_2x2v_ser_p1.c |  28 +
 ...s_flux_multib_boundary_surfy_3x2v_ser_p1.c |  54 ++
 ...s_flux_multib_boundary_surfz_3x2v_ser_p1.c |  54 ++
 ...onless_flux_no_by_edge_surfx_2x2v_ser_p1.c |   4 +
 ...onless_flux_no_by_edge_surfx_3x2v_ser_p1.c |   6 +
 ...onless_flux_no_by_edge_surfy_2x2v_ser_p1.c |   4 +
 ...onless_flux_no_by_edge_surfy_3x2v_ser_p1.c |   6 +
 ...onless_flux_no_by_edge_surfz_3x2v_ser_p1.c |   6 +
 ...y_multib_boundary_edge_surfx_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfx_3x2v_ser_p1.c |   6 +
 ...y_multib_boundary_edge_surfy_2x2v_ser_p1.c |   4 +
 ...y_multib_boundary_edge_surfy_3x2v_ser_p1.c |   6 +
 ...y_multib_boundary_edge_surfz_3x2v_ser_p1.c |   6 +
 ..._no_by_multib_boundary_surfx_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfx_3x2v_ser_p1.c |   6 +
 ..._no_by_multib_boundary_surfy_2x2v_ser_p1.c |   4 +
 ..._no_by_multib_boundary_surfy_3x2v_ser_p1.c |   6 +
 ..._no_by_multib_boundary_surfz_3x2v_ser_p1.c |   6 +
 ...sionless_flux_no_by_surfvpar_2x2v_ser_p1.c |  21 +
 ...sionless_flux_no_by_surfvpar_3x2v_ser_p1.c |  41 +
 ...llisionless_flux_no_by_surfx_2x2v_ser_p1.c |   4 +
 ...llisionless_flux_no_by_surfx_3x2v_ser_p1.c |   6 +
 ...llisionless_flux_no_by_surfy_2x2v_ser_p1.c |   4 +
 ...llisionless_flux_no_by_surfy_3x2v_ser_p1.c |   6 +
 ...llisionless_flux_no_by_surfz_3x2v_ser_p1.c |   6 +
 .../gk_collisionless_flux_surfconf_none.c     |  11 -
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |  11 +
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |  15 +
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  53 ++
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c | 137 +++
 .../gk_collisionless_flux_surfvpar_none.c     |  11 -
 .../gk_collisionless_flux_surfx_1x1v_ser_p1.c |   3 +
 .../gk_collisionless_flux_surfx_1x2v_ser_p1.c |   3 +
 .../gk_collisionless_flux_surfx_2x2v_ser_p1.c |  28 +
 .../gk_collisionless_flux_surfx_3x2v_ser_p1.c |  54 ++
 .../gk_collisionless_flux_surfy_2x2v_ser_p1.c |  28 +
 .../gk_collisionless_flux_surfy_3x2v_ser_p1.c |  54 ++
 .../gk_collisionless_flux_surfz_3x2v_ser_p1.c |  54 ++
 .../gkyl_gk_collisionless_flux_kernels.h      | 772 +---------------
 gyrokinetic/zero/dg_gyrokinetic.c             |   2 +-
 gyrokinetic/zero/dg_gyrokinetic_cu.cu         |   2 +-
 gyrokinetic/zero/gk_collisionless_flux.c      |  45 +-
 gyrokinetic/zero/gk_collisionless_flux_cu.cu  |  47 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 845 ++++--------------
 175 files changed, 1541 insertions(+), 33773 deletions(-)
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
 delete mode 100644 gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
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diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index b3679c218e..099650bf79 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -181,8 +181,6 @@ enum gkyl_gk_anomalous_diff_id {
 enum gkyl_gk_collisionless_type {
   GKYL_GK_COLLISIONLESS_NONE = 0, // Turns off collisionless terms.
   GKYL_GK_COLLISIONLESS_ES, // Electrostatic.
-  GKYL_GK_COLLISIONLESS_EM_BPERP, // Electromagnetic with B_perp fluctuations.
-  GKYL_GK_COLLISIONLESS_EM_BPAR, // Electromagnetic with B_par fluctuations.
   GKYL_GK_COLLISIONLESS_EM, // Electromagnetic with B_perp and B_par fluctuations.
   GKYL_GK_COLLISIONLESS_NEUTRAL, // Neutral collisionless terms.
 };
diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 3f78e63319..84c4562116 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -390,9 +390,7 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-    f->is_em = f->is_em || (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) || 
-                      (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP) ||
-                      (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPAR);
+    f->is_em = f->is_em || (s->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM);
   }
   if (f->is_em) {
     assert(f->info.mu0 > 0.0);
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 8b6eb5116d..985bad7d48 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -978,8 +978,7 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
 
   // Set function pointers.
   gks->rhs_func = gk_species_rhs_dynamic;
-  if ((gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM) 
-   || (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM_BPERP)){
+  if (gks->info.collisionless.type == GKYL_GK_COLLISIONLESS_EM){
     gks->rhs_em_complete_func = gk_species_rhs_em_complete_dynamic;
   } else {
     gks->rhs_em_complete_func = gk_species_rhs_static;
diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index 5202d5499d..d07f9c254e 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -199,7 +199,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     }
 
     // Electromagnetic set up.
-    if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) {
       // Set up ES + Apar contributions to flux and solver.
       complete_em = true;
       gkcls->surf_flux_em_star_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
@@ -254,7 +254,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_gk_collisionless_flux_release(gkcls->surf_flux_op);
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
-    if ((gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) || (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM_BPERP)) {
+    if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) {
       gkyl_gk_collisionless_flux_release(gkcls->surf_flux_em_star_op);
       gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_em_complete);
     }
diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 3d2edb9563..d5faff9d54 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -59,8 +59,6 @@ static const struct gkyl_str_int_pair position_map_type[] = {
 static const struct gkyl_str_int_pair gk_collisionless_type[] = {
   { "None", GKYL_GK_COLLISIONLESS_NONE },
   { "GKCollisionlessES", GKYL_GK_COLLISIONLESS_ES },
-  { "GKCollisionlessEM_Bperp", GKYL_GK_COLLISIONLESS_EM_BPERP },
-  { "GKCollisionlessEM_Bpar", GKYL_GK_COLLISIONLESS_EM_BPAR },
   { "GKCollisionlessEM", GKYL_GK_COLLISIONLESS_EM },
   { 0, 0 }
 };
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
index 8f17e490dc..4aa72445b1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
index 98068d61bd..b91a2fc316 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_1x2v_ser_p1(
   hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
index 3570650c26..12b2aa34fc 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,6 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -84,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -96,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -190,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -202,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
index 7222eb7a57..03a8b25f73 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,6 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -87,6 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -135,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,6 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -217,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,6 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -275,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -287,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,6 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,6 +377,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -369,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -381,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
index de86af7df4..fd592e6db1 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,6 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -84,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -96,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -190,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -202,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
index 31f7efb238..c11bbbc59b 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,6 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -101,6 +111,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,6 +191,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +205,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +233,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,6 +285,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +299,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +313,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +341,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -323,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,6 +379,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +393,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +407,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +421,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +435,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
index 9b36f8f09f..318d3b38df 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,6 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -87,6 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -135,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,6 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -217,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,6 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -275,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -287,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,6 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,6 +377,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -369,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -381,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 5bb6b0a75a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,107 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 5adfce3283..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,141 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index e8896c6d4b..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 87af2dae39..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 73ee4404df..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index e681b9589f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,452 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 31a7ccd890..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index ae20218be5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,109 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double JRatfR[3] = {0.}; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index b7a042a1fe..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,143 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double JRatfR[6] = {0.}; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 6a867658a9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 3735fbdf54..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 7441ae3793..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 97b2d0679d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,478 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 077c9205dd..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 1e42e613b9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,109 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double JRatfL[3] = {0.}; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
deleted file mode 100644
index ec14fa1571..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,143 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double JRatfL[6] = {0.}; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 68ab1cb353..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 9fff406b73..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 64dbe2da91..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 536e6c34d8..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,478 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index bc1cb3ba1e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index ba90f5a442..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index a3b36fbf3f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index e082865dc9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index adbfed0e0a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,356 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 00b7d70fe6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 7d0f83ae5f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 8899b591f9..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 1d1911e717..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 4023c31e6e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,382 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 939c66a928..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index bd65d6e496..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index a68f391f0e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index f460213950..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 352a5f8155..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,382 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index c1e212a51e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index 5a7695a864..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,176 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
-  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 7de5131f8b..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,297 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_; 
-  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[4] = 2.0*vmapSq[1]*m_; 
-  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[6] = 2.0*phi[4]*q_; 
-  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
-  hamil[8] = 2.0*phi[6]*q_; 
-  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 2.0*phi[7]*q_; 
-  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
-  hamil[32] = 2.0*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[72]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[4].bmag; 
-  B3_quad = gkdgv[4].B3; 
-  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[5].bmag; 
-  B3_quad = gkdgv[5].B3; 
-  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[6].bmag; 
-  B3_quad = gkdgv[6].B3; 
-  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[7].bmag; 
-  B3_quad = gkdgv[7].B3; 
-  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 0fc1866a80..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
deleted file mode 100644
index a7e78831e7..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
deleted file mode 100644
index b73446db49..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 0d0c2981ff..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,356 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 53d8775015..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 898f51cea6..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,107 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 1cac10f2af..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,141 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index e1db697a7a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 74499dc569..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index b034de3f86..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 373f4cd523..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,452 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index b9ffb09703..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
deleted file mode 100644
index b6234d654d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,109 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (1.7320508075688772*phi[1]+phi[0])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double JRatfR[3] = {0.}; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 2794ea343b..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,143 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+0.7071067811865475*vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double JRatfR[6] = {0.}; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.0; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index ec2773a9be..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 801cfd794d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 4b0279bad1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 8d590940f2..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,478 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index de6e8f5375..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 94941234a0..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,109 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double JRatfL[3] = {0.}; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 98e5834ab7..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,143 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double JRatfL[6] = {0.}; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.0; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 5b9a29e4d3..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 18e9c75f3c..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 6eb39e2e81..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,271 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index f67ec48d4d..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,478 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 86a4032c6c..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,476 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 16107a4bfd..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index e348146b19..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index c08a9acce7..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index d96fbc8007..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,356 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 5b80440dcb..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
deleted file mode 100644
index c92a1ac2c5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[1]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[2])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[2]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[1])-1.0*(jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+JfR[1]*jacobgeo_rat_surfR[1])-1.0*(jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[6])-1.0*(jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[8])-1.0*(jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[6])-1.0*(jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[8])-1.0*(jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[13])-1.0*(jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[13])-1.0*(jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[18]-3.0*jacobgeo_rat_surfR[0]*JfR[17])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])+15.0*jacobgeo_rat_surfR[0]*JfR[18]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 2707c88374..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[1]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(1.7320508075688772*bmag[1]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[2])*q_; 
-  hamil[2] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[3])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[1]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[6])*q_; 
-  hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[3]+jacobgeo_rat_surfR[1]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[1])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[8]+JfR[3]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[2]+JfR[0]*jacobgeo_rat_surfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[8]+JfR[2]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[8]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[2]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[9])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[12])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[23])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[37])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[34])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[33]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[34])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[44])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[34])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[33]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[32])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[37])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[41])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
-  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
deleted file mode 100644
index be05533432..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (2.4494897427831783*phi[2]+1.4142135623730951*phi[0])*q_+vmapSq[0]*m_+(1.7320508075688772*bmag[2]+bmag[0])*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[3]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[3]+bmag[1]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (1.7320508075688772*bmag[2]+bmag[0])*vmap[3]; 
-  hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfR[12] = {0.}; 
-  JRatfR[0] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[5]+jacobgeo_rat_surfR[0]*JfR[2])-1.0*(JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[5]+jacobgeo_rat_surfR[1]*JfR[2])-1.0*(JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[7])-1.0*(jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[3]))); 
-  JRatfR[3] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[9])-1.0*(jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[7])-1.0*(jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[3]))); 
-  JRatfR[5] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[9])-1.0*(jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[6] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[1]*JfR[15]+jacobgeo_rat_surfR[0]*JfR[14])-1.0*(jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[10]))); 
-  JRatfR[7] = -(0.5*(1.7320508075688772*(jacobgeo_rat_surfR[0]*JfR[15]+jacobgeo_rat_surfR[1]*JfR[14])-1.0*(jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[10]))); 
-  JRatfR[8] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[20])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[17]-3.0*jacobgeo_rat_surfR[0]*JfR[18])+15.0*jacobgeo_rat_surfR[0]*JfR[16]); 
-  JRatfR[9] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[16]-3.0*jacobgeo_rat_surfR[0]*JfR[20])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[18]+15.0*jacobgeo_rat_surfR[0]*JfR[17]); 
-  JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
-  JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])+0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*JRatfR[5]-0.3535533905932737*(JRatfR[3]+JRatfR[1])+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3162277660168379*JRatfR[11]-0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*JRatfR[7]-0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3952847075210473*JRatfR[11]-0.39528470752104733*JRatfR[10]+0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*JRatfR[5]+0.3535533905932737*JRatfR[3]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])+0.31622776601683794*JRatfR[10]-0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*JRatfR[7]+0.4743416490252568*JRatfR[6]-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]-0.3535533905932737*JRatfR[1]+0.3535533905932737*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3952847075210473*JRatfR[11]+0.39528470752104733*JRatfR[10]-0.39528470752104733*JRatfR[9]-0.3952847075210473*JRatfR[8]-0.3535533905932737*(JRatfR[5]+JRatfR[3])+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3162277660168379*JRatfR[11])-0.31622776601683794*JRatfR[10]+0.31622776601683794*JRatfR[9]+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])-0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]-0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]-0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]-0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]-0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3952847075210473*JRatfR[11])-0.39528470752104733*(JRatfR[10]+JRatfR[9])-0.3952847075210473*JRatfR[8]+0.3535533905932737*(JRatfR[5]+JRatfR[3]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3162277660168379*JRatfR[11]+0.31622776601683794*(JRatfR[10]+JRatfR[9])+0.3162277660168379*JRatfR[8]+0.4743416490252568*(JRatfR[7]+JRatfR[6])+0.3535533905932737*JRatfR[5]+0.4743416490252568*JRatfR[4]+0.3535533905932737*JRatfR[3]+0.4743416490252568*JRatfR[2]+0.3535533905932737*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 16a921c788..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,382 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[2]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (2.4494897427831783*phi[4]+1.4142135623730951*phi[1])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[3])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[5])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[6]+jacobgeo_rat_surfR[0]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[6]+jacobgeo_rat_surfR[1]*JfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[7]+JfR[1]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[0]*JfR[3]+JfR[0]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[7]+JfR[0]*jacobgeo_rat_surfR[3]+jacobgeo_rat_surfR[1]*JfR[3]+JfR[1]*jacobgeo_rat_surfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[35]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[38]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[38]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[35]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[34]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[38]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[37]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[35]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[42]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[45]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[35]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[34]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[37])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[38]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[45]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[42]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
deleted file mode 100644
index fe114feeb1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.4494897427831783*phi[3]*q_+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(1.7320508075688772*bmag[3]+bmag[0]); 
-  hamil[1] = (2.4494897427831783*phi[5]+1.4142135623730951*phi[1])*q_+vmap[2]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[2] = (2.4494897427831783*phi[6]+1.4142135623730951*phi[2])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (1.7320508075688772*bmag[3]+bmag[0])*vmap[3]; 
-  hamil[5] = (2.4494897427831783*phi[7]+1.4142135623730951*phi[4])*q_; 
-  hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfR[24] = {0.}; 
-  JRatfR[0] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[16]+jacobgeo_rat_surfR[2]*JfR[8]+jacobgeo_rat_surfR[1]*JfR[7]+jacobgeo_rat_surfR[0]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[2]+JfR[1]*jacobgeo_rat_surfR[1]+JfR[0]*jacobgeo_rat_surfR[0]))); 
-  JRatfR[1] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[16]+jacobgeo_rat_surfR[3]*JfR[8]+jacobgeo_rat_surfR[0]*JfR[7]+jacobgeo_rat_surfR[1]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[6]+JfR[2]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[1]+jacobgeo_rat_surfR[0]*JfR[1]))); 
-  JRatfR[2] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[16]+jacobgeo_rat_surfR[0]*JfR[8]+jacobgeo_rat_surfR[3]*JfR[7]+jacobgeo_rat_surfR[2]*JfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[6]+JfR[1]*jacobgeo_rat_surfR[3]+JfR[0]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[0]*JfR[2]))); 
-  JRatfR[3] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[26]+jacobgeo_rat_surfR[2]*JfR[19]+jacobgeo_rat_surfR[1]*JfR[18]+jacobgeo_rat_surfR[0]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[17]+jacobgeo_rat_surfR[2]*JfR[10]+jacobgeo_rat_surfR[1]*JfR[9]+jacobgeo_rat_surfR[0]*JfR[4]))); 
-  JRatfR[4] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[27]+jacobgeo_rat_surfR[2]*JfR[22]+jacobgeo_rat_surfR[1]*JfR[21]+jacobgeo_rat_surfR[0]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[20]+jacobgeo_rat_surfR[2]*JfR[13]+jacobgeo_rat_surfR[1]*JfR[12]+jacobgeo_rat_surfR[0]*JfR[5]))); 
-  JRatfR[5] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[16]+jacobgeo_rat_surfR[1]*JfR[8]+jacobgeo_rat_surfR[2]*JfR[7]+JfR[3]*jacobgeo_rat_surfR[3])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[6]+JfR[0]*jacobgeo_rat_surfR[3]+JfR[1]*jacobgeo_rat_surfR[2]+jacobgeo_rat_surfR[1]*JfR[2]))); 
-  JRatfR[6] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[26]+jacobgeo_rat_surfR[3]*JfR[19]+jacobgeo_rat_surfR[0]*JfR[18]+jacobgeo_rat_surfR[1]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[17]+jacobgeo_rat_surfR[3]*JfR[10]+jacobgeo_rat_surfR[0]*JfR[9]+jacobgeo_rat_surfR[1]*JfR[4]))); 
-  JRatfR[7] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[26]+jacobgeo_rat_surfR[0]*JfR[19]+jacobgeo_rat_surfR[3]*JfR[18]+jacobgeo_rat_surfR[2]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[17]+jacobgeo_rat_surfR[0]*JfR[10]+jacobgeo_rat_surfR[3]*JfR[9]+jacobgeo_rat_surfR[2]*JfR[4]))); 
-  JRatfR[8] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[27]+jacobgeo_rat_surfR[3]*JfR[22]+jacobgeo_rat_surfR[0]*JfR[21]+jacobgeo_rat_surfR[1]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[20]+jacobgeo_rat_surfR[3]*JfR[13]+jacobgeo_rat_surfR[0]*JfR[12]+jacobgeo_rat_surfR[1]*JfR[5]))); 
-  JRatfR[9] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[27]+jacobgeo_rat_surfR[0]*JfR[22]+jacobgeo_rat_surfR[3]*JfR[21]+jacobgeo_rat_surfR[2]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[20]+jacobgeo_rat_surfR[0]*JfR[13]+jacobgeo_rat_surfR[3]*JfR[12]+jacobgeo_rat_surfR[2]*JfR[5]))); 
-  JRatfR[10] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[3]*JfR[31]+jacobgeo_rat_surfR[2]*JfR[30]+jacobgeo_rat_surfR[1]*JfR[29]+jacobgeo_rat_surfR[0]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[3]*JfR[28]+jacobgeo_rat_surfR[2]*JfR[24]+jacobgeo_rat_surfR[1]*JfR[23]+jacobgeo_rat_surfR[0]*JfR[15]))); 
-  JRatfR[11] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[26]+jacobgeo_rat_surfR[1]*JfR[19]+jacobgeo_rat_surfR[2]*JfR[18]+jacobgeo_rat_surfR[3]*JfR[11])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[17]+jacobgeo_rat_surfR[1]*JfR[10]+jacobgeo_rat_surfR[2]*JfR[9]+jacobgeo_rat_surfR[3]*JfR[4]))); 
-  JRatfR[12] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[27]+jacobgeo_rat_surfR[1]*JfR[22]+jacobgeo_rat_surfR[2]*JfR[21]+jacobgeo_rat_surfR[3]*JfR[14])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[20]+jacobgeo_rat_surfR[1]*JfR[13]+jacobgeo_rat_surfR[2]*JfR[12]+jacobgeo_rat_surfR[3]*JfR[5]))); 
-  JRatfR[13] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[31]+jacobgeo_rat_surfR[3]*JfR[30]+jacobgeo_rat_surfR[0]*JfR[29]+jacobgeo_rat_surfR[1]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[2]*JfR[28]+jacobgeo_rat_surfR[3]*JfR[24]+jacobgeo_rat_surfR[0]*JfR[23]+jacobgeo_rat_surfR[1]*JfR[15]))); 
-  JRatfR[14] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[31]+jacobgeo_rat_surfR[0]*JfR[30]+jacobgeo_rat_surfR[3]*JfR[29]+jacobgeo_rat_surfR[2]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[1]*JfR[28]+jacobgeo_rat_surfR[0]*JfR[24]+jacobgeo_rat_surfR[3]*JfR[23]+jacobgeo_rat_surfR[2]*JfR[15]))); 
-  JRatfR[15] = -(0.25*(2.4494897427831783*(jacobgeo_rat_surfR[0]*JfR[31]+jacobgeo_rat_surfR[1]*JfR[30]+jacobgeo_rat_surfR[2]*JfR[29]+jacobgeo_rat_surfR[3]*JfR[25])-1.4142135623730951*(jacobgeo_rat_surfR[0]*JfR[28]+jacobgeo_rat_surfR[1]*JfR[24]+jacobgeo_rat_surfR[2]*JfR[23]+jacobgeo_rat_surfR[3]*JfR[15]))); 
-  JRatfR[16] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[34]+jacobgeo_rat_surfR[1]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[43]+jacobgeo_rat_surfR[0]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[39]+jacobgeo_rat_surfR[1]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[37]+jacobgeo_rat_surfR[0]*JfR[32])); 
-  JRatfR[17] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[43]+jacobgeo_rat_surfR[1]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[37]+jacobgeo_rat_surfR[1]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[39]+jacobgeo_rat_surfR[0]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[34]+jacobgeo_rat_surfR[0]*JfR[33])); 
-  JRatfR[18] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[43]+jacobgeo_rat_surfR[2]*JfR[35]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[37]+jacobgeo_rat_surfR[2]*JfR[32])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[39]+jacobgeo_rat_surfR[3]*JfR[38]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[34]+jacobgeo_rat_surfR[3]*JfR[33])); 
-  JRatfR[19] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[41]+jacobgeo_rat_surfR[1]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[47]+jacobgeo_rat_surfR[0]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[46]+jacobgeo_rat_surfR[1]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[44]+jacobgeo_rat_surfR[0]*JfR[36])); 
-  JRatfR[20] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[34]+jacobgeo_rat_surfR[2]*JfR[33])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[43]+jacobgeo_rat_surfR[3]*JfR[35]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[39]+jacobgeo_rat_surfR[2]*JfR[38])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[37]+jacobgeo_rat_surfR[3]*JfR[32])); 
-  JRatfR[21] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[2]*JfR[47]+jacobgeo_rat_surfR[1]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[2]*JfR[44]+jacobgeo_rat_surfR[1]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[3]*JfR[46]+jacobgeo_rat_surfR[0]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[3]*JfR[41]+jacobgeo_rat_surfR[0]*JfR[40])); 
-  JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
-  JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
-  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
-  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
-  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*(JRatfR[9]+JRatfR[8]+JRatfR[5])-0.25*(JRatfR[4]+JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*(JRatfR[9]+JRatfR[8])+0.25*(JRatfR[5]+JRatfR[4])-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*(JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*(JRatfR[2]+JRatfR[1])+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*JRatfR[18]+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*JRatfR[12]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.25*(JRatfR[5]+JRatfR[4])+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.22360679774997894*JRatfR[23]-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*JRatfR[15]-0.33541019662496846*JRatfR[14]+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.2795084971874738*JRatfR[23]-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18])+0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*JRatfR[12]+0.25*JRatfR[9]-0.25*(JRatfR[8]+JRatfR[5])+0.25*(JRatfR[4]+JRatfR[2])-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*JRatfR[18]-0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*JRatfR[15]+0.33541019662496846*JRatfR[14]-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*JRatfR[2]-0.25*JRatfR[1]+0.25*JRatfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*JRatfR[22]+0.2795084971874737*(JRatfR[21]+JRatfR[20])+0.2795084971874738*(JRatfR[19]+JRatfR[18])-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9])-0.25*(JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2])+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*JRatfR[22]-0.22360679774997896*(JRatfR[21]+JRatfR[20])-0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*JRatfR[9]-0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14])-0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]+0.33541019662496846*JRatfR[7]-0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*JRatfR[22]-0.2795084971874737*JRatfR[21]+0.2795084971874737*JRatfR[20]-0.2795084971874738*JRatfR[19]+0.2795084971874738*JRatfR[18]-0.2795084971874738*JRatfR[17]-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9])+0.25*JRatfR[8]-0.25*JRatfR[5]+0.25*JRatfR[4]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*JRatfR[22]+0.22360679774997896*JRatfR[21]-0.22360679774997896*JRatfR[20]+0.22360679774997894*JRatfR[19]-0.22360679774997902*JRatfR[18]+0.22360679774997902*JRatfR[17]+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14])+0.33541019662496846*JRatfR[13]-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*JRatfR[9]+0.25*JRatfR[8]-0.33541019662496846*JRatfR[7]+0.33541019662496846*JRatfR[6]-0.25*JRatfR[5]+0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]-0.25*JRatfR[2]+0.25*(JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]-0.33541019662496846*JRatfR[11]+0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.2795084971874738*JRatfR[23]+0.2795084971874737*(JRatfR[22]+JRatfR[21])-0.2795084971874737*JRatfR[20]+0.2795084971874738*JRatfR[19]-0.2795084971874738*(JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]-0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.22360679774997894*JRatfR[23])-0.22360679774997896*(JRatfR[22]+JRatfR[21])+0.22360679774997896*JRatfR[20]-0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])-0.25*JRatfR[12]+0.33541019662496846*JRatfR[11]-0.33541019662496846*JRatfR[10]-0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*JRatfR[5]-0.25*JRatfR[4]+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]-0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]-0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])-0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])-0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.2795084971874738*JRatfR[23])-0.2795084971874737*(JRatfR[22]+JRatfR[21]+JRatfR[20])-0.2795084971874738*(JRatfR[19]+JRatfR[18]+JRatfR[17])-0.2795084971874737*JRatfR[16]+0.25*(JRatfR[12]+JRatfR[9]+JRatfR[8]+JRatfR[5]+JRatfR[4]+JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.22360679774997894*JRatfR[23]+0.22360679774997896*(JRatfR[22]+JRatfR[21]+JRatfR[20])+0.22360679774997894*JRatfR[19]+0.22360679774997902*(JRatfR[18]+JRatfR[17])+0.22360679774997896*JRatfR[16]+0.33541019662496846*(JRatfR[15]+JRatfR[14]+JRatfR[13])+0.25*JRatfR[12]+0.33541019662496846*(JRatfR[11]+JRatfR[10])+0.25*(JRatfR[9]+JRatfR[8])+0.33541019662496846*(JRatfR[7]+JRatfR[6])+0.25*(JRatfR[5]+JRatfR[4])+0.33541019662496846*JRatfR[3]+0.25*(JRatfR[2]+JRatfR[1]+JRatfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 2ac072efa7..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[1])+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+JfL[1]*jacobgeo_rat_surfL[1])+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[6])+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[8])+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[6])+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[8])+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[13])+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[13])+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[18]+3.0*jacobgeo_rat_surfL[0]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+15.0*jacobgeo_rat_surfL[0]*JfL[18]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 484c74eea5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[3]+jacobgeo_rat_surfL[1]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[1])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[8]+JfL[3]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[2]+JfL[0]*jacobgeo_rat_surfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[8]+JfL[2]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[8]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[2]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[9])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[12])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[23])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[37])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[34])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[33])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[32])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[37]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[34])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[44])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[33])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[34]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[32])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[37])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[41])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 717ef56760..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,223 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double JRatfL[12] = {0.}; 
-  JRatfL[0] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[5]+jacobgeo_rat_surfL[0]*JfL[2])+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0]); 
-  JRatfL[1] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[5]+jacobgeo_rat_surfL[1]*JfL[2])+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1]); 
-  JRatfL[2] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[7])+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[3]); 
-  JRatfL[3] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[9])+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[4]); 
-  JRatfL[4] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[7])+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[3]); 
-  JRatfL[5] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[9])+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[4]); 
-  JRatfL[6] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[1]*JfL[15]+jacobgeo_rat_surfL[0]*JfL[14])+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[10]); 
-  JRatfL[7] = 0.5*(1.7320508075688772*(jacobgeo_rat_surfL[0]*JfL[15]+jacobgeo_rat_surfL[1]*JfL[14])+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[10]); 
-  JRatfL[8] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[20]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[18]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[17])+15.0*jacobgeo_rat_surfL[0]*JfL[16]); 
-  JRatfL[9] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[20]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[16])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[18]+15.0*jacobgeo_rat_surfL[0]*JfL[17]); 
-  JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
-  JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])+0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*JRatfL[5]-0.3535533905932737*(JRatfL[3]+JRatfL[1])+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]-0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*JRatfL[7]-0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]-0.39528470752104733*JRatfL[10]+0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*JRatfL[5]+0.3535533905932737*JRatfL[3]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])+0.31622776601683794*JRatfL[10]-0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*JRatfL[7]+0.4743416490252568*JRatfL[6]-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]-0.3535533905932737*JRatfL[1]+0.3535533905932737*JRatfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3952847075210473*JRatfL[11]+0.39528470752104733*JRatfL[10]-0.39528470752104733*JRatfL[9]-0.3952847075210473*JRatfL[8]-0.3535533905932737*(JRatfL[5]+JRatfL[3])+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3162277660168379*JRatfL[11])-0.31622776601683794*JRatfL[10]+0.31622776601683794*JRatfL[9]+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])-0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]-0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]-0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]-0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]-0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3952847075210473*JRatfL[11])-0.39528470752104733*(JRatfL[10]+JRatfL[9])-0.3952847075210473*JRatfL[8]+0.3535533905932737*(JRatfL[5]+JRatfL[3]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3162277660168379*JRatfL[11]+0.31622776601683794*(JRatfL[10]+JRatfL[9])+0.3162277660168379*JRatfL[8]+0.4743416490252568*(JRatfL[7]+JRatfL[6])+0.3535533905932737*JRatfL[5]+0.4743416490252568*JRatfL[4]+0.3535533905932737*JRatfL[3]+0.4743416490252568*JRatfL[2]+0.3535533905932737*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
deleted file mode 100644
index dc082abd14..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,382 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[6]+jacobgeo_rat_surfL[0]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[6]+jacobgeo_rat_surfL[1]*JfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[7]+JfL[1]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[0]*JfL[3]+JfL[0]*jacobgeo_rat_surfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[7]+JfL[0]*jacobgeo_rat_surfL[3]+jacobgeo_rat_surfL[1]*JfL[3]+JfL[1]*jacobgeo_rat_surfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[35]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[38]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[38]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[35]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[34])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[37])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[38]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[35]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[42]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[45]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[34])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[35]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[37])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[38]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[45]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[42]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 0191a5c18f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,380 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double JRatfL[24] = {0.}; 
-  JRatfL[0] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[16]+jacobgeo_rat_surfL[2]*JfL[8]+jacobgeo_rat_surfL[1]*JfL[7]+jacobgeo_rat_surfL[0]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[2]+JfL[1]*jacobgeo_rat_surfL[1]+JfL[0]*jacobgeo_rat_surfL[0])); 
-  JRatfL[1] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[16]+jacobgeo_rat_surfL[3]*JfL[8]+jacobgeo_rat_surfL[0]*JfL[7]+jacobgeo_rat_surfL[1]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[6]+JfL[2]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[1]+jacobgeo_rat_surfL[0]*JfL[1])); 
-  JRatfL[2] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[16]+jacobgeo_rat_surfL[0]*JfL[8]+jacobgeo_rat_surfL[3]*JfL[7]+jacobgeo_rat_surfL[2]*JfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[6]+JfL[1]*jacobgeo_rat_surfL[3]+JfL[0]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[0]*JfL[2])); 
-  JRatfL[3] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[26]+jacobgeo_rat_surfL[2]*JfL[19]+jacobgeo_rat_surfL[1]*JfL[18]+jacobgeo_rat_surfL[0]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[17]+jacobgeo_rat_surfL[2]*JfL[10]+jacobgeo_rat_surfL[1]*JfL[9]+jacobgeo_rat_surfL[0]*JfL[4])); 
-  JRatfL[4] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[27]+jacobgeo_rat_surfL[2]*JfL[22]+jacobgeo_rat_surfL[1]*JfL[21]+jacobgeo_rat_surfL[0]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[20]+jacobgeo_rat_surfL[2]*JfL[13]+jacobgeo_rat_surfL[1]*JfL[12]+jacobgeo_rat_surfL[0]*JfL[5])); 
-  JRatfL[5] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[16]+jacobgeo_rat_surfL[1]*JfL[8]+jacobgeo_rat_surfL[2]*JfL[7]+JfL[3]*jacobgeo_rat_surfL[3])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[6]+JfL[0]*jacobgeo_rat_surfL[3]+JfL[1]*jacobgeo_rat_surfL[2]+jacobgeo_rat_surfL[1]*JfL[2])); 
-  JRatfL[6] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[26]+jacobgeo_rat_surfL[3]*JfL[19]+jacobgeo_rat_surfL[0]*JfL[18]+jacobgeo_rat_surfL[1]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[17]+jacobgeo_rat_surfL[3]*JfL[10]+jacobgeo_rat_surfL[0]*JfL[9]+jacobgeo_rat_surfL[1]*JfL[4])); 
-  JRatfL[7] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[26]+jacobgeo_rat_surfL[0]*JfL[19]+jacobgeo_rat_surfL[3]*JfL[18]+jacobgeo_rat_surfL[2]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[17]+jacobgeo_rat_surfL[0]*JfL[10]+jacobgeo_rat_surfL[3]*JfL[9]+jacobgeo_rat_surfL[2]*JfL[4])); 
-  JRatfL[8] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[27]+jacobgeo_rat_surfL[3]*JfL[22]+jacobgeo_rat_surfL[0]*JfL[21]+jacobgeo_rat_surfL[1]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[20]+jacobgeo_rat_surfL[3]*JfL[13]+jacobgeo_rat_surfL[0]*JfL[12]+jacobgeo_rat_surfL[1]*JfL[5])); 
-  JRatfL[9] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[27]+jacobgeo_rat_surfL[0]*JfL[22]+jacobgeo_rat_surfL[3]*JfL[21]+jacobgeo_rat_surfL[2]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[20]+jacobgeo_rat_surfL[0]*JfL[13]+jacobgeo_rat_surfL[3]*JfL[12]+jacobgeo_rat_surfL[2]*JfL[5])); 
-  JRatfL[10] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[3]*JfL[31]+jacobgeo_rat_surfL[2]*JfL[30]+jacobgeo_rat_surfL[1]*JfL[29]+jacobgeo_rat_surfL[0]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[3]*JfL[28]+jacobgeo_rat_surfL[2]*JfL[24]+jacobgeo_rat_surfL[1]*JfL[23]+jacobgeo_rat_surfL[0]*JfL[15])); 
-  JRatfL[11] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[26]+jacobgeo_rat_surfL[1]*JfL[19]+jacobgeo_rat_surfL[2]*JfL[18]+jacobgeo_rat_surfL[3]*JfL[11])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[17]+jacobgeo_rat_surfL[1]*JfL[10]+jacobgeo_rat_surfL[2]*JfL[9]+jacobgeo_rat_surfL[3]*JfL[4])); 
-  JRatfL[12] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[27]+jacobgeo_rat_surfL[1]*JfL[22]+jacobgeo_rat_surfL[2]*JfL[21]+jacobgeo_rat_surfL[3]*JfL[14])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[20]+jacobgeo_rat_surfL[1]*JfL[13]+jacobgeo_rat_surfL[2]*JfL[12]+jacobgeo_rat_surfL[3]*JfL[5])); 
-  JRatfL[13] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[31]+jacobgeo_rat_surfL[3]*JfL[30]+jacobgeo_rat_surfL[0]*JfL[29]+jacobgeo_rat_surfL[1]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[2]*JfL[28]+jacobgeo_rat_surfL[3]*JfL[24]+jacobgeo_rat_surfL[0]*JfL[23]+jacobgeo_rat_surfL[1]*JfL[15])); 
-  JRatfL[14] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[31]+jacobgeo_rat_surfL[0]*JfL[30]+jacobgeo_rat_surfL[3]*JfL[29]+jacobgeo_rat_surfL[2]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[1]*JfL[28]+jacobgeo_rat_surfL[0]*JfL[24]+jacobgeo_rat_surfL[3]*JfL[23]+jacobgeo_rat_surfL[2]*JfL[15])); 
-  JRatfL[15] = 0.25*(2.4494897427831783*(jacobgeo_rat_surfL[0]*JfL[31]+jacobgeo_rat_surfL[1]*JfL[30]+jacobgeo_rat_surfL[2]*JfL[29]+jacobgeo_rat_surfL[3]*JfL[25])+1.4142135623730951*(jacobgeo_rat_surfL[0]*JfL[28]+jacobgeo_rat_surfL[1]*JfL[24]+jacobgeo_rat_surfL[2]*JfL[23]+jacobgeo_rat_surfL[3]*JfL[15])); 
-  JRatfL[16] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[43]+jacobgeo_rat_surfL[0]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[34]+jacobgeo_rat_surfL[1]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[39]+jacobgeo_rat_surfL[1]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[37]+jacobgeo_rat_surfL[0]*JfL[32])); 
-  JRatfL[17] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[43]+jacobgeo_rat_surfL[1]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[39]+jacobgeo_rat_surfL[0]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[37]+jacobgeo_rat_surfL[1]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[34]+jacobgeo_rat_surfL[0]*JfL[33])); 
-  JRatfL[18] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[43]+jacobgeo_rat_surfL[2]*JfL[35])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[39]+jacobgeo_rat_surfL[3]*JfL[38])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[37]+jacobgeo_rat_surfL[2]*JfL[32]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[34]+jacobgeo_rat_surfL[3]*JfL[33])); 
-  JRatfL[19] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[47]+jacobgeo_rat_surfL[0]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[41]+jacobgeo_rat_surfL[1]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[46]+jacobgeo_rat_surfL[1]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[44]+jacobgeo_rat_surfL[0]*JfL[36])); 
-  JRatfL[20] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[43]+jacobgeo_rat_surfL[3]*JfL[35])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[34]+jacobgeo_rat_surfL[2]*JfL[33]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[39]+jacobgeo_rat_surfL[2]*JfL[38])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[37]+jacobgeo_rat_surfL[3]*JfL[32])); 
-  JRatfL[21] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[2]*JfL[47]+jacobgeo_rat_surfL[1]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[3]*JfL[46]+jacobgeo_rat_surfL[0]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[2]*JfL[44]+jacobgeo_rat_surfL[1]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[3]*JfL[41]+jacobgeo_rat_surfL[0]*JfL[40])); 
-  JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
-  JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*(JRatfL[9]+JRatfL[8]+JRatfL[5])-0.25*(JRatfL[4]+JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*(JRatfL[9]+JRatfL[8])+0.25*(JRatfL[5]+JRatfL[4])-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*(JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*(JRatfL[2]+JRatfL[1])+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*JRatfL[18]+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*JRatfL[12]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.25*(JRatfL[5]+JRatfL[4])+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*JRatfL[15]-0.33541019662496846*JRatfL[14]+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18])+0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*JRatfL[12]+0.25*JRatfL[9]-0.25*(JRatfL[8]+JRatfL[5])+0.25*(JRatfL[4]+JRatfL[2])-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*JRatfL[18]-0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*JRatfL[15]+0.33541019662496846*JRatfL[14]-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*JRatfL[2]-0.25*JRatfL[1]+0.25*JRatfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*JRatfL[22]+0.2795084971874737*(JRatfL[21]+JRatfL[20])+0.2795084971874738*(JRatfL[19]+JRatfL[18])-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9])-0.25*(JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2])+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*JRatfL[22]-0.22360679774997896*(JRatfL[21]+JRatfL[20])-0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*JRatfL[9]-0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14])-0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]+0.33541019662496846*JRatfL[7]-0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*JRatfL[22]-0.2795084971874737*JRatfL[21]+0.2795084971874737*JRatfL[20]-0.2795084971874738*JRatfL[19]+0.2795084971874738*JRatfL[18]-0.2795084971874738*JRatfL[17]-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9])+0.25*JRatfL[8]-0.25*JRatfL[5]+0.25*JRatfL[4]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*JRatfL[22]+0.22360679774997896*JRatfL[21]-0.22360679774997896*JRatfL[20]+0.22360679774997894*JRatfL[19]-0.22360679774997902*JRatfL[18]+0.22360679774997902*JRatfL[17]+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14])+0.33541019662496846*JRatfL[13]-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*JRatfL[9]+0.25*JRatfL[8]-0.33541019662496846*JRatfL[7]+0.33541019662496846*JRatfL[6]-0.25*JRatfL[5]+0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]-0.25*JRatfL[2]+0.25*(JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]-0.33541019662496846*JRatfL[11]+0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.2795084971874738*JRatfL[23]+0.2795084971874737*(JRatfL[22]+JRatfL[21])-0.2795084971874737*JRatfL[20]+0.2795084971874738*JRatfL[19]-0.2795084971874738*(JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]-0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.22360679774997894*JRatfL[23])-0.22360679774997896*(JRatfL[22]+JRatfL[21])+0.22360679774997896*JRatfL[20]-0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])-0.25*JRatfL[12]+0.33541019662496846*JRatfL[11]-0.33541019662496846*JRatfL[10]-0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*JRatfL[5]-0.25*JRatfL[4]+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]-0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]-0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])-0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])-0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.2795084971874738*JRatfL[23])-0.2795084971874737*(JRatfL[22]+JRatfL[21]+JRatfL[20])-0.2795084971874738*(JRatfL[19]+JRatfL[18]+JRatfL[17])-0.2795084971874737*JRatfL[16]+0.25*(JRatfL[12]+JRatfL[9]+JRatfL[8]+JRatfL[5]+JRatfL[4]+JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.22360679774997894*JRatfL[23]+0.22360679774997896*(JRatfL[22]+JRatfL[21]+JRatfL[20])+0.22360679774997894*JRatfL[19]+0.22360679774997902*(JRatfL[18]+JRatfL[17])+0.22360679774997896*JRatfL[16]+0.33541019662496846*(JRatfL[15]+JRatfL[14]+JRatfL[13])+0.25*JRatfL[12]+0.33541019662496846*(JRatfL[11]+JRatfL[10])+0.25*(JRatfL[9]+JRatfL[8])+0.33541019662496846*(JRatfL[7]+JRatfL[6])+0.25*(JRatfL[5]+JRatfL[4])+0.33541019662496846*JRatfL[3]+0.25*(JRatfL[2]+JRatfL[1]+JRatfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index a4d4852316..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,168 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
-  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index 9db01b0ddb..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,281 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_; 
-  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[4] = 2.0*vmapSq[1]*m_; 
-  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[6] = 2.0*phi[4]*q_; 
-  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
-  hamil[8] = 2.0*phi[6]*q_; 
-  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 2.0*phi[7]*q_; 
-  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
-  hamil[32] = 2.0*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[72]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[4].bmag; 
-  B3_quad = gkdgv[4].B3; 
-  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[5].bmag; 
-  B3_quad = gkdgv[5].B3; 
-  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[6].bmag; 
-  B3_quad = gkdgv[6].B3; 
-  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[7].bmag; 
-  B3_quad = gkdgv[7].B3; 
-  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 021c3b4c0f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 16322da7ec..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 6df6055c88..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,209 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 5a717ab448..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,356 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
deleted file mode 100644
index c143d2e516..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,354 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index 81863bd899..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,93 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
-  hamil[1] = 1.4142135623730951*phi[1]*q_; 
-  hamil[2] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[3]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index d86d28cdd8..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,117 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[6]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index 6f884a9f3a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,216 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
-  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index c210c0e1f1..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,425 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_; 
-  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[4] = 2.0*vmapSq[1]*m_; 
-  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[6] = 2.0*phi[4]*q_; 
-  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
-  hamil[8] = 2.0*phi[6]*q_; 
-  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 2.0*phi[7]*q_; 
-  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
-  hamil[32] = 2.0*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[72]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[4].bmag; 
-  B3_quad = gkdgv[4].B3; 
-  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[5].bmag; 
-  B3_quad = gkdgv[5].B3; 
-  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[6].bmag; 
-  B3_quad = gkdgv[6].B3; 
-  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[7].bmag; 
-  B3_quad = gkdgv[7].B3; 
-  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 37cbe773dc..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,107 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
deleted file mode 100644
index 06aa03bcf5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,141 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 83fbd9d73a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 8c775e0b8e..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
deleted file mode 100644
index e617ddb95c..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 3e950f1ca2..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,452 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
deleted file mode 100644
index 927f268fc5..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_star_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
deleted file mode 100644
index cc407711b2..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x1v_ser_p1.c
+++ /dev/null
@@ -1,95 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = 1.4142135623730951*phi[0]*q_+0.7071067811865475*vmapSq[0]*m_; 
-  hamil[1] = 1.4142135623730951*phi[1]*q_; 
-  hamil[2] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[3]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(1.1180339887498951*JfR[5])+1.118033988749895*JfR[4]+0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]-0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (1.1180339887498951*JfR[5]+1.118033988749895*JfR[4]-0.8660254037844386*JfR[3]-0.8660254037844386*JfR[2]+0.5*JfR[1]+0.5*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
deleted file mode 100644
index 23fb41943f..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_1x2v_ser_p1.c
+++ /dev/null
@@ -1,121 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+vmapSq[0]*m_+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[6]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]-0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])+0.7905694150420948*JfR[10]-0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]+0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]-0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.7905694150420947*JfR[11])-0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]+0.6123724356957944*JfR[7]+0.6123724356957944*JfR[6]-0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.7905694150420947*JfR[11]+0.7905694150420948*JfR[10]+0.7905694150420948*JfR[9]+0.7905694150420947*JfR[8]-0.6123724356957944*JfR[7]-0.6123724356957944*JfR[6]+0.3535533905932737*JfR[5]-0.6123724356957944*JfR[4]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[2]+0.3535533905932737*JfR[1]+0.3535533905932737*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
deleted file mode 100644
index b577e243d0..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_2x2v_ser_p1.c
+++ /dev/null
@@ -1,224 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = 2.0*phi[0]*q_+1.4142135623730951*(vmapSq[0]*m_+bmag[0]*vmap[2]); 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_+1.4142135623730951*bmag[2]*vmap[2]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[5] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[8] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[9] = 1.4142135623730951*bmag[2]*vmap[3]; 
-  hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]-0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]+0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]-0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]+0.25*JfR[12]+0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]+0.25*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]-0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]-0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]-0.25*JfR[12]+0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]-0.25*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]-0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]-0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.5590169943749476*JfR[23])-0.5590169943749475*JfR[22]-0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]-0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]+0.4330127018922193*JfR[15]+0.4330127018922193*JfR[14]+0.4330127018922193*JfR[13]-0.25*JfR[12]-0.4330127018922193*JfR[11]+0.4330127018922193*JfR[10]-0.25*JfR[9]-0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
-  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.5590169943749476*JfR[23]+0.5590169943749475*JfR[22]+0.5590169943749475*JfR[21]+0.5590169943749475*JfR[20]+0.5590169943749476*JfR[19]+0.5590169943749476*JfR[18]+0.5590169943749476*JfR[17]+0.5590169943749475*JfR[16]-0.4330127018922193*JfR[15]-0.4330127018922193*JfR[14]-0.4330127018922193*JfR[13]+0.25*JfR[12]-0.4330127018922193*JfR[11]-0.4330127018922193*JfR[10]+0.25*JfR[9]+0.25*JfR[8]-0.4330127018922193*JfR[7]-0.4330127018922193*JfR[6]+0.25*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[3]+0.25*JfR[2]+0.25*JfR[1]+0.25*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
deleted file mode 100644
index b7cd11600a..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfvpar_3x2v_ser_p1.c
+++ /dev/null
@@ -1,441 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv, 
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap_prime_l,vmap_prime_r: velocity space mapping derivative in left and right cells.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgv: volume DG geometry.
-  // gkdgv: gyrokinetic volume DG geometry.
-  // bmag: magnetic field amplitude.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = 2.0*(phi[0]*q_+vmapSq[0]*m_)+1.4142135623730951*bmag[0]*vmap[2]; 
-  hamil[1] = 2.0*phi[1]*q_+1.4142135623730951*bmag[1]*vmap[2]; 
-  hamil[2] = 2.0*phi[2]*q_; 
-  hamil[3] = 2.0*phi[3]*q_+1.4142135623730951*vmap[2]*bmag[3]; 
-  hamil[4] = 2.0*vmapSq[1]*m_; 
-  hamil[5] = 1.4142135623730951*bmag[0]*vmap[3]; 
-  hamil[6] = 2.0*phi[4]*q_; 
-  hamil[7] = 2.0*phi[5]*q_+1.4142135623730951*vmap[2]*bmag[5]; 
-  hamil[8] = 2.0*phi[6]*q_; 
-  hamil[12] = 1.4142135623730951*bmag[1]*vmap[3]; 
-  hamil[14] = 1.4142135623730951*bmag[3]*vmap[3]; 
-  hamil[16] = 2.0*phi[7]*q_; 
-  hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
-  hamil[32] = 2.0*vmapSq[2]*m_; 
-
-  double *flux_surf_nodal = &flux_surf[72]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double dualcurlbhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double bioverJB_quad[3] = {0.0}; 
-
-  bmag_quad = gkdgv[0].bmag; 
-  B3_quad = gkdgv[0].B3; 
-  dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[1].bmag; 
-  B3_quad = gkdgv[1].B3; 
-  dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[2].bmag; 
-  B3_quad = gkdgv[2].B3; 
-  dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[3].bmag; 
-  B3_quad = gkdgv[3].B3; 
-  dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]-0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]+0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[4].bmag; 
-  B3_quad = gkdgv[4].B3; 
-  dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[5].bmag; 
-  B3_quad = gkdgv[5].B3; 
-  dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]-0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]-0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]+0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]+0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[6].bmag; 
-  B3_quad = gkdgv[6].B3; 
-  dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]-0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]-0.3952847075210473*JfR[39]-0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]-0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]+0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*JfR[19]+0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]-0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]-0.1767766952966368*JfR[8]-0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  bmag_quad = gkdgv[7].bmag; 
-  B3_quad = gkdgv[7].B3; 
-  dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
-  dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
-  dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
-  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
-  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
-  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
-
-  alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (-(0.3952847075210473*JfR[47])-0.39528470752104733*JfR[46]-0.39528470752104733*JfR[45]-0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]-0.3952847075210473*JfR[42]-0.3952847075210473*JfR[41]-0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]-0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]+0.3061862178478971*JfR[31]+0.3061862178478971*JfR[30]+0.3061862178478971*JfR[29]+0.3061862178478971*JfR[28]-0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]+0.3061862178478971*JfR[25]+0.3061862178478971*JfR[24]+0.3061862178478971*JfR[23]-0.1767766952966368*JfR[22]-0.1767766952966368*JfR[21]-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]+0.3061862178478971*JfR[15]-0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-  alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
-  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
-  JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
-  JfR_quad =  (0.3952847075210473*JfR[47]+0.39528470752104733*JfR[46]+0.39528470752104733*JfR[45]+0.39528470752104733*JfR[44]+0.39528470752104733*JfR[43]+0.3952847075210473*JfR[42]+0.3952847075210473*JfR[41]+0.3952847075210473*JfR[40]+0.3952847075210473*JfR[39]+0.3952847075210473*JfR[38]+0.3952847075210473*JfR[37]+0.39528470752104733*JfR[36]+0.39528470752104733*JfR[35]+0.39528470752104733*JfR[34]+0.39528470752104733*JfR[33]+0.3952847075210473*JfR[32]-0.3061862178478971*JfR[31]-0.3061862178478971*JfR[30]-0.3061862178478971*JfR[29]-0.3061862178478971*JfR[28]+0.1767766952966368*JfR[27]-0.3061862178478971*JfR[26]-0.3061862178478971*JfR[25]-0.3061862178478971*JfR[24]-0.3061862178478971*JfR[23]+0.1767766952966368*JfR[22]+0.1767766952966368*JfR[21]+0.1767766952966368*JfR[20]-0.3061862178478971*JfR[19]-0.3061862178478971*JfR[18]-0.3061862178478971*JfR[17]+0.1767766952966368*JfR[16]-0.3061862178478971*JfR[15]+0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[11]-0.3061862178478971*JfR[10]-0.3061862178478971*JfR[9]+0.1767766952966368*JfR[8]+0.1767766952966368*JfR[7]+0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[4]+0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]+0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0])/vmap_prime_r[0];
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0 ;
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0 ;
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
-
-
-  double vmap_prime_min = fmin(fabs(vmap_prime_l[0]),fabs(vmap_prime_r[0]));
-
-  return cfl/vmap_prime_min*2.5*rdvpar2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
deleted file mode 100644
index 7240774398..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x1v_ser_p1.c
+++ /dev/null
@@ -1,107 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[6] = {0.}; 
-  hamil[0] = (phi[0]-1.7320508075688772*phi[1])*q_+0.5*vmapSq[0]*m_; 
-  hamil[1] = 0.5*vmapSq[1]*m_; 
-  hamil[2] = 0.5*vmapSq[2]*m_; 
-
-  double apar_surf[3] = {0.}; 
-  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(1.224744871391589*hamil[1]-3.6742346141747664*hamil[2]))/vmap[1]; 
-  dHdvpar_quad[1] = (1.0*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(3.6742346141747664*hamil[2]+1.224744871391589*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]-1.1618950038622249*JfL[3]-0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]+1.1618950038622249*JfR[3]-0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.9682458365518543*JfL[5])-0.5590169943749475*JfL[4]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = 0.9682458365518543*JfR[5]-0.5590169943749475*JfR[4]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.7745966692414834*JfL[5]+0.4472135954999579*JfL[4]+1.1618950038622249*JfL[3]+0.6708203932499369*JfL[2]+0.8660254037844386*JfL[1]+0.5*JfL[0]; 
-  JfR_quad = -(0.7745966692414834*JfR[5])+0.4472135954999579*JfR[4]-1.1618950038622249*JfR[3]+0.6708203932499369*JfR[2]-0.8660254037844386*JfR[1]+0.5*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
deleted file mode 100644
index c0917aa28c..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_1x2v_ser_p1.c
+++ /dev/null
@@ -1,141 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdvpar2 = 2.0/dxv[1];
-
-  double hamil[12] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+0.7071067811865475*vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = 0.7071067811865475*vmapSq[1]*m_; 
-  hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
-
-  double apar_surf[6] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.8660254037844386*hamil[1]-2.5980762113533156*hamil[4]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.7071067811865476*hamil[1])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(2.5980762113533156*hamil[4]+0.8660254037844386*hamil[1]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.6846531968814573*JfL[11]+0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]-0.6123724356957944*JfL[5]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.6846531968814573*JfR[11])+0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]+0.6123724356957944*JfR[5]-0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.5477225575051661*JfL[11])-0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]-0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]-0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.5477225575051661*JfR[11]-0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]+0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]-0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]-0.8215838362577489*JfL[7]-0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]-0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]-0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]+0.8215838362577489*JfR[7]-0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]+0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]-0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.6846531968814573*JfL[11])-0.39528470752104733*JfL[10]-0.6846531968814574*JfL[9]-0.3952847075210473*JfL[8]+0.6123724356957944*JfL[5]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = 0.6846531968814573*JfR[11]-0.39528470752104733*JfR[10]+0.6846531968814574*JfR[9]-0.3952847075210473*JfR[8]-0.6123724356957944*JfR[5]+0.3535533905932737*JfR[3]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.5477225575051661*JfL[11]+0.3162277660168379*JfL[10]+0.5477225575051661*JfL[9]+0.3162277660168379*JfL[8]+0.8215838362577489*JfL[7]+0.4743416490252568*JfL[6]+0.6123724356957944*JfL[5]+0.8215838362577489*JfL[4]+0.3535533905932737*JfL[3]+0.4743416490252568*JfL[2]+0.6123724356957944*JfL[1]+0.3535533905932737*JfL[0]; 
-  JfR_quad = -(0.5477225575051661*JfR[11])+0.3162277660168379*JfR[10]-0.5477225575051661*JfR[9]+0.3162277660168379*JfR[8]-0.8215838362577489*JfR[7]+0.4743416490252568*JfR[6]-0.6123724356957944*JfR[5]-0.8215838362577489*JfR[4]+0.3535533905932737*JfR[3]+0.4743416490252568*JfR[2]-0.6123724356957944*JfR[1]+0.3535533905932737*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
deleted file mode 100644
index 256d3fa931..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[1])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[2]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]+0.4841229182759271*(JfL[21]+JfL[20])+0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]-0.4330127018922193*(JfL[8]+JfL[5])-0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]-0.4841229182759271*(JfR[21]+JfR[20])+0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]+0.4330127018922193*(JfR[8]+JfR[5])-0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]-0.38729833462074165*(JfL[21]+JfL[20])-0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]+0.38729833462074165*(JfR[21]+JfR[20])-0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]-0.4841229182759271*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]+0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]+0.4841229182759271*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]-0.4330127018922193*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]+0.38729833462074165*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]-0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]-0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]-0.38729833462074165*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]+0.2795084971874737*JfL[22]+0.4841229182759271*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.2795084971874738*JfL[18]-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.2795084971874737*JfR[22]-0.4841229182759271*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]-0.2795084971874738*JfR[18]+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.25*JfR[9]+0.4330127018922193*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.22360679774997896*JfL[22]-0.38729833462074165*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.25*JfL[9]-0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.22360679774997896*JfR[22]+0.38729833462074165*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.25*JfR[9]+0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]-0.33541019662496846*JfL[14]-0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]-0.33541019662496846*JfL[7]-0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.33541019662496846*JfR[14]+0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]-0.33541019662496846*JfR[7]+0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])-0.2795084971874737*JfL[22]-0.4841229182759271*(JfL[21]+JfL[20])-0.2795084971874738*(JfL[19]+JfL[18])-0.4841229182759271*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]+0.25*JfL[9]+0.4330127018922193*(JfL[8]+JfL[5])+0.25*(JfL[4]+JfL[2])+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.2795084971874737*JfR[22]+0.4841229182759271*(JfR[21]+JfR[20])-0.2795084971874738*(JfR[19]+JfR[18])+0.4841229182759271*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.25*JfR[9]-0.4330127018922193*(JfR[8]+JfR[5])+0.25*(JfR[4]+JfR[2])-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.22360679774997896*JfL[22]+0.38729833462074165*(JfL[21]+JfL[20])+0.22360679774997894*JfL[19]+0.22360679774997902*JfL[18]+0.3872983346207417*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]+0.33541019662496846*JfL[14]+0.5809475019311124*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.25*JfL[9]+0.4330127018922193*JfL[8]+0.33541019662496846*JfL[7]+0.5809475019311124*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.25*JfL[2]+0.4330127018922193*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.22360679774997896*JfR[22]-0.38729833462074165*(JfR[21]+JfR[20])+0.22360679774997894*JfR[19]+0.22360679774997902*JfR[18]-0.3872983346207417*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.33541019662496846*JfR[14]-0.5809475019311124*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.25*JfR[9]-0.4330127018922193*JfR[8]+0.33541019662496846*JfR[7]-0.5809475019311124*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]+0.25*JfR[2]-0.4330127018922193*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
deleted file mode 100644
index 670244e151..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfx_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[1]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+(bmag[0]-1.7320508075688772*bmag[1])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[4])*q_; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[6]-2.4494897427831783*phi[7])*q_; 
-  hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
-  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
-  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[0]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]+0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*JfL[36]+0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]-0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*JfR[36]+0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]-0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]-0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]-0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]+0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]-0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]+0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]-0.34232659844072866*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])+0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]+0.34232659844072866*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]+0.273861278752583*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]-0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]+0.3061862178478971*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]-0.273861278752583*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]-0.3061862178478971*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.19764235376052364*JfL[41]+0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.19764235376052364*JfR[41]-0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.15811388300841892*JfL[41]-0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*JfL[21]-0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.15811388300841892*JfR[41]+0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*JfR[21]+0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.1767766952966368*JfR[13]+0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.2371708245126284*JfL[24]-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]+0.2371708245126284*JfL[19]+0.41079191812887433*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]+0.2371708245126284*JfL[11]-0.2371708245126284*JfL[10]-0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.2371708245126284*JfR[24]+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.2371708245126284*JfR[19]-0.41079191812887433*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]+0.2371708245126284*JfR[11]-0.2371708245126284*JfR[10]+0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.19764235376052364*JfL[41]-0.34232659844072866*JfL[40]+0.19764235376052364*JfL[39]+0.34232659844072866*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.19764235376052366*JfL[34]-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.19764235376052364*JfR[41]+0.34232659844072866*JfR[40]+0.19764235376052364*JfR[39]-0.34232659844072866*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]-0.19764235376052366*JfR[34]+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.15811388300841892*JfL[41]+0.273861278752583*JfL[40]-0.15811388300841892*JfL[39]-0.273861278752583*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.15811388300841894*JfL[34]+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.2371708245126284*JfL[24]+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*JfL[21]+0.3061862178478971*JfL[20]-0.2371708245126284*JfL[19]-0.41079191812887433*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.3061862178478971*JfL[12]-0.2371708245126284*JfL[11]+0.2371708245126284*JfL[10]+0.41079191812887433*JfL[9]-0.1767766952966368*JfL[8]-0.3061862178478971*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.15811388300841892*JfR[41]-0.273861278752583*JfR[40]-0.15811388300841892*JfR[39]+0.273861278752583*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]+0.15811388300841894*JfR[34]-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.2371708245126284*JfR[24]-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*JfR[21]-0.3061862178478971*JfR[20]-0.2371708245126284*JfR[19]+0.41079191812887433*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.1767766952966368*JfR[13]-0.3061862178478971*JfR[12]-0.2371708245126284*JfR[11]+0.2371708245126284*JfR[10]-0.41079191812887433*JfR[9]-0.1767766952966368*JfR[8]+0.3061862178478971*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]+0.1767766952966368*JfR[2]-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.19764235376052366*JfL[46]+0.3423265984407287*(JfL[45]+JfL[44])-0.3423265984407287*JfL[43]+0.19764235376052364*(JfL[42]+JfL[41])+0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])+0.19764235376052366*JfL[36]-0.19764235376052366*(JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.3061862178478971*JfL[16]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.19764235376052366*JfR[46]-0.3423265984407287*(JfR[45]+JfR[44])+0.3423265984407287*JfR[43]+0.19764235376052364*(JfR[42]+JfR[41])-0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])+0.19764235376052366*JfR[36]-0.19764235376052366*(JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])-0.3061862178478971*JfR[16]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.15811388300841892*JfL[46]-0.27386127875258304*(JfL[45]+JfL[44])+0.27386127875258304*JfL[43]-0.15811388300841892*(JfL[42]+JfL[41])-0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])-0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]-0.1767766952966368*JfL[22]-0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*(JfL[14]+JfL[13])-0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.15811388300841892*JfR[46]+0.27386127875258304*(JfR[45]+JfR[44])-0.27386127875258304*JfR[43]-0.15811388300841892*(JfR[42]+JfR[41])+0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])-0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]-0.1767766952966368*JfR[22]+0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*(JfR[14]+JfR[13])+0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]-0.2371708245126284*JfL[30]-0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*(JfL[25]+JfL[24])-0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])-0.2371708245126284*JfL[19]-0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]-0.2371708245126284*(JfL[11]+JfL[10])-0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.2371708245126284*JfR[30]+0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*(JfR[25]+JfR[24])+0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])-0.2371708245126284*JfR[19]+0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]-0.2371708245126284*(JfR[11]+JfR[10])+0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.19764235376052366*JfL[46]-0.3423265984407287*(JfL[45]+JfL[44]+JfL[43])-0.19764235376052364*(JfL[42]+JfL[41])-0.34232659844072866*JfL[40]-0.19764235376052364*JfL[39]-0.34232659844072866*(JfL[38]+JfL[37])-0.19764235376052366*(JfL[36]+JfL[35]+JfL[34])-0.3423265984407287*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20]+JfL[16])+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*(JfL[5]+JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.19764235376052366*JfR[46]+0.3423265984407287*(JfR[45]+JfR[44]+JfR[43])-0.19764235376052364*(JfR[42]+JfR[41])+0.34232659844072866*JfR[40]-0.19764235376052364*JfR[39]+0.34232659844072866*(JfR[38]+JfR[37])-0.19764235376052366*(JfR[36]+JfR[35]+JfR[34])+0.3423265984407287*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20]+JfR[16])+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*(JfR[5]+JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.15811388300841892*JfL[46]+0.27386127875258304*(JfL[45]+JfL[44]+JfL[43])+0.15811388300841892*(JfL[42]+JfL[41])+0.273861278752583*JfL[40]+0.15811388300841892*JfL[39]+0.273861278752583*(JfL[38]+JfL[37])+0.15811388300841892*JfL[36]+0.15811388300841894*(JfL[35]+JfL[34])+0.27386127875258304*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]+0.2371708245126284*JfL[30]+0.41079191812887433*(JfL[29]+JfL[28])+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*(JfL[25]+JfL[24])+0.41079191812887433*JfL[23]+0.1767766952966368*JfL[22]+0.3061862178478971*(JfL[21]+JfL[20])+0.2371708245126284*JfL[19]+0.41079191812887433*(JfL[18]+JfL[17])+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*(JfL[14]+JfL[13])+0.3061862178478971*JfL[12]+0.2371708245126284*(JfL[11]+JfL[10])+0.41079191812887433*JfL[9]+0.1767766952966368*JfL[8]+0.3061862178478971*(JfL[7]+JfL[6])+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*(JfL[3]+JfL[2])+0.3061862178478971*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.15811388300841892*JfR[46]-0.27386127875258304*(JfR[45]+JfR[44]+JfR[43])+0.15811388300841892*(JfR[42]+JfR[41])-0.273861278752583*JfR[40]+0.15811388300841892*JfR[39]-0.273861278752583*(JfR[38]+JfR[37])+0.15811388300841892*JfR[36]+0.15811388300841894*(JfR[35]+JfR[34])-0.27386127875258304*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.2371708245126284*JfR[30]-0.41079191812887433*(JfR[29]+JfR[28])-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*(JfR[25]+JfR[24])-0.41079191812887433*JfR[23]+0.1767766952966368*JfR[22]-0.3061862178478971*(JfR[21]+JfR[20])+0.2371708245126284*JfR[19]-0.41079191812887433*(JfR[18]+JfR[17])-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*(JfR[14]+JfR[13])-0.3061862178478971*JfR[12]+0.2371708245126284*(JfR[11]+JfR[10])-0.41079191812887433*JfR[9]+0.1767766952966368*JfR[8]-0.3061862178478971*(JfR[7]+JfR[6])+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*(JfR[3]+JfR[2])-0.3061862178478971*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdx2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
deleted file mode 100644
index 496e3bc191..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_2x2v_ser_p1.c
+++ /dev/null
@@ -1,257 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdz2 = 2.0/dxv[1];
-  double rdvpar2 = 2.0/dxv[2];
-
-  double hamil[24] = {0.}; 
-  hamil[0] = (1.4142135623730951*phi[0]-2.4494897427831783*phi[2])*q_+vmapSq[0]*m_+(bmag[0]-1.7320508075688772*bmag[2])*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[3])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[3]); 
-  hamil[2] = vmapSq[1]*m_; 
-  hamil[3] = (bmag[0]-1.7320508075688772*bmag[2])*vmap[3]; 
-  hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[8] = vmapSq[2]*m_; 
-
-  double apar_surf[12] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
-
-  double *flux_surf_nodal = &flux_surf[12]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.6123724356957944*hamil[2]-1.837117307087383*hamil[8]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.49999999999999994*hamil[2])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.837117307087383*hamil[8]+0.6123724356957944*hamil[2]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*JfL[23])+0.4841229182759271*JfL[22]-0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*JfL[12]-0.4330127018922193*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.4841229182759271*JfR[23]-0.4841229182759271*JfR[22]-0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*JfR[12]+0.4330127018922193*JfR[9]+0.25*JfR[8]+0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]-0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.3872983346207417*JfR[23])+0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*JfL[15]-0.5809475019311124*JfL[14]+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*JfR[15]+0.5809475019311124*JfR[14]+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*JfL[23]-0.4841229182759271*JfL[22]+0.2795084971874737*JfL[21]+0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]+0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*JfL[12]+0.4330127018922193*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = -(0.4841229182759271*JfR[23])+0.4841229182759271*JfR[22]+0.2795084971874737*JfR[21]-0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]+0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*JfR[12]-0.4330127018922193*JfR[9]-0.25*JfR[8]+0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])+0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]-0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]-0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*JfL[15]+0.5809475019311124*JfL[14]-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]-0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]-0.25*JfL[1]+0.25*JfL[0]; 
-  JfR_quad = 0.3872983346207417*JfR[23]-0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]+0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]-0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*JfR[15]-0.5809475019311124*JfR[14]-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]+0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]-0.25*JfR[1]+0.25*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.4841229182759271*(JfL[23]+JfL[22])+0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]+0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]-0.4330127018922193*(JfL[12]+JfL[9])-0.25*JfL[8]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.4841229182759271*(JfR[23]+JfR[22]))+0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]+0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]+0.4330127018922193*(JfR[12]+JfR[9])-0.25*JfR[8]-0.4330127018922193*JfR[5]-0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.3872983346207417*JfL[23])-0.38729833462074165*JfL[22]-0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]-0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]-0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]-0.4330127018922193*JfL[9]-0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]-0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.3872983346207417*JfR[23]+0.38729833462074165*JfR[22]-0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]-0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]+0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]+0.4330127018922193*JfR[9]-0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]-0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]-0.5809475019311124*(JfL[15]+JfL[14])-0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]-0.5809475019311124*JfL[11]-0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]-0.5809475019311124*JfL[7]-0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]-0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]+0.5809475019311124*(JfR[15]+JfR[14])-0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]+0.5809475019311124*JfR[11]-0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]+0.5809475019311124*JfR[7]-0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.4841229182759271*(JfL[23]+JfL[22]))-0.2795084971874737*JfL[21]-0.4841229182759271*JfL[20]-0.2795084971874738*JfL[19]-0.4841229182759271*JfL[18]-0.2795084971874738*JfL[17]-0.2795084971874737*JfL[16]+0.4330127018922193*(JfL[12]+JfL[9])+0.25*JfL[8]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.4841229182759271*(JfR[23]+JfR[22])-0.2795084971874737*JfR[21]+0.4841229182759271*JfR[20]-0.2795084971874738*JfR[19]+0.4841229182759271*JfR[18]-0.2795084971874738*JfR[17]-0.2795084971874737*JfR[16]-0.4330127018922193*(JfR[12]+JfR[9])+0.25*JfR[8]-0.4330127018922193*JfR[5]+0.25*JfR[4]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
-  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.3872983346207417*JfL[23]+0.38729833462074165*JfL[22]+0.22360679774997896*JfL[21]+0.38729833462074165*JfL[20]+0.22360679774997894*JfL[19]+0.3872983346207417*JfL[18]+0.22360679774997902*JfL[17]+0.22360679774997896*JfL[16]+0.5809475019311124*(JfL[15]+JfL[14])+0.33541019662496846*JfL[13]+0.4330127018922193*JfL[12]+0.5809475019311124*JfL[11]+0.33541019662496846*JfL[10]+0.4330127018922193*JfL[9]+0.25*JfL[8]+0.5809475019311124*JfL[7]+0.33541019662496846*JfL[6]+0.4330127018922193*JfL[5]+0.25*JfL[4]+0.33541019662496846*JfL[3]+0.4330127018922193*JfL[2]+0.25*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.3872983346207417*JfR[23])-0.38729833462074165*JfR[22]+0.22360679774997896*JfR[21]-0.38729833462074165*JfR[20]+0.22360679774997894*JfR[19]-0.3872983346207417*JfR[18]+0.22360679774997902*JfR[17]+0.22360679774997896*JfR[16]-0.5809475019311124*(JfR[15]+JfR[14])+0.33541019662496846*JfR[13]-0.4330127018922193*JfR[12]-0.5809475019311124*JfR[11]+0.33541019662496846*JfR[10]-0.4330127018922193*JfR[9]+0.25*JfR[8]-0.5809475019311124*JfR[7]+0.33541019662496846*JfR[6]-0.4330127018922193*JfR[5]+0.25*JfR[4]+0.33541019662496846*JfR[3]-0.4330127018922193*JfR[2]+0.25*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
deleted file mode 100644
index 3b0af0a204..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfy_3x2v_ser_p1.c
+++ /dev/null
@@ -1,452 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[2]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+bmag[0]*vmap[2]; 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[4])*q_+bmag[1]*vmap[2]; 
-  hamil[2] = (1.4142135623730951*phi[3]-2.4494897427831783*phi[6])*q_+vmap[2]*bmag[3]; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = bmag[0]*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[5]-2.4494897427831783*phi[7])*q_+vmap[2]*bmag[5]; 
-  hamil[8] = bmag[1]*vmap[3]; 
-  hamil[9] = bmag[3]*vmap[3]; 
-  hamil[12] = vmap[3]*bmag[5]; 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
-  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[24]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]+0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]-0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]-0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]-0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]+0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]+0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]+0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]-0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]-0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]+0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]-0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]+0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]-0.3423265984407287*JfL[44]+0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]+0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*JfL[36]+0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]+0.3423265984407287*JfR[44]-0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*JfR[36]+0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]+0.27386127875258304*JfL[44]-0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]-0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]-0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]-0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]-0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]-0.27386127875258304*JfR[44]+0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]-0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]+0.19764235376052366*JfL[45]+0.3423265984407287*JfL[44]-0.3423265984407287*JfL[43]+0.19764235376052364*JfL[42]+0.34232659844072866*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]+0.19764235376052366*JfL[36]-0.19764235376052366*JfL[35]-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.3061862178478971*JfL[16]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.19764235376052366*JfR[45]-0.3423265984407287*JfR[44]+0.3423265984407287*JfR[43]+0.19764235376052364*JfR[42]-0.34232659844072866*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]+0.19764235376052366*JfR[36]-0.19764235376052366*JfR[35]+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.3061862178478971*JfR[16]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]-0.15811388300841892*JfL[45]-0.27386127875258304*JfL[44]+0.27386127875258304*JfL[43]-0.15811388300841892*JfL[42]-0.273861278752583*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]-0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]-0.1767766952966368*JfL[21]-0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.1767766952966368*JfL[14]-0.3061862178478971*JfL[13]-0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.15811388300841892*JfR[45]+0.27386127875258304*JfR[44]-0.27386127875258304*JfR[43]-0.15811388300841892*JfR[42]+0.273861278752583*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]-0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.1767766952966368*JfR[21]+0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.1767766952966368*JfR[14]+0.3061862178478971*JfR[13]-0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])-0.2371708245126284*JfL[29]-0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]-0.2371708245126284*JfL[25]-0.41079191812887433*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]-0.41079191812887433*JfL[19]-0.2371708245126284*JfL[18]-0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]-0.2371708245126284*JfL[11]-0.41079191812887433*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.2371708245126284*JfR[29]+0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.2371708245126284*JfR[25]+0.41079191812887433*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]+0.41079191812887433*JfR[19]-0.2371708245126284*JfR[18]+0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.2371708245126284*JfR[11]+0.41079191812887433*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]-0.19764235376052366*JfL[45]-0.3423265984407287*(JfL[44]+JfL[43])-0.19764235376052364*JfL[42]-0.34232659844072866*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]-0.19764235376052364*JfL[38]-0.34232659844072866*JfL[37]-0.19764235376052366*(JfL[36]+JfL[35])-0.3423265984407287*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])+0.1767766952966368*JfL[21]+0.3061862178478971*(JfL[20]+JfL[16])+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*(JfL[5]+JfL[3])+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.19764235376052366*JfR[45]+0.3423265984407287*(JfR[44]+JfR[43])-0.19764235376052364*JfR[42]+0.34232659844072866*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.19764235376052364*JfR[38]+0.34232659844072866*JfR[37]-0.19764235376052366*(JfR[36]+JfR[35])+0.3423265984407287*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.1767766952966368*JfR[21]-0.3061862178478971*(JfR[20]+JfR[16])+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*(JfR[5]+JfR[3])-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = 0.0; 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]+0.15811388300841892*JfL[45]+0.27386127875258304*(JfL[44]+JfL[43])+0.15811388300841892*JfL[42]+0.273861278752583*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]+0.15811388300841892*JfL[38]+0.273861278752583*JfL[37]+0.15811388300841892*JfL[36]+0.15811388300841894*JfL[35]+0.27386127875258304*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])+0.2371708245126284*JfL[29]+0.41079191812887433*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]+0.2371708245126284*JfL[25]+0.41079191812887433*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]+0.1767766952966368*JfL[21]+0.3061862178478971*JfL[20]+0.41079191812887433*JfL[19]+0.2371708245126284*JfL[18]+0.41079191812887433*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.1767766952966368*JfL[14]+0.3061862178478971*JfL[13]+0.1767766952966368*JfL[12]+0.2371708245126284*JfL[11]+0.41079191812887433*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]+0.1767766952966368*JfL[7]+0.3061862178478971*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.1767766952966368*JfL[3]+0.3061862178478971*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.15811388300841892*JfR[45]-0.27386127875258304*(JfR[44]+JfR[43])+0.15811388300841892*JfR[42]-0.273861278752583*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.15811388300841892*JfR[38]-0.273861278752583*JfR[37]+0.15811388300841892*JfR[36]+0.15811388300841894*JfR[35]-0.27386127875258304*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.2371708245126284*JfR[29]-0.41079191812887433*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.2371708245126284*JfR[25]-0.41079191812887433*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.1767766952966368*JfR[21]-0.3061862178478971*JfR[20]-0.41079191812887433*JfR[19]+0.2371708245126284*JfR[18]-0.41079191812887433*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.1767766952966368*JfR[14]-0.3061862178478971*JfR[13]+0.1767766952966368*JfR[12]+0.2371708245126284*JfR[11]-0.41079191812887433*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.1767766952966368*JfR[7]-0.3061862178478971*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]+0.1767766952966368*JfR[3]-0.3061862178478971*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdy2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
deleted file mode 100644
index ee0ef2c9bf..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_em_surfz_3x2v_ser_p1.c
+++ /dev/null
@@ -1,450 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot,
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  // w[NDIM]: cell-center.
-  // dxv[NDIM]: cell length.
-  // vmap: velocity space mapping.
-  // vmapSq: velocity space mapping squared.
-  // q_,m_: species charge and mass.
-  // dgs: surface DG geometry.
-  // gkdgs: gyrokinetic surface DG geometry.
-  // bmag: bmag represented on the surface.
-  // jacobgeo_rat_surfL: Ratio of surface conf-space Jacobians in left cell.
-  // jacobgeo_rat_surfR: Ratio of surface conf-space Jacobians in right cell.
-  // phi: electrostatic potential.
-  // apar: parallel component of vector potential.
-  // apardot: time derivative of parallel component of vector potential.
-  // JfL: distribution times total jacobian in left cell.
-  // JfR: distribution times total jacobian in right cell.
-  // flux_surf: output surface phase space flux in each direction (cdim + 1 components).
-  //            Note: Each cell owns their *lower* edge surface evaluation.
-
-  double rdx2 = 2.0/dxv[0];
-  double rdy2 = 2.0/dxv[1];
-  double rdz2 = 2.0/dxv[2];
-  double rdvpar2 = 2.0/dxv[3];
-
-  double hamil[48] = {0.}; 
-  hamil[0] = -(2.4494897427831783*phi[3]*q_)+1.4142135623730951*(phi[0]*q_+vmapSq[0]*m_)+vmap[2]*(bmag[0]-1.7320508075688772*bmag[3]); 
-  hamil[1] = (1.4142135623730951*phi[1]-2.4494897427831783*phi[5])*q_+vmap[2]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[2] = (1.4142135623730951*phi[2]-2.4494897427831783*phi[6])*q_; 
-  hamil[3] = 1.4142135623730951*vmapSq[1]*m_; 
-  hamil[4] = (bmag[0]-1.7320508075688772*bmag[3])*vmap[3]; 
-  hamil[5] = (1.4142135623730951*phi[4]-2.4494897427831783*phi[7])*q_; 
-  hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
-  hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
-
-  double apar_surf[24] = {0.}; 
-  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
-  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
-  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
-  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
-
-  double *flux_surf_nodal = &flux_surf[48]; 
-  double cfl = 0.0; 
-  double bmag_quad = 0.0; 
-  double Jc_quad = 0.0; 
-  double B3_quad = 0.0; 
-  double normcurlbhat_quad = 0.0; 
-  double area_elem_quad = 0.0; 
-  double bhat_quad[3] = {0.0}; 
-  double alpha_quad = 0.0; 
-  double JfL_quad = 0.0; 
-  double JfR_quad = 0.0; 
-  double Jfavg_quad = 0.0; 
-  double Jfjump_quad = 0.0; 
-  double dHdvpar_quad[3] = {0.0}; 
-  dHdvpar_quad[0] = (0.8164965809277261*(0.4330127018922193*hamil[3]-1.2990381056766578*hamil[16]))/vmap[1]; 
-  dHdvpar_quad[1] = (0.3535533905932738*hamil[3])/vmap[1]; 
-  dHdvpar_quad[2] = (0.8164965809277261*(1.2990381056766578*hamil[16]+0.4330127018922193*hamil[3]))/vmap[1]; 
-  double mvparsq_quad[3] = {0.0}; 
-  mvparsq_quad[0] = dHdvpar_quad[0]*dHdvpar_quad[0]/m_; 
-  mvparsq_quad[1] = dHdvpar_quad[1]*dHdvpar_quad[1]/m_; 
-  mvparsq_quad[2] = dHdvpar_quad[2]*dHdvpar_quad[2]/m_; 
-
-  bmag_quad = gkdgs[0].bmag; 
-  Jc_quad = gkdgs[0].Jc; 
-  B3_quad = gkdgs[0].B3; 
-  normcurlbhat_quad = gkdgs[0].normcurlbhat; 
-  bhat_quad[0] = gkdgs[0].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[0].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[0].bhat.x[2]; 
-  area_elem_quad = dgs[0].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[1] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*(JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*(JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[3] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])+0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*(JfL[13]+JfL[12])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])-0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*(JfR[13]+JfR[12])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])-0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*(JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])-0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*(JfL[2]+JfL[1])+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])+0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*(JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])+0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*(JfR[2]+JfR[1])+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[5] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[1].bmag; 
-  Jc_quad = gkdgs[1].Jc; 
-  B3_quad = gkdgs[1].B3; 
-  normcurlbhat_quad = gkdgs[1].normcurlbhat; 
-  bhat_quad[0] = gkdgs[1].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[1].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[1].bhat.x[2]; 
-  area_elem_quad = dgs[1].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*JfL[27]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.34232659844072866*JfR[47]-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*JfR[27]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[7] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.273861278752583*JfR[47])+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*JfL[31]-0.41079191812887433*JfL[30]+0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*JfR[31]+0.41079191812887433*JfR[30]-0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[9] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]-0.34232659844072866*JfL[39]+0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*JfL[34]+0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*JfL[27]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = -(0.34232659844072866*JfR[47])+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]+0.34232659844072866*JfR[39]-0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*JfR[34]+0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*JfR[27]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]+0.273861278752583*JfL[39]-0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*JfL[34]-0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*JfL[31]+0.41079191812887433*JfL[30]-0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]+0.3061862178478971*JfL[8]-0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0]; 
-  JfR_quad = 0.273861278752583*JfR[47]-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]-0.273861278752583*JfR[39]+0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*JfR[34]-0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*JfR[31]-0.41079191812887433*JfR[30]+0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]-0.3061862178478971*JfR[8]+0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*JfR[2]-0.1767766952966368*JfR[1]+0.1767766952966368*JfR[0]; 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[11] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[2].bmag; 
-  Jc_quad = gkdgs[2].Jc; 
-  B3_quad = gkdgs[2].B3; 
-  normcurlbhat_quad = gkdgs[2].normcurlbhat; 
-  bhat_quad[0] = gkdgs[2].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[2].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[2].bhat.x[2]; 
-  area_elem_quad = dgs[2].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*JfL[46]+0.3423265984407287*JfL[45]-0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]-0.19764235376052364*JfL[41]+0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22])-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*JfR[46]-0.3423265984407287*JfR[45]-0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]-0.19764235376052364*JfR[41]+0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22])+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[13] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*JfL[46]-0.27386127875258304*JfL[45]+0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]+0.15811388300841892*JfL[41]-0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]+0.3061862178478971*JfL[22]-0.3061862178478971*JfL[21]+0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*JfR[46]+0.27386127875258304*JfR[45]+0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]+0.15811388300841892*JfR[41]-0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]-0.3061862178478971*JfR[22]+0.3061862178478971*JfR[21]+0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]+0.1767766952966368*JfR[13]-0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30])-0.41079191812887433*JfL[29]+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]+0.2371708245126284*JfL[24]-0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]+0.41079191812887433*JfL[19]-0.41079191812887433*JfL[18]+0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.41079191812887433*JfL[11]+0.2371708245126284*JfL[10]-0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30])+0.41079191812887433*JfR[29]+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]+0.2371708245126284*JfR[24]-0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]-0.41079191812887433*JfR[19]+0.41079191812887433*JfR[18]+0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.41079191812887433*JfR[11]+0.2371708245126284*JfR[10]-0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[15] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*JfL[46]-0.3423265984407287*JfL[45]+0.19764235376052366*JfL[44]+0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]+0.19764235376052364*JfL[41]-0.19764235376052364*JfL[40]+0.34232659844072866*JfL[39]-0.34232659844072866*JfL[38]+0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]+0.19764235376052366*JfL[34]-0.19764235376052366*JfL[33]-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22])+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[16]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*JfR[46]+0.3423265984407287*JfR[45]+0.19764235376052366*JfR[44]-0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]+0.19764235376052364*JfR[41]-0.19764235376052364*JfR[40]-0.34232659844072866*JfR[39]+0.34232659844072866*JfR[38]+0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]+0.19764235376052366*JfR[34]-0.19764235376052366*JfR[33]-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22])-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.3061862178478971*JfR[16]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[16] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*JfL[46]+0.27386127875258304*JfL[45]-0.15811388300841892*JfL[44]-0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]-0.15811388300841892*JfL[41]+0.15811388300841892*JfL[40]-0.273861278752583*JfL[39]+0.273861278752583*JfL[38]-0.15811388300841892*JfL[37]+0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]-0.15811388300841894*JfL[34]+0.15811388300841894*JfL[33]+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30])+0.41079191812887433*JfL[29]-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]-0.2371708245126284*JfL[24]+0.2371708245126284*JfL[23]-0.3061862178478971*JfL[22]+0.3061862178478971*JfL[21]-0.1767766952966368*JfL[20]-0.41079191812887433*JfL[19]+0.41079191812887433*JfL[18]-0.2371708245126284*JfL[17]-0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.41079191812887433*JfL[11]-0.2371708245126284*JfL[10]+0.2371708245126284*JfL[9]-0.3061862178478971*JfL[8]+0.3061862178478971*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*(JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*JfR[46]-0.27386127875258304*JfR[45]-0.15811388300841892*JfR[44]+0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]-0.15811388300841892*JfR[41]+0.15811388300841892*JfR[40]+0.273861278752583*JfR[39]-0.273861278752583*JfR[38]-0.15811388300841892*JfR[37]+0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]-0.15811388300841894*JfR[34]+0.15811388300841894*JfR[33]+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30])-0.41079191812887433*JfR[29]-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]-0.2371708245126284*JfR[24]+0.2371708245126284*JfR[23]+0.3061862178478971*JfR[22]-0.3061862178478971*JfR[21]-0.1767766952966368*JfR[20]+0.41079191812887433*JfR[19]-0.41079191812887433*JfR[18]-0.2371708245126284*JfR[17]+0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]-0.1767766952966368*JfR[13]+0.1767766952966368*JfR[12]-0.41079191812887433*JfR[11]-0.2371708245126284*JfR[10]+0.2371708245126284*JfR[9]+0.3061862178478971*JfR[8]-0.3061862178478971*JfR[7]-0.1767766952966368*JfR[6]+0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]-0.1767766952966368*JfR[2]+0.1767766952966368*(JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[17] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  bmag_quad = gkdgs[3].bmag; 
-  Jc_quad = gkdgs[3].Jc; 
-  B3_quad = gkdgs[3].B3; 
-  normcurlbhat_quad = gkdgs[3].normcurlbhat; 
-  bhat_quad[0] = gkdgs[3].bhat.x[0]; 
-  bhat_quad[1] = gkdgs[3].bhat.x[1]; 
-  bhat_quad[2] = gkdgs[3].bhat.x[2]; 
-  area_elem_quad = dgs[3].area_elem; 
-
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]-0.41079191812887433*JfL[26]+0.41079191812887433*JfL[25]+0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]+0.41079191812887433*JfR[26]-0.41079191812887433*JfR[25]+0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[18] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.34232659844072866*JfL[47]+0.3423265984407287*(JfL[46]+JfL[45])+0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]+0.34232659844072866*JfL[42]+0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]+0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]-0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[16]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.34232659844072866*JfR[47])-0.3423265984407287*(JfR[46]+JfR[45])+0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]-0.34232659844072866*JfR[42]+0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]+0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]+0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.3061862178478971*JfR[16]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[19] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.273861278752583*JfL[47])-0.27386127875258304*(JfL[46]+JfL[45])-0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]-0.273861278752583*JfL[42]-0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*JfL[37]-0.15811388300841892*JfL[36]+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]-0.3061862178478971*JfL[27]+0.41079191812887433*JfL[26]-0.41079191812887433*JfL[25]-0.2371708245126284*(JfL[24]+JfL[23])-0.3061862178478971*(JfL[22]+JfL[21])-0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]-0.3061862178478971*JfL[14]-0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.273861278752583*JfR[47]+0.27386127875258304*(JfR[46]+JfR[45])-0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]+0.273861278752583*JfR[42]-0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*JfR[37]-0.15811388300841892*JfR[36]-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]+0.3061862178478971*JfR[27]-0.41079191812887433*JfR[26]+0.41079191812887433*JfR[25]-0.2371708245126284*(JfR[24]+JfR[23])+0.3061862178478971*(JfR[22]+JfR[21])-0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]+0.3061862178478971*JfR[14]-0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*JfR[6]-0.1767766952966368*JfR[5]+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[20] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]-0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])-0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]-0.41079191812887433*(JfL[26]+JfL[25])-0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]-0.41079191812887433*(JfL[19]+JfL[18])-0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]-0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])-0.41079191812887433*JfL[11]-0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])-0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]+0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])-0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]+0.41079191812887433*(JfR[26]+JfR[25])-0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]+0.41079191812887433*(JfR[19]+JfR[18])-0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]-0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])+0.41079191812887433*JfR[11]-0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[21] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = -(0.34232659844072866*JfL[47])-0.3423265984407287*(JfL[46]+JfL[45])-0.19764235376052366*JfL[44]-0.3423265984407287*JfL[43]-0.34232659844072866*JfL[42]-0.19764235376052364*(JfL[41]+JfL[40])-0.34232659844072866*(JfL[39]+JfL[38])-0.19764235376052364*JfL[37]-0.19764235376052366*JfL[36]-0.3423265984407287*JfL[35]-0.19764235376052366*(JfL[34]+JfL[33])-0.19764235376052364*JfL[32]+0.3061862178478971*(JfL[27]+JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.3061862178478971*(JfL[16]+JfL[14])+0.1767766952966368*(JfL[13]+JfL[12])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = 0.34232659844072866*JfR[47]+0.3423265984407287*(JfR[46]+JfR[45])-0.19764235376052366*JfR[44]+0.3423265984407287*JfR[43]+0.34232659844072866*JfR[42]-0.19764235376052364*(JfR[41]+JfR[40])+0.34232659844072866*(JfR[39]+JfR[38])-0.19764235376052364*JfR[37]-0.19764235376052366*JfR[36]+0.3423265984407287*JfR[35]-0.19764235376052366*(JfR[34]+JfR[33])-0.19764235376052364*JfR[32]-0.3061862178478971*(JfR[27]+JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.3061862178478971*(JfR[16]+JfR[14])+0.1767766952966368*(JfR[13]+JfR[12])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[22] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-  alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
-  alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
-  alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
-  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
-  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
-  alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
-
-  cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
-  JfL_quad = 0.273861278752583*JfL[47]+0.27386127875258304*(JfL[46]+JfL[45])+0.15811388300841892*JfL[44]+0.27386127875258304*JfL[43]+0.273861278752583*JfL[42]+0.15811388300841892*(JfL[41]+JfL[40])+0.273861278752583*(JfL[39]+JfL[38])+0.15811388300841892*(JfL[37]+JfL[36])+0.27386127875258304*JfL[35]+0.15811388300841894*(JfL[34]+JfL[33])+0.15811388300841892*JfL[32]+0.41079191812887433*(JfL[31]+JfL[30]+JfL[29])+0.2371708245126284*JfL[28]+0.3061862178478971*JfL[27]+0.41079191812887433*(JfL[26]+JfL[25])+0.2371708245126284*(JfL[24]+JfL[23])+0.3061862178478971*(JfL[22]+JfL[21])+0.1767766952966368*JfL[20]+0.41079191812887433*(JfL[19]+JfL[18])+0.2371708245126284*JfL[17]+0.3061862178478971*JfL[16]+0.2371708245126284*JfL[15]+0.3061862178478971*JfL[14]+0.1767766952966368*(JfL[13]+JfL[12])+0.41079191812887433*JfL[11]+0.2371708245126284*(JfL[10]+JfL[9])+0.3061862178478971*(JfL[8]+JfL[7])+0.1767766952966368*(JfL[6]+JfL[5])+0.2371708245126284*JfL[4]+0.3061862178478971*JfL[3]+0.1767766952966368*(JfL[2]+JfL[1]+JfL[0]); 
-  JfR_quad = -(0.273861278752583*JfR[47])-0.27386127875258304*(JfR[46]+JfR[45])+0.15811388300841892*JfR[44]-0.27386127875258304*JfR[43]-0.273861278752583*JfR[42]+0.15811388300841892*(JfR[41]+JfR[40])-0.273861278752583*(JfR[39]+JfR[38])+0.15811388300841892*(JfR[37]+JfR[36])-0.27386127875258304*JfR[35]+0.15811388300841894*(JfR[34]+JfR[33])+0.15811388300841892*JfR[32]-0.41079191812887433*(JfR[31]+JfR[30]+JfR[29])+0.2371708245126284*JfR[28]-0.3061862178478971*JfR[27]-0.41079191812887433*(JfR[26]+JfR[25])+0.2371708245126284*(JfR[24]+JfR[23])-0.3061862178478971*(JfR[22]+JfR[21])+0.1767766952966368*JfR[20]-0.41079191812887433*(JfR[19]+JfR[18])+0.2371708245126284*JfR[17]-0.3061862178478971*JfR[16]+0.2371708245126284*JfR[15]-0.3061862178478971*JfR[14]+0.1767766952966368*(JfR[13]+JfR[12])-0.41079191812887433*JfR[11]+0.2371708245126284*(JfR[10]+JfR[9])-0.3061862178478971*(JfR[8]+JfR[7])+0.1767766952966368*(JfR[6]+JfR[5])+0.2371708245126284*JfR[4]-0.3061862178478971*JfR[3]+0.1767766952966368*(JfR[2]+JfR[1]+JfR[0]); 
-  Jfavg_quad = (JfL_quad + JfR_quad)/2.0; 
-  Jfjump_quad = (JfR_quad - JfL_quad)/2.0; 
-  flux_surf_nodal[23] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad; 
-
-
-  return cfl*1.5*rdz2; 
-
-} 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
index ec0aaed538..20cb1de5fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1(
 
   double JRatfR[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = 1.7320508075688772*apar[1]+apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
index 4ec2aa04fb..79ba15b224 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1(
 
   double JRatfR[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
index b72fa0bc56..db13a0392d 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -98,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -110,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,6 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -204,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -216,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,6 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
index b8926ad492..ad91da2c74 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,6 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -161,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -231,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -243,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -313,6 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -325,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -395,6 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -407,6 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 25790c6de8..91bd8d0353 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -98,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -110,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,6 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -204,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -216,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,6 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 0cd555a507..31d234d6e7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -127,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -151,6 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,6 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -221,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,6 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -245,6 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -315,6 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -327,6 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -349,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,6 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -409,6 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 126b740838..6b35dbdfd8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,6 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -161,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -231,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -243,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -313,6 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -325,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -395,6 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -407,6 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
index 013f2db119..1ae0a018bf 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1.c
@@ -35,6 +35,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1(
 
   double JRatfL[3] = {0.}; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
index 4beb85d6e5..88c7ba441c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1.c
@@ -36,6 +36,9 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1(
 
   double JRatfL[6] = {0.}; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
index 7173fab4de..3ffcbb20e6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -98,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -110,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,6 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -204,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -216,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,6 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
index 68e15b6e58..71438a6185 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,6 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -161,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -231,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -243,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -313,6 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -325,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -395,6 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -407,6 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
index 9e5e1b48fa..ab2bc4b14f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -86,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -98,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -110,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -122,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -134,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -146,6 +160,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -168,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -180,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -192,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -204,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -216,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -228,6 +254,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
index 95686206c1..24e6d694e6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -103,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -115,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -127,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -139,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -151,6 +165,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -163,6 +179,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -185,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -197,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -209,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -221,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -233,6 +259,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -245,6 +273,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -267,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -279,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -291,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -303,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -315,6 +353,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -327,6 +367,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -349,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -361,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -373,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -385,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -397,6 +447,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -409,6 +461,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
index 6c1090ddc4..81d7446ca0 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -101,6 +107,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +121,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +135,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +149,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -149,6 +163,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -161,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +201,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +215,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +229,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +243,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -231,6 +257,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -243,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +295,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +309,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +323,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +337,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -313,6 +351,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -325,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +389,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +403,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +417,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +431,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -395,6 +445,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -407,6 +459,8 @@ GKYL_CU_DH double gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
index 072bab42e4..226d1e5196 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[2])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
index beef88b515..72bcbe3e03 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[3]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
index 75019f7489..3a1f1bffc8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1(
   hamil[5] = (1.7320508075688772*bmag[3]+bmag[1])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
index c4e86d67ff..57678d3630 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
index 21d73e1f3f..7a047e8a82 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(1.7320508075688772*bmag[5]+bmag[1]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
index 720e058d01..22eba49ed6 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_se
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[22]-3.0*jacobgeo_rat_surfR[0]*JfR[21])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])+15.0*jacobgeo_rat_surfR[0]*JfR[22]-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[2]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
index 99790bdf4b..91932a28d2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_se
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[40]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[41])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[41])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[40]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[36])-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[1]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[2]; 
+  apar_surf[2] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[6]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
index 7e96b4cd7c..31e4b560b7 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_se
   JRatfR[10] = 0.03333333333333333*(-(25.980762113533157*jacobgeo_rat_surfR[1]*JfR[23])+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[21]-3.0*jacobgeo_rat_surfR[0]*JfR[22])+15.0*jacobgeo_rat_surfR[0]*JfR[19]); 
   JRatfR[11] = 0.03333333333333333*(8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfR[1]*JfR[19]-3.0*jacobgeo_rat_surfR[0]*JfR[23])-25.980762113533157*jacobgeo_rat_surfR[1]*JfR[22]+15.0*jacobgeo_rat_surfR[0]*JfR[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
index 8a5feaa8de..b40227bce2 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_se
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[41]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[45]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[44]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[42]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[42]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[41]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[44])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[45]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[2]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[4]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[3]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[5]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
index 8266e5b4b4..f6fcf85856 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_se
   JRatfR[22] = 0.016666666666666666*(-(36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[47]+jacobgeo_rat_surfR[2]*JfR[42]))+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[44]+jacobgeo_rat_surfR[2]*JfR[36])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[46]+jacobgeo_rat_surfR[3]*JfR[45]))+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[41]+jacobgeo_rat_surfR[3]*JfR[40])); 
   JRatfR[23] = 0.016666666666666666*(8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfR[1]*JfR[41]+jacobgeo_rat_surfR[2]*JfR[40])-4.242640687119286*(jacobgeo_rat_surfR[0]*JfR[47]+jacobgeo_rat_surfR[3]*JfR[42]))-36.742346141747674*(jacobgeo_rat_surfR[1]*JfR[46]+jacobgeo_rat_surfR[2]*JfR[45])+21.213203435596427*(jacobgeo_rat_surfR[0]*JfR[44]+jacobgeo_rat_surfR[3]*JfR[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 2.4494897427831783*apar[3]+1.4142135623730951*apar[0]; 
+  apar_surf[1] = 2.4494897427831783*apar[5]+1.4142135623730951*apar[1]; 
+  apar_surf[2] = 2.4494897427831783*apar[6]+1.4142135623730951*apar[2]; 
+  apar_surf[5] = 2.4494897427831783*apar[7]+1.4142135623730951*apar[4]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
index 1b3a1c3259..1c0639d806 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[22]+3.0*jacobgeo_rat_surfL[0]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+15.0*jacobgeo_rat_surfL[0]*JfL[22]+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
index 94fe4931bc..2eb9560faa 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[40])+8.660254037844387*(2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[36])+4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[44]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[41])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[40])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[41]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[36])+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[44])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
index 8f1a28700e..8383619c80 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1.c
@@ -51,6 +51,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1(
   JRatfL[10] = 0.03333333333333333*(25.980762113533157*jacobgeo_rat_surfL[1]*JfL[23]+8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[22]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[21])+15.0*jacobgeo_rat_surfL[0]*JfL[19]); 
   JRatfL[11] = 0.03333333333333333*(8.660254037844387*(3.0*jacobgeo_rat_surfL[0]*JfL[23]+1.7320508075688772*jacobgeo_rat_surfL[1]*JfL[19])+25.980762113533157*jacobgeo_rat_surfL[1]*JfL[22]+15.0*jacobgeo_rat_surfL[0]*JfL[21]); 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
index 74969cd7a1..882993d129 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1.c
@@ -68,6 +68,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[41])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[44])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[45]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[42]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[41])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[42]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[44])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[45]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
index ab2dea1556..0d6b99d1e5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1.c
@@ -66,6 +66,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1(
   JRatfL[22] = 0.016666666666666666*(36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[47]+jacobgeo_rat_surfL[2]*JfL[42])+8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[46]+jacobgeo_rat_surfL[3]*JfL[45])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[44]+jacobgeo_rat_surfL[2]*JfL[36]))+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[41]+jacobgeo_rat_surfL[3]*JfL[40])); 
   JRatfL[23] = 0.016666666666666666*(8.660254037844387*(4.242640687119286*(jacobgeo_rat_surfL[0]*JfL[47]+jacobgeo_rat_surfL[3]*JfL[42])+2.4494897427831783*(jacobgeo_rat_surfL[1]*JfL[41]+jacobgeo_rat_surfL[2]*JfL[40]))+36.742346141747674*(jacobgeo_rat_surfL[1]*JfL[46]+jacobgeo_rat_surfL[2]*JfL[45])+21.213203435596427*(jacobgeo_rat_surfL[0]*JfL[44]+jacobgeo_rat_surfL[3]*JfL[36])); 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
index d87bbae7cc..6f0c89ba2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1.c
@@ -50,14 +50,19 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -67,6 +72,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -80,8 +86,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -91,6 +101,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -104,8 +115,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -115,6 +130,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -128,8 +144,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -139,6 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
index 2a02044eb8..1d35fe4d02 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1.c
@@ -55,14 +55,19 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -72,6 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[0] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -85,8 +91,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -96,6 +106,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[2] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -109,8 +120,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -120,6 +135,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[4] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -133,8 +149,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -144,6 +164,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[6] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -157,8 +178,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -168,6 +193,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[8] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -181,8 +207,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -192,6 +222,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[10] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -205,8 +236,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -216,6 +251,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[12] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -229,8 +265,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -240,6 +280,7 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   flux_surf_nodal[14] = alpha_quad*Jfavg_quad - fabs(alpha_quad)*Jfjump_quad ;
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
index 74c598c8b5..821a8bfe8a 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
index 6311c4e78b..0036aa5a19 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
index eefb8d3120..df86e95bed 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
index 8514d1f80d..44fab0ed28 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
index 0c3fcdce96..4d4a8e8044 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_no_by_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
deleted file mode 100644
index 341b6e2c2c..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
+++ /dev/null
@@ -1,11 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfconf_none(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR, 
-    const double *phi, const double *apar, const double *apardot, 
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  return 0.0; 
-}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index f15895d3c4..055c7bee14 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -43,15 +43,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(1.1180339887498951*JfL[5])+1.118033988749895*JfL[4]-0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]-0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
@@ -65,9 +71,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
+  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (1.1180339887498951*JfL[5]+1.118033988749895*JfL[4]+0.8660254037844386*JfL[3]+0.8660254037844386*JfL[2]+0.5*JfL[1]+0.5*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 3039e2e84a..922fdb0552 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -45,15 +45,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]-0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -64,6 +70,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])+0.7905694150420948*JfL[10]-0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]-0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]-0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -77,9 +85,14 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
+  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.7905694150420947*JfL[11])-0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]-0.6123724356957944*JfL[7]-0.6123724356957944*JfL[6]-0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]-0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
@@ -90,6 +103,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
+  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.7905694150420947*JfL[11]+0.7905694150420948*JfL[10]+0.7905694150420948*JfL[9]+0.7905694150420947*JfL[8]+0.6123724356957944*JfL[7]+0.6123724356957944*JfL[6]+0.3535533905932737*JfL[5]+0.6123724356957944*JfL[4]+0.3535533905932737*JfL[3]+0.6123724356957944*JfL[2]+0.3535533905932737*JfL[1]+0.3535533905932737*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 1b6b303679..bcde53a400 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -50,16 +50,25 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -71,6 +80,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -84,10 +98,18 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -99,6 +121,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]-0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]-0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]-0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -112,10 +139,18 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]+0.25*JfL[12]-0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]+0.25*JfL[9]-0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -127,6 +162,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]-0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]-0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]-0.25*JfL[12]-0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]-0.25*JfL[9]+0.25*JfL[8]-0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]-0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]-0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -140,10 +180,18 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.5590169943749476*JfL[23])-0.5590169943749475*JfL[22]-0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]-0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]-0.4330127018922193*JfL[15]-0.4330127018922193*JfL[14]-0.4330127018922193*JfL[13]-0.25*JfL[12]+0.4330127018922193*JfL[11]-0.4330127018922193*JfL[10]-0.25*JfL[9]-0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]-0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
@@ -155,6 +203,11 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.5590169943749476*JfL[23]+0.5590169943749475*JfL[22]+0.5590169943749475*JfL[21]+0.5590169943749475*JfL[20]+0.5590169943749476*JfL[19]+0.5590169943749476*JfL[18]+0.5590169943749476*JfL[17]+0.5590169943749475*JfL[16]+0.4330127018922193*JfL[15]+0.4330127018922193*JfL[14]+0.4330127018922193*JfL[13]+0.25*JfL[12]+0.4330127018922193*JfL[11]+0.4330127018922193*JfL[10]+0.25*JfL[9]+0.25*JfL[8]+0.4330127018922193*JfL[7]+0.4330127018922193*JfL[6]+0.25*JfL[5]+0.25*JfL[4]+0.4330127018922193*JfL[3]+0.25*JfL[2]+0.25*JfL[1]+0.25*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index f328a124fe..388b4a2609 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -55,17 +55,28 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   double JfR_quad = 0.0; 
   double Jfavg_quad = 0.0; 
   double Jfjump_quad = 0.0; 
+  double bioverJB_quad[3] = {0.0}; 
 
   bmag_quad = gkdgv[0].bmag; 
   B3_quad = gkdgv[0].B3; 
   dualcurlbhat_quad[0] = gkdgv[0].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[0].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[0].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[0].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[0].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[0].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -78,6 +89,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -91,11 +109,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[1].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[1].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[1].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[1].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[1].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[1].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -108,6 +136,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -121,11 +156,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[2].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[2].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[2].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[2].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[2].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[2].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -138,6 +183,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -151,11 +203,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[3].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[3].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[3].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[3].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[3].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[3].bioverJB.x[2]; 
 
   alpha_quad = -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -168,6 +230,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]-0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]-0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]-0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -181,11 +250,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[4].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[4].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[4].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[4].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[4].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[4].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -198,6 +277,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -211,11 +297,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[5].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[5].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[5].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[5].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[5].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[5].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -228,6 +324,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]-0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]-0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]-0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]-0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]-0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]-0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -241,11 +344,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[6].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[6].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[6].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[6].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[6].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[6].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -258,6 +371,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]-0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]-0.3952847075210473*JfL[39]-0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]-0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]-0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]-0.3061862178478971*JfL[19]-0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]-0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]-0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]-0.1767766952966368*JfL[8]-0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]-0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -271,11 +391,21 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   dualcurlbhat_quad[0] = gkdgv[7].dualcurlbhat.x[0]; 
   dualcurlbhat_quad[1] = gkdgv[7].dualcurlbhat.x[1]; 
   dualcurlbhat_quad[2] = gkdgv[7].dualcurlbhat.x[2]; 
+  bioverJB_quad[0] = gkdgv[7].bioverJB.x[0]; 
+  bioverJB_quad[1] = gkdgv[7].bioverJB.x[1]; 
+  bioverJB_quad[2] = gkdgv[7].bioverJB.x[2]; 
 
   alpha_quad = -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (-(0.3952847075210473*JfL[47])-0.39528470752104733*JfL[46]-0.39528470752104733*JfL[45]-0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]-0.3952847075210473*JfL[42]-0.3952847075210473*JfL[41]-0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]-0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]-0.3061862178478971*JfL[31]-0.3061862178478971*JfL[30]-0.3061862178478971*JfL[29]-0.3061862178478971*JfL[28]-0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]-0.3061862178478971*JfL[25]-0.3061862178478971*JfL[24]-0.3061862178478971*JfL[23]-0.1767766952966368*JfL[22]-0.1767766952966368*JfL[21]-0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]-0.3061862178478971*JfL[15]-0.1767766952966368*JfL[14]-0.1767766952966368*JfL[13]-0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]-0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
@@ -288,6 +418,13 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
   JfL_quad =  (0.3952847075210473*JfL[47]+0.39528470752104733*JfL[46]+0.39528470752104733*JfL[45]+0.39528470752104733*JfL[44]+0.39528470752104733*JfL[43]+0.3952847075210473*JfL[42]+0.3952847075210473*JfL[41]+0.3952847075210473*JfL[40]+0.3952847075210473*JfL[39]+0.3952847075210473*JfL[38]+0.3952847075210473*JfL[37]+0.39528470752104733*JfL[36]+0.39528470752104733*JfL[35]+0.39528470752104733*JfL[34]+0.39528470752104733*JfL[33]+0.3952847075210473*JfL[32]+0.3061862178478971*JfL[31]+0.3061862178478971*JfL[30]+0.3061862178478971*JfL[29]+0.3061862178478971*JfL[28]+0.1767766952966368*JfL[27]+0.3061862178478971*JfL[26]+0.3061862178478971*JfL[25]+0.3061862178478971*JfL[24]+0.3061862178478971*JfL[23]+0.1767766952966368*JfL[22]+0.1767766952966368*JfL[21]+0.1767766952966368*JfL[20]+0.3061862178478971*JfL[19]+0.3061862178478971*JfL[18]+0.3061862178478971*JfL[17]+0.1767766952966368*JfL[16]+0.3061862178478971*JfL[15]+0.1767766952966368*JfL[14]+0.1767766952966368*JfL[13]+0.1767766952966368*JfL[12]+0.3061862178478971*JfL[11]+0.3061862178478971*JfL[10]+0.3061862178478971*JfL[9]+0.1767766952966368*JfL[8]+0.1767766952966368*JfL[7]+0.1767766952966368*JfL[6]+0.1767766952966368*JfL[5]+0.3061862178478971*JfL[4]+0.1767766952966368*JfL[3]+0.1767766952966368*JfL[2]+0.1767766952966368*JfL[1]+0.1767766952966368*JfL[0])/vmap_prime_l[0];
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
deleted file mode 100644
index 8be40ca284..0000000000
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
+++ /dev/null
@@ -1,11 +0,0 @@
-#include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_none(
-    const double *w, const double *dxv,
-    const double *vmap_prime_l, const double *vmap_prime_r,
-    const double *vmap, const double *vmapSq, const double q_, const double m_, 
-    const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv, 
-    const double *bmag, const double *phi, const double *apar, const double *apardot, 
-    const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf) 
-{ 
-  return 0.0; 
-}
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
index 5d6b2632d6..3b6d30ba92 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x1v_ser_p1.c
@@ -33,6 +33,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x1v_ser_p1(
   hamil[1] = 0.5*vmapSq[1]*m_; 
   hamil[2] = 0.5*vmapSq[2]*m_; 
 
+  double apar_surf[3] = {0.}; 
+  apar_surf[0] = apar[0]-1.7320508075688772*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
index 61705ec812..a8cca34080 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_1x2v_ser_p1.c
@@ -34,6 +34,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_1x2v_ser_p1(
   hamil[2] = (bmag[0]-1.7320508075688772*bmag[1])*vmap[3]; 
   hamil[4] = 0.7071067811865475*vmapSq[2]*m_; 
 
+  double apar_surf[6] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
index ee444d7199..6a9c86893e 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   hamil[5] = (bmag[2]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,6 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -84,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -96,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -190,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -202,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_2x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdz2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad -= 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdz2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
index 9586cf6447..61ea6bdc19 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfx_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   hamil[9] = vmap[3]*(bmag[3]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[1]; 
+  apar_surf[1] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[5]; 
+  apar_surf[5] = 1.4142135623730951*apar[6]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[0]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,6 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -87,6 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -135,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,6 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -217,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,6 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -275,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -287,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[1]-0.4330127018922193*hamil[5])*rdy2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,6 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,6 +377,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((-(0.4330127018922193*hamil[9])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -369,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -381,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfx_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[1]*((0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2) - bhat_quad[2]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdy2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdy2) * bhat_quad[2] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[1]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
index ba4fbb65a3..edb4ae6f4c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_2x2v_ser_p1.c
@@ -37,6 +37,10 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   hamil[5] = (bmag[1]-1.7320508075688772*bmag[3])*vmap[3]; 
   hamil[8] = vmapSq[2]*m_; 
 
+  double apar_surf[12] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[3]; 
+
   double *flux_surf_nodal = &flux_surf[12]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -72,6 +76,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -84,6 +90,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -96,6 +104,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -108,6 +118,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -120,6 +132,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -132,6 +146,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[0]-0.3535533905932737*apar_surf[1]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -154,6 +170,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -166,6 +184,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -178,6 +198,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -190,6 +212,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -202,6 +226,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -214,6 +240,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_2x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad -= 1/(q_*bmag_quad*area_elem_quad) * bhat_quad[1]*((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2); 
+  alpha_quad += 1/m_ * (0.3535533905932737*apar_surf[1]+0.3535533905932737*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (0.6123724356957944*apar_surf[1]*rdx2) * bhat_quad[1] * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
index 33da4fed8c..c51261dfc5 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfy_3x2v_ser_p1.c
@@ -42,6 +42,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   hamil[12] = vmap[3]*bmag[5]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[2]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[4]; 
+  apar_surf[2] = 1.4142135623730951*apar[3]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[5]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -77,6 +83,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -89,6 +97,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -101,6 +111,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -113,6 +125,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -125,6 +139,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -137,6 +153,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -159,6 +177,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -171,6 +191,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -183,6 +205,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -195,6 +219,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -207,6 +233,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -219,6 +247,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -241,6 +271,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -253,6 +285,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -265,6 +299,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -277,6 +313,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -289,6 +327,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -301,6 +341,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -323,6 +365,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -335,6 +379,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -347,6 +393,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -359,6 +407,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -371,6 +421,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -383,6 +435,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfy_3x2v_ser_p1(
   alpha_quad = 0.0; 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[2]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2) - bhat_quad[0]*((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdz2) * bhat_quad[0] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[2]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
index 002ed373e7..cd0550b00f 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfz_3x2v_ser_p1.c
@@ -40,6 +40,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   hamil[8] = vmap[3]*(bmag[1]-1.7320508075688772*bmag[5]); 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double apar_surf[24] = {0.}; 
+  apar_surf[0] = 1.4142135623730951*apar[0]-2.4494897427831783*apar[3]; 
+  apar_surf[1] = 1.4142135623730951*apar[1]-2.4494897427831783*apar[5]; 
+  apar_surf[2] = 1.4142135623730951*apar[2]-2.4494897427831783*apar[6]; 
+  apar_surf[5] = 1.4142135623730951*apar[4]-2.4494897427831783*apar[7]; 
+
   double *flux_surf_nodal = &flux_surf[48]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -75,6 +81,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -87,6 +95,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -99,6 +109,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -111,6 +123,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -123,6 +137,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -135,6 +151,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]-0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -157,6 +175,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -169,6 +189,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -181,6 +203,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -193,6 +217,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -205,6 +231,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -217,6 +245,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[2]-0.4330127018922193*hamil[5])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])+0.25*apar_surf[2]-0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[2]-0.4330127018922193*apar_surf[5])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -239,6 +269,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -251,6 +283,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -263,6 +297,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -275,6 +311,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -287,6 +325,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -299,6 +339,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (-(0.25*apar_surf[5])-0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[1]-0.4330127018922193*apar_surf[5])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -321,6 +363,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -333,6 +377,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -345,6 +391,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((-(0.4330127018922193*hamil[8])+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -357,6 +405,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[0]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[0]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[0]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[0]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -369,6 +419,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[1]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[1]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[1]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[1]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
@@ -381,6 +433,8 @@ GKYL_CU_DH double gk_collisionless_flux_surfz_3x2v_ser_p1(
   alpha_quad = (dHdvpar_quad[2]*B3_quad/(m_*bmag_quad)); 
   alpha_quad += mvparsq_quad[2]*normcurlbhat_quad/(bmag_quad*q_); 
   alpha_quad += 1/(q_*bmag_quad*area_elem_quad) * (bhat_quad[0]*((0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdy2) - bhat_quad[1]*((0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)); 
+  alpha_quad += 1/m_ * (0.25*apar_surf[5]+0.25*apar_surf[2]+0.25*apar_surf[1]+0.25*apar_surf[0]) * normcurlbhat_quad/bmag_quad * dHdvpar_quad[2]; 
+  alpha_quad += 1/(m_*bmag_quad*area_elem_quad) * (((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[1])*rdx2) * bhat_quad[1] - ((0.4330127018922193*apar_surf[5]+0.4330127018922193*apar_surf[2])*rdy2) * bhat_quad[0]) * dHdvpar_quad[2]; 
   alpha_quad = alpha_quad * area_elem_quad/Jc_quad; 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
index 7f6ddefc61..52dc9eb953 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
+++ b/gyrokinetic/ker/gk_collisionless_flux/gkyl_gk_collisionless_flux_kernels.h
@@ -391,781 +391,13 @@ GKYL_CU_DH double gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1(
   const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
   double* GKYL_RESTRICT flux_surf); 
 
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x1v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x1v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_1x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_1x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_2x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_2x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfx_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfy_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_multib_boundary_edge_surfz_3x2v_ser_p1(
-    const double *w, const double *dxv,
-    const double *vmap, const double *vmapSq, const double q_, const double m_,
-    const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
-    const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-    const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-    double* GKYL_RESTRICT flux_surf); 
-GKYL_CU_DH double gk_collisionless_flux_em_star_no_by_surfvpar_3x2v_ser_p1(
-  const double *w, const double *dxv,
-  const double *vmap_prime_l, const double *vmap_prime_r,
-  const double *vmap, const double *vmapSq, const double q_, const double m_,
-  const struct gkyl_dg_vol_geom *dgv, const struct gkyl_gk_dg_vol_geom *gkdgv,
-  const double *bmag, const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR,
-  double* GKYL_RESTRICT flux_surf); 
-
 GKYL_CU_DH double gk_collisionless_flux_surfconf_none(
   const double *w, const double *dxv,
   const double *vmap, const double *vmapSq, const double q_, const double m_,
   const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs,
   const double *bmag, const double *jacobgeo_rat_surfL, const double *jacobgeo_rat_surfR,
-  const double *phi, const double *apar, const double *apardot, const double *JfL, const double *JfR, 
-  double* GKYL_RESTRICT flux_surf);
+  const double *phi, const double *apar, const double *apardot,
+  const double *JfL, const double *JfR, double* GKYL_RESTRICT flux_surf);
 
 GKYL_CU_DH double gk_collisionless_flux_surfvpar_none(
   const double *w, const double *dxv,
diff --git a/gyrokinetic/zero/dg_gyrokinetic.c b/gyrokinetic/zero/dg_gyrokinetic.c
index 141e9357db..6617460afa 100644
--- a/gyrokinetic/zero/dg_gyrokinetic.c
+++ b/gyrokinetic/zero/dg_gyrokinetic.c
@@ -118,7 +118,7 @@ gkyl_dg_gyrokinetic_new(const struct gkyl_basis *cbasis, const struct gkyl_basis
   }
 
   // Setup electromagnetic terms if needed.
-  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
+  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM);
   gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
   gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
   if (is_em) {
diff --git a/gyrokinetic/zero/dg_gyrokinetic_cu.cu b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
index 7da89ba3a0..bd9de9d914 100644
--- a/gyrokinetic/zero/dg_gyrokinetic_cu.cu
+++ b/gyrokinetic/zero/dg_gyrokinetic_cu.cu
@@ -95,7 +95,7 @@ dg_gyrokinetic_set_cu_dev_ptrs(struct dg_gyrokinetic *gyrokinetic, enum gkyl_bas
   }
 
   // Setup electromagnetic terms if needed.
-  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM) || (collless_type == GKYL_GK_COLLISIONLESS_EM_BPERP);
+  bool is_em = (collless_type == GKYL_GK_COLLISIONLESS_EM);
   gyrokinetic->vol_add_apar_kernel = dg_gyrokinetic_add_apar_vol_none;
   gyrokinetic->vol_add_apardot_kernel = dg_gyrokinetic_add_apardot_vol_none;
   if (is_em) {
diff --git a/gyrokinetic/zero/gk_collisionless_flux.c b/gyrokinetic/zero/gk_collisionless_flux.c
index af46dd313c..385ae7bda0 100644
--- a/gyrokinetic/zero/gk_collisionless_flux.c
+++ b/gyrokinetic/zero/gk_collisionless_flux.c
@@ -43,29 +43,48 @@ gkyl_gk_collisionless_flux_new(const struct gkyl_rect_grid *phase_grid,
   up->gk_dg_geom = gkyl_gk_dg_geom_acquire(gk_dg_geom);
   up->vel_map = gkyl_velocity_map_acquire(vel_map);
 
+  // Set none kernels by default
+  for (int d=0; d<cdim; ++d) {
+    up->flux_surf[d] = gk_collisionless_flux_surfconf_none;
+    up->flux_surf_edge_lo[d] = gk_collisionless_flux_surfconf_none;
+    up->flux_surf_edge_up[d] = gk_collisionless_flux_surfconf_none;
+  }
+  up->flux_surfvpar[0] = gk_collisionless_flux_surfvpar_none;
+
   // Choose appropriate kernels.
-  int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
-  em = complete_em ? 2 : em; // If complete_em is true, use EM kernels without Apardot contribution.
   if (no_by) {
     for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
-  } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+  } else {
     for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
+  }
+
+  // If EM, we split the flux contribution between two updaters.
+  if (type == GKYL_GK_COLLISIONLESS_EM) {
+    if (complete_em) {
+      // To complete RHS star.
+      for (int d=0; d<cdim; ++d) {
+        up->flux_surf[d] = gk_collisionless_flux_surfconf_none;
+        up->flux_surf_edge_lo[d] = gk_collisionless_flux_surfconf_none;
+        up->flux_surf_edge_up[d] = gk_collisionless_flux_surfconf_none;
+      }
+    } else {
+      // To compute RHS star.
+      up->flux_surfvpar[0] = gk_collisionless_flux_surfvpar_none;
+    }
   }
 
   up->flags = 0;
diff --git a/gyrokinetic/zero/gk_collisionless_flux_cu.cu b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
index e21e34ee05..648aa93999 100644
--- a/gyrokinetic/zero/gk_collisionless_flux_cu.cu
+++ b/gyrokinetic/zero/gk_collisionless_flux_cu.cu
@@ -209,28 +209,49 @@ gk_collisionless_flux_set_cu_dev_ptrs(struct gkyl_gk_collisionless_flux *up,
   bool no_by, bool complete_em,
   const enum gkyl_gyrokinetic_bc_type *bctype_conf)
 {
+
+  // Set none kernels by default
+  for (int d=0; d<cdim; ++d) {
+    up->flux_surf[d] = gk_collisionless_flux_surfconf_none;
+    up->flux_surf_edge_lo[d] = gk_collisionless_flux_surfconf_none;
+    up->flux_surf_edge_up[d] = gk_collisionless_flux_surfconf_none;
+  }
+  up->flux_surfvpar[0] = gk_collisionless_flux_surfvpar_none;
+
   // Choose appropriate kernels.
-  em = complete_em ? 2 : em; // If complete_em is true, use EM kernels without Apardot contribution.
   if (no_by) {
     for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_no_by_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(em, cdim, vdim, poly_order);
-  } else { // The Apar term is included in the kernels. If we are ES, Apar=0.
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_no_by_surf_vpar_kern(cdim, vdim, poly_order);
+  } else {
     for (int d=0; d<cdim; ++d) {
-      // BC option in ->flux_surf kernel doesn't matter as long as it's not SKIP.
-      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
-      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim, poly_order, GKYL_BC_GK_SPECIES_ABSORB);
+      up->flux_surf_edge_lo[d] = choose_gk_collisionless_flux_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[d]);
-      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(em, d, cdim, vdim,
+      up->flux_surf_edge_up[d] = choose_gk_collisionless_flux_edge_surf_conf_kern(d, cdim, vdim,
         poly_order, bctype_conf[GKYL_MAX_CDIM+d]);
     }
-    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(em, cdim, vdim, poly_order);
+    up->flux_surfvpar[0] = choose_gk_collisionless_flux_surf_vpar_kern(cdim, vdim, poly_order);
+  }
+
+  // If EM, we split the flux contribution between two updaters.
+  if (em) {
+    if (complete_em) {
+      // To complete RHS star.
+      for (int d=0; d<cdim; ++d) {
+        up->flux_surf[d] = gk_collisionless_flux_surfconf_none;
+        up->flux_surf_edge_lo[d] = gk_collisionless_flux_surfconf_none;
+        up->flux_surf_edge_up[d] = gk_collisionless_flux_surfconf_none;
+      }
+    } else {
+      // To compute RHS star.
+      up->flux_surfvpar[0] = gk_collisionless_flux_surfvpar_none;
+    }
   }
 }
 
@@ -256,7 +277,7 @@ gkyl_gk_collisionless_flux_cu_dev_new(const struct gkyl_rect_grid *phase_grid,
 
   up->charge = charge;
   up->mass = mass;
-  int em = ((type == GKYL_GK_COLLISIONLESS_EM) || (type == GKYL_GK_COLLISIONLESS_EM_BPERP)) ? 1 : 0;
+  int em = (type == GKYL_GK_COLLISIONLESS_EM) ? 1 : 0;
 
   // Acquire pointers to on_dev objects so memcpy below copies those too.
   struct gk_geometry *geom_ho = gkyl_gk_geometry_acquire(gk_geom);
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index 8eaa13efbf..c9e42d4c2e 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -67,382 +67,149 @@ struct gkyl_gk_collisionless_flux {
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_surfvpar_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_surfvpar_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_surfvpar_3x2v_ser_p1, NULL }, // 3
-    },
-  }
 };
+
 //
 // Kernels used at multiblock boundaries.
 //
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[] = {
-  {
-    .kernels_list= {
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list= {
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels = {
+  .kernels_list= {
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list= {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-      },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
     },
-  }
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfz_kernels[] = {
-  { 
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 
@@ -451,205 +218,79 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_surfz_3x2v_ser_p1, NULL }, // 3
-    },  
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_no_by_surfvpar_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfvpar_none, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_no_by_surfvpar_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_surfvpar_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_surfvpar_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
-    },
-  }
 };
 //
 // Kernels used at multiblock boundaries.
@@ -657,199 +298,91 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[] = {
-  { 
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels = {
+  .kernels_list = {
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-      { NULL, gk_collisionless_flux_em_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 0
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[] = {
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels = {
+  .kernels_list = {
+    { NULL, NULL, NULL }, // 0
+    { NULL, NULL, NULL }, // 1
+    { NULL, NULL, NULL }, // 2
+    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
   },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_em_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-    },
-  },
-  {
-    .kernels_list = {
-      { NULL, NULL, NULL }, // 0
-      { NULL, NULL, NULL }, // 1
-      { NULL, NULL, NULL }, // 2
-      { NULL, gk_collisionless_flux_surfconf_none, NULL }, // 3
-    },
-  }
 };
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -857,25 +390,25 @@ choose_gk_collisionless_flux_surf_conf_kern(int em, int dir, int cdim, int vdim,
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_edge_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -883,32 +416,32 @@ choose_gk_collisionless_flux_edge_surf_conf_kern(int em, int dir, int cdim, int
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_surf_vpar_kern(int em, int cdim, int vdim, int poly_order)
+choose_gk_collisionless_flux_surf_vpar_kern(int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_surfvpar_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_surfvpar_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -916,25 +449,25 @@ choose_gk_collisionless_flux_no_by_surf_conf_kern(int em, int dir, int cdim, int
 
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
-choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int em, int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
+choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -942,9 +475,9 @@ choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int em, int dir, int cdim
 
 GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
-choose_gk_collisionless_flux_no_by_surf_vpar_kern(int em, int cdim, int vdim, int poly_order)
+choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[em].kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_no_by_surfvpar_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 #ifdef GKYL_HAVE_CUDA

From b0f904fc03d6bca5c01e19a28fbfbe640e74725a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 27 Apr 2026 17:56:06 -0400
Subject: [PATCH 155/181] bug fix in the EM 2x2v kernels, the 2D limit of the
 Apar cross product was wrong.

---
 .../dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c | 48 +++++++++----------
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c | 24 ++++------
 2 files changed, 32 insertions(+), 40 deletions(-)

diff --git a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
index ee1caa15a7..f01c94ae3d 100644
--- a/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/dg_gyrokinetic/dg_gyrokinetic_add_apar_vol_2x2v_ser_p1.c
@@ -55,14 +55,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   hamil2[1] = hamil[16]*hamil[16]; 
 
   double alphax[24] = {0.}; 
-  alphax[0] = (((-(0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[1] = (((-(0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[3] = (((-(1.369306393762915*bioverJB_3[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_3[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[0]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[3])-0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
-  alphax[6] = (((-(1.369306393762915*bioverJB_3[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_3[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_3[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_3[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
-  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_3[3]*hamil[16])-1.369306393762915*bioverJB_3[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[0] = (((-(0.6123724356957944*bioverJB_2[1]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_2[0]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[1] = (((-(0.6123724356957944*bioverJB_2[0]*apar[3]*hamil[3])-0.6123724356957944*bioverJB_2[1]*apar[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[2] = (((-(0.6123724356957944*apar[3]*bioverJB_2[3]*hamil[3])-0.6123724356957944*apar[2]*bioverJB_2[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[3] = (((-(1.369306393762915*bioverJB_2[1]*apar[3]*hamil[16])-1.369306393762915*bioverJB_2[0]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[0]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[5] = (((-(0.6123724356957944*apar[2]*bioverJB_2[3]*hamil[3])-0.6123724356957944*bioverJB_2[2]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[3])*rdx2)/vmap[1])/m_; 
+  alphax[6] = (((-(1.369306393762915*bioverJB_2[0]*apar[3]*hamil[16])-1.369306393762915*bioverJB_2[1]*apar[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[1]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[7] = (((-(1.369306393762915*apar[3]*bioverJB_2[3]*hamil[16])-1.369306393762915*apar[2]*bioverJB_2[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
+  alphax[11] = (((-(1.369306393762915*apar[2]*bioverJB_2[3]*hamil[16])-1.369306393762915*bioverJB_2[2]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_1[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_1[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_1[1]*apar[2]*hamil[16])*rdx2)/vmap[1])/m_; 
 
 
   out[1] += 0.4330127018922193*(alphax[11]*fin[11]+alphax[7]*fin[7]+alphax[6]*fin[6]+alphax[5]*fin[5]+alphax[3]*fin[3]+alphax[2]*fin[2]+alphax[1]*fin[1]+alphax[0]*fin[0]); 
@@ -79,14 +79,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphax[1]*fin[23]+0.43301270189221935*(alphax[0]*fin[22]+alphax[5]*fin[21])+0.4330127018922193*alphax[2]*fin[19]+0.3872983346207417*(alphax[6]*fin[15]+alphax[3]*fin[14]+alphax[11]*fin[13]+alphax[7]*fin[10]); 
 
   double alphaz[24] = {0.}; 
-  alphaz[0] = (((0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[2] = (((0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[3] = (((1.369306393762915*bioverJB_3[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_3[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[0]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[3]+0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
-  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_3[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_3[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[7] = (((1.369306393762915*bioverJB_3[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_3[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
-  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_3[3]*hamil[16]+1.369306393762915*bioverJB_3[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[0] = (((0.6123724356957944*bioverJB_2[2]*apar[3]*hamil[3]+0.6123724356957944*bioverJB_2[0]*apar[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[1] = (((0.6123724356957944*apar[3]*bioverJB_2[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_2[1]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[2] = (((0.6123724356957944*bioverJB_2[0]*apar[3]*hamil[3]+0.6123724356957944*apar[1]*bioverJB_2[2]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[3]+0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[3] = (((1.369306393762915*bioverJB_2[2]*apar[3]*hamil[16]+1.369306393762915*bioverJB_2[0]*apar[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[3]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*apar[2]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[0]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[5] = (((0.6123724356957944*apar[1]*bioverJB_2[3]*hamil[3]+0.6123724356957944*bioverJB_2[1]*apar[3]*hamil[3])*rdx2*rdz2)/vmap[1]+((0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[3]+0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[3]+0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[3])*rdz2)/vmap[1])/m_; 
+  alphaz[6] = (((1.369306393762915*apar[3]*bioverJB_2[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_2[1]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[2]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[2]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[1]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[1]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[7] = (((1.369306393762915*bioverJB_2[0]*apar[3]*hamil[16]+1.369306393762915*apar[1]*bioverJB_2[2]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[1]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[3]*hamil[16]+0.7905694150420947*apar[0]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
+  alphaz[11] = (((1.369306393762915*apar[1]*bioverJB_2[3]*hamil[16]+1.369306393762915*bioverJB_2[1]*apar[3]*hamil[16])*rdx2*rdz2)/vmap[1]+((0.7905694150420947*apar[0]*dualcurlbhatoverB_3[3]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[0]*apar[3]*hamil[16]+0.7905694150420947*apar[1]*dualcurlbhatoverB_3[2]*hamil[16]+0.7905694150420947*dualcurlbhatoverB_3[1]*apar[2]*hamil[16])*rdz2)/vmap[1])/m_; 
 
 
   out[2] += 0.4330127018922193*(alphaz[11]*fin[11]+alphaz[7]*fin[7]+alphaz[6]*fin[6]+alphaz[5]*fin[5]+alphaz[3]*fin[3]+alphaz[2]*fin[2]+alphaz[1]*fin[1]+alphaz[0]*fin[0]); 
@@ -103,14 +103,14 @@ GKYL_CU_DH double dg_gyrokinetic_add_apar_vol_2x2v_ser_p1(const double *w, const
   out[23] += 0.4330127018922193*alphaz[2]*fin[23]+0.43301270189221935*(alphaz[5]*fin[22]+alphaz[0]*fin[21])+0.4330127018922193*alphaz[1]*fin[19]+0.3872983346207417*(alphaz[7]*fin[15]+alphaz[11]*fin[14]+alphaz[3]*fin[13]+alphaz[6]*fin[10]); 
 
   double alphavpar[24] = {0.}; 
-  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[5]-0.6123724356957944*bioverJB_3[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_3[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_3[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_3[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[5]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_3[3]+0.6123724356957944*bioverJB_3[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[2]+0.6123724356957944*bioverJB_3[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_1[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
-  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[5])+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_3[3]-0.6123724356957944*bioverJB_3[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_3[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[12]-0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[5])+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_3[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_3[3]-0.6123724356957944*bioverJB_3[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_3[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
-  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[12]-0.6123724356957944*bioverJB_3[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_3[1]*hamil[9]+0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[12])+0.6123724356957944*bioverJB_3[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_3[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_3[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_3[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
-  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_3[2]*hamil[12])+0.6123724356957944*bioverJB_3[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_3[3]*hamil[9]-0.6123724356957944*bioverJB_3[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_3[3]*hamil[8]+0.6123724356957944*bioverJB_3[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[0] = (((0.6123724356957944*apar[2]*bioverJB_2[2]*hamil[5]-0.6123724356957944*apar[1]*bioverJB_2[1]*hamil[5]-0.6123724356957944*bioverJB_2[2]*hamil[2]*apar[3]+0.6123724356957944*bioverJB_2[1]*hamil[1]*apar[3]-0.6123724356957944*bioverJB_2[0]*apar[1]*hamil[2]+0.6123724356957944*bioverJB_2[0]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[5]-0.3535533905932737*hamil[2]*apar[3]*dualcurlbhatoverB_3[3]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[3]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[2]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[1] = (((0.6123724356957944*apar[2]*bioverJB_2[3]*hamil[5]-0.6123724356957944*bioverJB_2[0]*apar[1]*hamil[5]-0.6123724356957944*hamil[2]*apar[3]*bioverJB_2[3]+0.6123724356957944*bioverJB_2[0]*hamil[1]*apar[3]-0.6123724356957944*apar[1]*bioverJB_2[1]*hamil[2]+0.6123724356957944*bioverJB_2[1]*hamil[1]*apar[2])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[5]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[5]-0.3535533905932737*apar[2]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[2]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[2])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[5]-0.3535533905932737*hamil[1]*apar[2]*dualcurlbhatoverB_1[3]-0.3535533905932737*hamil[1]*dualcurlbhatoverB_1[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[1]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[1])*rdx2)/vmap[1])/m_; 
+  alphavpar[2] = (((-(0.6123724356957944*apar[1]*bioverJB_2[3]*hamil[5])+0.6123724356957944*bioverJB_2[0]*apar[2]*hamil[5]+0.6123724356957944*hamil[1]*apar[3]*bioverJB_2[3]-0.6123724356957944*bioverJB_2[0]*hamil[2]*apar[3]-0.6123724356957944*apar[1]*bioverJB_2[2]*hamil[2]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_2[2])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[5])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[5]-0.3535533905932737*apar[1]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[1]*hamil[2]*apar[3]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[5]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[5]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[3]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[4] = (((0.6123724356957944*apar[2]*bioverJB_2[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_2[1]*hamil[12]-0.6123724356957944*bioverJB_2[2]*apar[3]*hamil[9]-0.6123724356957944*bioverJB_2[0]*apar[1]*hamil[9]+0.6123724356957944*bioverJB_2[1]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_2[0]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[12]-0.3535533905932737*apar[3]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[5] = (((-(0.6123724356957944*apar[1]*bioverJB_2[2]*hamil[5])+0.6123724356957944*bioverJB_2[1]*apar[2]*hamil[5]-0.6123724356957944*apar[1]*hamil[2]*bioverJB_2[3]+0.6123724356957944*hamil[1]*apar[2]*bioverJB_2[3]-0.6123724356957944*bioverJB_2[1]*hamil[2]*apar[3]+0.6123724356957944*hamil[1]*bioverJB_2[2]*apar[3])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[5]-0.3535533905932737*apar[0]*hamil[2]*dualcurlbhatoverB_3[3]-0.3535533905932737*dualcurlbhatoverB_3[0]*hamil[2]*apar[3]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[2]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[2])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[5])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[5]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[5]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[5]-0.3535533905932737*apar[0]*hamil[1]*dualcurlbhatoverB_1[3]-0.3535533905932737*dualcurlbhatoverB_1[0]*hamil[1]*apar[3]-0.3535533905932737*apar[1]*hamil[1]*dualcurlbhatoverB_1[2]-0.3535533905932737*dualcurlbhatoverB_1[1]*hamil[1]*apar[2])*rdx2)/vmap[1])/m_; 
+  alphavpar[8] = (((0.6123724356957944*apar[2]*bioverJB_2[3]*hamil[12]-0.6123724356957944*bioverJB_2[0]*apar[1]*hamil[12]-0.6123724356957944*apar[3]*bioverJB_2[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_2[1]*hamil[9]+0.6123724356957944*bioverJB_2[0]*apar[3]*hamil[8]+0.6123724356957944*bioverJB_2[1]*apar[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[2]*hamil[12]-0.6363961030678926*apar[1]*dualcurlbhatoverB_3[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[0]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[2]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[1]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[1]*hamil[9])*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[12]-0.3535533905932737*apar[2]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[2]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[9] = (((-(0.6123724356957944*apar[1]*bioverJB_2[3]*hamil[12])+0.6123724356957944*bioverJB_2[0]*apar[2]*hamil[12]-0.6123724356957944*bioverJB_2[0]*apar[3]*hamil[9]-0.6123724356957944*apar[1]*bioverJB_2[2]*hamil[9]+0.6123724356957944*apar[3]*bioverJB_2[3]*hamil[8]+0.6123724356957944*apar[2]*bioverJB_2[2]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[12])-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[3]*hamil[9]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[3]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*apar[2]*dualcurlbhatoverB_1[2]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[0]*hamil[12]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[3]*hamil[8]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
+  alphavpar[12] = (((-(0.6123724356957944*apar[1]*bioverJB_2[2]*hamil[12])+0.6123724356957944*bioverJB_2[1]*apar[2]*hamil[12]-0.6123724356957944*apar[1]*bioverJB_2[3]*hamil[9]-0.6123724356957944*bioverJB_2[1]*apar[3]*hamil[9]+0.6123724356957944*apar[2]*bioverJB_2[3]*hamil[8]+0.6123724356957944*bioverJB_2[2]*apar[3]*hamil[8])*rdx2*rdz2)/vmap[1]+((-(0.6363961030678926*apar[1]*dualcurlbhatoverB_3[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_3[1]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[2]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[2]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_3[3]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[0]*apar[3]*hamil[9]-0.3535533905932737*apar[1]*dualcurlbhatoverB_3[2]*hamil[9]-0.3535533905932737*dualcurlbhatoverB_3[1]*apar[2]*hamil[9])*rdz2)/vmap[1]+((-(0.6363961030678926*apar[2]*dualcurlbhatoverB_1[3]*hamil[12])-0.6363961030678926*dualcurlbhatoverB_1[2]*apar[3]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[1]*hamil[12]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[1]*hamil[12]-0.3535533905932737*apar[0]*dualcurlbhatoverB_1[3]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[0]*apar[3]*hamil[8]-0.3535533905932737*apar[1]*dualcurlbhatoverB_1[2]*hamil[8]-0.3535533905932737*dualcurlbhatoverB_1[1]*apar[2]*hamil[8])*rdx2)/vmap[1])/m_; 
 
 
   out[3] += 0.4330127018922193*(alphavpar[12]*fin[12]+alphavpar[9]*fin[9]+alphavpar[8]*fin[8]+alphavpar[5]*fin[5]+alphavpar[4]*fin[4]+alphavpar[2]*fin[2]+alphavpar[1]*fin[1]+alphavpar[0]*fin[0]); 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index bcde53a400..e88c9ec8fb 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -66,8 +66,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -82,8 +81,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -107,8 +105,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -123,8 +120,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -148,8 +144,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -164,8 +159,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -189,8 +183,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -205,8 +198,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *(0); 
-  alpha_quad += -bioverJB_quad[2]/m_ *(0); 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;

From 3a1f97cf25b20a6325dcd5d3b272728cc8c3c345 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 28 Apr 2026 13:01:28 -0400
Subject: [PATCH 156/181] refactor the inactive flux surface kernels

---
 ...conf_return_zero.c => gk_collisionless_flux_surfconf_none.c} | 2 +-
 ...vpar_return_zero.c => gk_collisionless_flux_surfvpar_none.c} | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfconf_return_zero.c => gk_collisionless_flux_surfconf_none.c} (89%)
 rename gyrokinetic/ker/gk_collisionless_flux/{gk_collisionless_flux_surfvpar_return_zero.c => gk_collisionless_flux_surfvpar_none.c} (88%)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
similarity index 89%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
index b8e1844650..341b6e2c2c 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_return_zero.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfconf_none.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfconf_return_zero(
+GKYL_CU_DH double gk_collisionless_flux_surfconf_none(
     const double *w, const double *dxv,
     const double *vmap, const double *vmapSq, const double q_, const double m_,
     const struct gkyl_dg_surf_geom *dgs, const struct gkyl_gk_dg_surf_geom *gkdgs, 
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
similarity index 88%
rename from gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
rename to gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
index 6ebfb94492..8be40ca284 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_return_zero.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_none.c
@@ -1,5 +1,5 @@
 #include <gkyl_gk_collisionless_flux_kernels.h> 
-GKYL_CU_DH double gk_collisionless_flux_surfvpar_return_zero(
+GKYL_CU_DH double gk_collisionless_flux_surfvpar_none(
     const double *w, const double *dxv,
     const double *vmap_prime_l, const double *vmap_prime_r,
     const double *vmap, const double *vmapSq, const double q_, const double m_, 

From 336fdde636ff382547860a306f531fdccda40a05 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 28 Apr 2026 14:56:33 -0400
Subject: [PATCH 157/181] vpar surface flux kernels written with the nodal
 expansion done after mutliplication of gradA x gradH and A . gradH

---
 ..._collisionless_flux_surfvpar_1x1v_ser_p1.c |   4 +-
 ..._collisionless_flux_surfvpar_1x2v_ser_p1.c |   8 +-
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  48 ++---
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c | 192 +++++++++---------
 4 files changed, 126 insertions(+), 126 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
index 055c7bee14..56b2e82817 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x1v_ser_p1.c
@@ -56,7 +56,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.8660254037844386*(0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*hamil[1]*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -77,7 +77,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x1v_ser_p1(
 
   alpha_quad = -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.8660254037844386*hamil[2]-3.3541019662496847*hamil[4]))/vmap[1]); 
-  alpha_quad += -(0.8660254037844386*hamil[1]*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.8660254037844386*(0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*hamil[1]*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
index 922fdb0552..e916144b42 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_1x2v_ser_p1.c
@@ -58,7 +58,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*(0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -70,7 +70,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.7071067811865475*apar[0]-0.7071067811865475*apar[1])*(0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[0]-0.7071067811865475*apardot[1]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -91,7 +91,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*(0.6123724356957944*hamil[1]-0.6123724356957944*hamil[5])*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -103,7 +103,7 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_1x2v_ser_p1(
 
   alpha_quad = -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.6123724356957944*hamil[2]-2.371708245126284*hamil[8]))/vmap[1]); 
-  alpha_quad += -((0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)/m_/bmag_quad * (0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.7071067811865475*apar[1]+0.7071067811865475*apar[0])*(0.6123724356957944*hamil[5]+0.6123724356957944*hamil[1])*rdx2)*dualcurlbhat_quad[2]; 
   alpha_quad += -q_/m_*(0.7071067811865475*apardot[1]+0.7071067811865475*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index e88c9ec8fb..7ac8ec5933 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -64,9 +64,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -79,9 +79,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -103,9 +103,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -118,9 +118,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -142,9 +142,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -157,9 +157,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -181,9 +181,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -196,9 +196,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * (0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index 388b4a2609..a1c6a84102 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -70,12 +70,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -89,12 +89,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -117,12 +117,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -136,12 +136,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -164,12 +164,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -183,12 +183,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -211,12 +211,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -230,12 +230,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -258,12 +258,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -277,12 +277,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -305,12 +305,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -324,12 +324,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -352,12 +352,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -371,12 +371,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -399,12 +399,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -418,12 +418,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * (0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;

From efb002f5719def633f0c2e0295bbf8c4c00b6481 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 28 Apr 2026 15:55:24 -0400
Subject: [PATCH 158/181] down projection of gradH x gradA and A . gradH

---
 ..._collisionless_flux_surfvpar_2x2v_ser_p1.c |  82 ++++--
 ..._collisionless_flux_surfvpar_3x2v_ser_p1.c | 276 ++++++++++++------
 2 files changed, 238 insertions(+), 120 deletions(-)

diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
index 7ac8ec5933..67c457bcb8 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_2x2v_ser_p1.c
@@ -40,6 +40,40 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   hamil[12] = 1.4142135623730951*bmag[3]*vmap[3]; 
   hamil[16] = 1.4142135623730951*vmapSq[2]*m_; 
 
+  double gradHxgradA_1[24] = {0.}; 
+
+  double gradHxgradA_2[24] = {0.}; 
+  gradHxgradA_2[0] = (1.5*apar[1]*hamil[2]-1.5*hamil[1]*apar[2])*rdx2*rdz2; 
+  gradHxgradA_2[1] = (1.5*apar[1]*hamil[5]-1.5*hamil[1]*apar[3])*rdx2*rdz2; 
+  gradHxgradA_2[2] = (1.5*hamil[2]*apar[3]-1.5*apar[2]*hamil[5])*rdx2*rdz2; 
+  gradHxgradA_2[4] = (1.5*apar[1]*hamil[9]-1.5*apar[2]*hamil[8])*rdx2*rdz2; 
+  gradHxgradA_2[8] = (1.5*apar[1]*hamil[12]-1.5*apar[3]*hamil[8])*rdx2*rdz2; 
+  gradHxgradA_2[9] = (1.5*apar[3]*hamil[9]-1.5*apar[2]*hamil[12])*rdx2*rdz2; 
+
+  double gradHxgradA_3[24] = {0.}; 
+
+  double apargradH_1[24] = {0.}; 
+  apargradH_1[0] = 0.8660254037844386*(apar[2]*hamil[5]+apar[0]*hamil[1])*rdx2; 
+  apargradH_1[1] = 0.8660254037844386*(apar[3]*hamil[5]+apar[1]*hamil[1])*rdx2; 
+  apargradH_1[2] = 0.8660254037844386*(apar[0]*hamil[5]+hamil[1]*apar[2])*rdx2; 
+  apargradH_1[4] = 0.8660254037844386*(apar[2]*hamil[12]+apar[0]*hamil[8])*rdx2; 
+  apargradH_1[5] = 0.8660254037844386*(apar[1]*hamil[5]+hamil[1]*apar[3])*rdx2; 
+  apargradH_1[8] = 0.8660254037844386*(apar[3]*hamil[12]+apar[1]*hamil[8])*rdx2; 
+  apargradH_1[9] = 0.8660254037844386*(apar[0]*hamil[12]+apar[2]*hamil[8])*rdx2; 
+  apargradH_1[12] = 0.8660254037844386*(apar[1]*hamil[12]+apar[3]*hamil[8])*rdx2; 
+
+  double apargradH_2[24] = {0.}; 
+
+  double apargradH_3[24] = {0.}; 
+  apargradH_3[0] = 0.8660254037844386*(apar[1]*hamil[5]+apar[0]*hamil[2])*rdz2; 
+  apargradH_3[1] = 0.8660254037844386*(apar[0]*hamil[5]+apar[1]*hamil[2])*rdz2; 
+  apargradH_3[2] = 0.8660254037844386*(apar[3]*hamil[5]+apar[2]*hamil[2])*rdz2; 
+  apargradH_3[4] = 0.8660254037844386*(apar[1]*hamil[12]+apar[0]*hamil[9])*rdz2; 
+  apargradH_3[5] = 0.8660254037844386*(apar[2]*hamil[5]+hamil[2]*apar[3])*rdz2; 
+  apargradH_3[8] = 0.8660254037844386*(apar[0]*hamil[12]+apar[1]*hamil[9])*rdz2; 
+  apargradH_3[9] = 0.8660254037844386*(apar[3]*hamil[12]+apar[2]*hamil[9])*rdz2; 
+  apargradH_3[12] = 0.8660254037844386*(apar[2]*hamil[12]+apar[3]*hamil[9])*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[24]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -64,9 +98,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.25*apargradH_1[12])+0.25*apargradH_1[9]+0.25*apargradH_1[8]+0.25*apargradH_1[5]-0.25*apargradH_1[4]-0.25*apargradH_1[2]-0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.25*gradHxgradA_2[9]+0.25*gradHxgradA_2[8]-0.25*gradHxgradA_2[4]-0.25*gradHxgradA_2[2]-0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -79,9 +113,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]-0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.25*apargradH_1[12]-0.25*apargradH_1[9]-0.25*apargradH_1[8]+0.25*apargradH_1[5]+0.25*apargradH_1[4]-0.25*apargradH_1[2]-0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.25*gradHxgradA_2[9])-0.25*gradHxgradA_2[8]+0.25*gradHxgradA_2[4]-0.25*gradHxgradA_2[2]-0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(0.5*apardot[3]-0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -103,9 +137,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.25*apargradH_1[12]-0.25*apargradH_1[9]+0.25*apargradH_1[8]-0.25*apargradH_1[5]-0.25*apargradH_1[4]+0.25*apargradH_1[2]-0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.25*gradHxgradA_2[9])+0.25*gradHxgradA_2[8]-0.25*gradHxgradA_2[4]+0.25*gradHxgradA_2[2]-0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -118,9 +152,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])+0.5*apar[2]-0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[9]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[2]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.25*apargradH_1[12])+0.25*apargradH_1[9]-0.25*apargradH_1[8]-0.25*apargradH_1[5]+0.25*apargradH_1[4]+0.25*apargradH_1[2]-0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.25*gradHxgradA_2[9]-0.25*gradHxgradA_2[8]+0.25*gradHxgradA_2[4]+0.25*gradHxgradA_2[2]-0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])+0.5*apardot[2]-0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -142,9 +176,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]-0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.25*apargradH_1[12]+0.25*apargradH_1[9]-0.25*apargradH_1[8]-0.25*apargradH_1[5]-0.25*apargradH_1[4]-0.25*apargradH_1[2]+0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.25*gradHxgradA_2[9]-0.25*gradHxgradA_2[8]-0.25*gradHxgradA_2[4]-0.25*gradHxgradA_2[2]+0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -157,9 +191,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.5*apar[3])-0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[1]-0.8660254037844386*apar[3])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])+0.4330127018922193*hamil[8]-0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.25*apargradH_1[12])-0.25*apargradH_1[9]+0.25*apargradH_1[8]-0.25*apargradH_1[5]+0.25*apargradH_1[4]-0.25*apargradH_1[2]+0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.25*gradHxgradA_2[9])+0.25*gradHxgradA_2[8]+0.25*gradHxgradA_2[4]-0.25*gradHxgradA_2[2]+0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(-(0.5*apardot[3])-0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -181,9 +215,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(-(0.4330127018922193*hamil[12])-0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.25*apargradH_1[12])-0.25*apargradH_1[9]-0.25*apargradH_1[8]+0.25*apargradH_1[5]-0.25*apargradH_1[4]+0.25*apargradH_1[2]+0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.25*gradHxgradA_2[9])-0.25*gradHxgradA_2[8]-0.25*gradHxgradA_2[4]+0.25*gradHxgradA_2[2]+0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -196,9 +230,9 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_2x2v_ser_p1(
   alpha_quad = -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * B3_quad; 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
   alpha_quad += -((0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.4330127018922193*hamil[3]-1.6770509831248424*hamil[16]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.5*apar[3]+0.5*apar[2]+0.5*apar[1]+0.5*apar[0])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.8660254037844386*apar[3]+0.8660254037844386*apar[1])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[9]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[2])*rdx2*rdz2-1.0*(0.8660254037844386*apar[3]+0.8660254037844386*apar[2])*(0.4330127018922193*hamil[12]+0.4330127018922193*hamil[8]+0.4330127018922193*hamil[5]+0.4330127018922193*hamil[1])*rdx2*rdz2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.25*apargradH_1[12]+0.25*apargradH_1[9]+0.25*apargradH_1[8]+0.25*apargradH_1[5]+0.25*apargradH_1[4]+0.25*apargradH_1[2]+0.25*apargradH_1[1]+0.25*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -1.0/m_/bmag_quad * (0.0)*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.25*gradHxgradA_2[9]+0.25*gradHxgradA_2[8]+0.25*gradHxgradA_2[4]+0.25*gradHxgradA_2[2]+0.25*gradHxgradA_2[1]+0.25*gradHxgradA_2[0]); 
   alpha_quad += -q_/m_*(0.5*apardot[3]+0.5*apardot[2]+0.5*apardot[1]+0.5*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
diff --git a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
index a1c6a84102..2338f22427 100644
--- a/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
+++ b/gyrokinetic/ker/gk_collisionless_flux/gk_collisionless_flux_surfvpar_3x2v_ser_p1.c
@@ -45,6 +45,90 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   hamil[21] = 1.4142135623730951*vmap[3]*bmag[5]; 
   hamil[32] = 2.0*vmapSq[2]*m_; 
 
+  double gradHxgradA_1[48] = {0.}; 
+  gradHxgradA_1[0] = (-(1.060660171779821*apar[4]*hamil[7])+1.060660171779821*apar[5]*hamil[6]-1.060660171779821*apar[2]*hamil[3]+1.060660171779821*hamil[2]*apar[3])*rdy2*rdz2; 
+  gradHxgradA_1[1] = (-(1.060660171779821*apar[2]*hamil[7])+1.060660171779821*(apar[3]*hamil[6]+hamil[2]*apar[5])-1.060660171779821*hamil[3]*apar[4])*rdy2*rdz2; 
+  gradHxgradA_1[2] = (1.060660171779821*(hamil[6]*apar[7]+hamil[2]*apar[6])-1.060660171779821*(apar[4]*hamil[16]+apar[2]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[3] = (1.060660171779821*(apar[5]*hamil[16]+apar[3]*hamil[8])-1.060660171779821*(apar[7]*hamil[7]+hamil[3]*apar[6]))*rdy2*rdz2; 
+  gradHxgradA_1[5] = -(1.060660171779821*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[6] = (1.060660171779821*(hamil[2]*apar[7]+apar[6]*hamil[6])-1.060660171779821*(apar[2]*hamil[16]+apar[4]*hamil[8]))*rdy2*rdz2; 
+  gradHxgradA_1[7] = (1.060660171779821*(apar[3]*hamil[16]+apar[5]*hamil[8])-1.060660171779821*(apar[6]*hamil[7]+hamil[3]*apar[7]))*rdy2*rdz2; 
+  gradHxgradA_1[12] = -(1.060660171779821*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[14] = -(1.060660171779821*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdy2*rdz2); 
+  gradHxgradA_1[21] = -(1.060660171779821*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdy2*rdz2); 
+
+  double gradHxgradA_2[48] = {0.}; 
+  gradHxgradA_2[0] = (1.060660171779821*apar[4]*hamil[8]-1.060660171779821*apar[6]*hamil[6]+1.060660171779821*apar[1]*hamil[3]-1.060660171779821*hamil[1]*apar[3])*rdx2*rdz2; 
+  gradHxgradA_2[1] = (1.060660171779821*(apar[4]*hamil[16]+apar[1]*hamil[7])-1.060660171779821*(hamil[6]*apar[7]+hamil[1]*apar[5]))*rdx2*rdz2; 
+  gradHxgradA_2[2] = (1.060660171779821*apar[1]*hamil[8]-1.060660171779821*(apar[3]*hamil[6]+hamil[1]*apar[6])+1.060660171779821*hamil[3]*apar[4])*rdx2*rdz2; 
+  gradHxgradA_2[3] = (-(1.060660171779821*apar[6]*hamil[16])+1.060660171779821*apar[7]*hamil[8]-1.060660171779821*apar[3]*hamil[7]+1.060660171779821*hamil[3]*apar[5])*rdx2*rdz2; 
+  gradHxgradA_2[5] = (1.060660171779821*apar[1]*hamil[14]-1.060660171779821*apar[3]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[6] = (1.060660171779821*(apar[1]*hamil[16]+apar[4]*hamil[7])-1.060660171779821*(hamil[1]*apar[7]+apar[5]*hamil[6]))*rdx2*rdz2; 
+  gradHxgradA_2[8] = (-(1.060660171779821*apar[3]*hamil[16])+1.060660171779821*apar[5]*hamil[8]-1.060660171779821*apar[6]*hamil[7]+1.060660171779821*hamil[3]*apar[7])*rdx2*rdz2; 
+  gradHxgradA_2[12] = (1.060660171779821*apar[1]*hamil[21]-1.060660171779821*apar[5]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[13] = (1.060660171779821*apar[4]*hamil[14]-1.060660171779821*apar[6]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[14] = (1.060660171779821*apar[5]*hamil[14]-1.060660171779821*apar[3]*hamil[21])*rdx2*rdz2; 
+  gradHxgradA_2[20] = (1.060660171779821*apar[4]*hamil[21]-1.060660171779821*apar[7]*hamil[12])*rdx2*rdz2; 
+  gradHxgradA_2[22] = (1.060660171779821*apar[7]*hamil[14]-1.060660171779821*apar[6]*hamil[21])*rdx2*rdz2; 
+
+  double gradHxgradA_3[48] = {0.}; 
+  gradHxgradA_3[0] = (-(1.060660171779821*apar[5]*hamil[8])+1.060660171779821*apar[6]*hamil[7]-1.060660171779821*apar[1]*hamil[2]+1.060660171779821*hamil[1]*apar[2])*rdx2*rdy2; 
+  gradHxgradA_3[1] = (-(1.060660171779821*apar[5]*hamil[16])+1.060660171779821*apar[7]*hamil[7]-1.060660171779821*apar[1]*hamil[6]+1.060660171779821*hamil[1]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[2] = (1.060660171779821*apar[6]*hamil[16]-1.060660171779821*apar[7]*hamil[8]+1.060660171779821*apar[2]*hamil[6]-1.060660171779821*hamil[2]*apar[4])*rdx2*rdy2; 
+  gradHxgradA_3[3] = (-(1.060660171779821*apar[1]*hamil[8])+1.060660171779821*(apar[2]*hamil[7]+hamil[1]*apar[6])-1.060660171779821*hamil[2]*apar[5])*rdx2*rdy2; 
+  gradHxgradA_3[5] = 1.060660171779821*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[7] = (-(1.060660171779821*apar[1]*hamil[16])+1.060660171779821*(apar[4]*hamil[7]+hamil[1]*apar[7])-1.060660171779821*apar[5]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[8] = (1.060660171779821*apar[2]*hamil[16]-1.060660171779821*(apar[4]*hamil[8]+hamil[2]*apar[7])+1.060660171779821*apar[6]*hamil[6])*rdx2*rdy2; 
+  gradHxgradA_3[12] = 1.060660171779821*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[14] = 1.060660171779821*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2*rdy2; 
+  gradHxgradA_3[21] = 1.060660171779821*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2*rdy2; 
+
+  double apargradH_1[48] = {0.}; 
+  apargradH_1[0] = 0.6123724356957944*(apar[6]*hamil[16]+apar[3]*hamil[7]+apar[2]*hamil[6]+apar[0]*hamil[1])*rdx2; 
+  apargradH_1[1] = 0.6123724356957944*(apar[7]*hamil[16]+apar[5]*hamil[7]+apar[4]*hamil[6]+apar[1]*hamil[1])*rdx2; 
+  apargradH_1[2] = 0.6123724356957944*(apar[3]*hamil[16]+apar[6]*hamil[7]+apar[0]*hamil[6]+hamil[1]*apar[2])*rdx2; 
+  apargradH_1[3] = 0.6123724356957944*(apar[2]*hamil[16]+apar[0]*hamil[7]+apar[6]*hamil[6]+hamil[1]*apar[3])*rdx2; 
+  apargradH_1[5] = 0.6123724356957944*(apar[3]*hamil[21]+apar[0]*hamil[12])*rdx2; 
+  apargradH_1[6] = 0.6123724356957944*(apar[5]*hamil[16]+apar[7]*hamil[7]+apar[1]*hamil[6]+hamil[1]*apar[4])*rdx2; 
+  apargradH_1[7] = 0.6123724356957944*(apar[4]*hamil[16]+apar[1]*hamil[7]+hamil[6]*apar[7]+hamil[1]*apar[5])*rdx2; 
+  apargradH_1[8] = 0.6123724356957944*(apar[0]*hamil[16]+apar[2]*hamil[7]+apar[3]*hamil[6]+hamil[1]*apar[6])*rdx2; 
+  apargradH_1[12] = 0.6123724356957944*(apar[5]*hamil[21]+apar[1]*hamil[12])*rdx2; 
+  apargradH_1[13] = 0.6123724356957944*(apar[6]*hamil[21]+apar[2]*hamil[12])*rdx2; 
+  apargradH_1[14] = 0.6123724356957944*(apar[0]*hamil[21]+apar[3]*hamil[12])*rdx2; 
+  apargradH_1[16] = 0.6123724356957944*(apar[1]*hamil[16]+apar[4]*hamil[7]+hamil[1]*apar[7]+apar[5]*hamil[6])*rdx2; 
+  apargradH_1[20] = 0.6123724356957944*(apar[7]*hamil[21]+apar[4]*hamil[12])*rdx2; 
+  apargradH_1[21] = 0.6123724356957944*(apar[1]*hamil[21]+apar[5]*hamil[12])*rdx2; 
+  apargradH_1[22] = 0.6123724356957944*(apar[2]*hamil[21]+apar[6]*hamil[12])*rdx2; 
+  apargradH_1[27] = 0.6123724356957944*(apar[4]*hamil[21]+apar[7]*hamil[12])*rdx2; 
+
+  double apargradH_2[48] = {0.}; 
+  apargradH_2[0] = 0.6123724356957944*(apar[5]*hamil[16]+apar[3]*hamil[8]+apar[1]*hamil[6]+apar[0]*hamil[2])*rdy2; 
+  apargradH_2[1] = 0.6123724356957944*(apar[3]*hamil[16]+apar[5]*hamil[8]+apar[0]*hamil[6]+apar[1]*hamil[2])*rdy2; 
+  apargradH_2[2] = 0.6123724356957944*(apar[7]*hamil[16]+apar[6]*hamil[8]+apar[4]*hamil[6]+apar[2]*hamil[2])*rdy2; 
+  apargradH_2[3] = 0.6123724356957944*(apar[1]*hamil[16]+apar[0]*hamil[8]+apar[5]*hamil[6]+hamil[2]*apar[3])*rdy2; 
+  apargradH_2[6] = 0.6123724356957944*(apar[6]*hamil[16]+apar[7]*hamil[8]+apar[2]*hamil[6]+hamil[2]*apar[4])*rdy2; 
+  apargradH_2[7] = 0.6123724356957944*(apar[0]*hamil[16]+apar[1]*hamil[8]+apar[3]*hamil[6]+hamil[2]*apar[5])*rdy2; 
+  apargradH_2[8] = 0.6123724356957944*(apar[4]*hamil[16]+apar[2]*hamil[8]+hamil[6]*apar[7]+hamil[2]*apar[6])*rdy2; 
+  apargradH_2[16] = 0.6123724356957944*(apar[2]*hamil[16]+apar[4]*hamil[8]+hamil[2]*apar[7]+apar[6]*hamil[6])*rdy2; 
+
+  double apargradH_3[48] = {0.}; 
+  apargradH_3[0] = 0.6123724356957944*(apar[4]*hamil[16]+apar[2]*hamil[8]+apar[1]*hamil[7]+apar[0]*hamil[3])*rdz2; 
+  apargradH_3[1] = 0.6123724356957944*(apar[2]*hamil[16]+apar[4]*hamil[8]+apar[0]*hamil[7]+apar[1]*hamil[3])*rdz2; 
+  apargradH_3[2] = 0.6123724356957944*(apar[1]*hamil[16]+apar[0]*hamil[8]+apar[4]*hamil[7]+apar[2]*hamil[3])*rdz2; 
+  apargradH_3[3] = 0.6123724356957944*(apar[7]*hamil[16]+apar[6]*hamil[8]+apar[5]*hamil[7]+apar[3]*hamil[3])*rdz2; 
+  apargradH_3[5] = 0.6123724356957944*(apar[1]*hamil[21]+apar[0]*hamil[14])*rdz2; 
+  apargradH_3[6] = 0.6123724356957944*(apar[0]*hamil[16]+apar[1]*hamil[8]+apar[2]*hamil[7]+hamil[3]*apar[4])*rdz2; 
+  apargradH_3[7] = 0.6123724356957944*(apar[6]*hamil[16]+apar[7]*hamil[8]+apar[3]*hamil[7]+hamil[3]*apar[5])*rdz2; 
+  apargradH_3[8] = 0.6123724356957944*(apar[5]*hamil[16]+apar[3]*hamil[8]+apar[7]*hamil[7]+hamil[3]*apar[6])*rdz2; 
+  apargradH_3[12] = 0.6123724356957944*(apar[0]*hamil[21]+apar[1]*hamil[14])*rdz2; 
+  apargradH_3[13] = 0.6123724356957944*(apar[4]*hamil[21]+apar[2]*hamil[14])*rdz2; 
+  apargradH_3[14] = 0.6123724356957944*(apar[5]*hamil[21]+apar[3]*hamil[14])*rdz2; 
+  apargradH_3[16] = 0.6123724356957944*(apar[3]*hamil[16]+apar[5]*hamil[8]+apar[6]*hamil[7]+hamil[3]*apar[7])*rdz2; 
+  apargradH_3[20] = 0.6123724356957944*(apar[2]*hamil[21]+apar[4]*hamil[14])*rdz2; 
+  apargradH_3[21] = 0.6123724356957944*(apar[3]*hamil[21]+apar[5]*hamil[14])*rdz2; 
+  apargradH_3[22] = 0.6123724356957944*(apar[7]*hamil[21]+apar[6]*hamil[14])*rdz2; 
+  apargradH_3[27] = 0.6123724356957944*(apar[6]*hamil[21]+apar[7]*hamil[14])*rdz2; 
+
   double *flux_surf_nodal = &flux_surf[72]; 
   double cfl = 0.0; 
   double bmag_quad = 0.0; 
@@ -70,12 +154,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]-0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])+0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])+0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])-0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]-0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])+0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -89,12 +173,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])+0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]-0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])+0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]+0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])+0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]-0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -117,12 +201,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])+0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]-0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]-0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]-0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])+0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]-0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -136,12 +220,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]-0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])+0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]-0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])+0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]-0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])+0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -164,12 +248,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])+0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])+0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]-0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]+0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])+0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])+0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -183,12 +267,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]-0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]-0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]-0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]-0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])-0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]-0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]-0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -211,12 +295,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]-0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]-0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])+0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])+0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]-0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]-0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -230,12 +314,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]-0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[6]-0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])+0.3061862178478971*hamil[8]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])+0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]-0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])+0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]-0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])+0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]-0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]-0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]-0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])+0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]-0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])+0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]-0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]-0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -258,12 +342,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])-0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]+0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]+0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])+0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])-0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]+0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -277,12 +361,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]-0.3535533905932737*apar[5]-0.3535533905932737*apar[4]-0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]-0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]+0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])-0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]+0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]-0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]+0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])-0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -305,12 +389,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]+0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])-0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])-0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]+0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]+0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])-0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -324,12 +408,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]+0.3535533905932737*apar[5]-0.3535533905932737*apar[4]+0.3535533905932737*apar[3]-0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]-0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])+0.6123724356957944*apar[5]-0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])-0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]-0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]-0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]+0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]-0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]-0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])-0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]-0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]-0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])-0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]-0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]-0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])-0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]-0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]-0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]+0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]-0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]-0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]-0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -352,12 +436,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]-0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]+0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]+0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])-0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]-0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]+0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]+0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -371,12 +455,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((-(0.3535533905932737*apar[7])-0.3535533905932737*apar[6]-0.3535533905932737*apar[5]+0.3535533905932737*apar[4]-0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((-(0.6123724356957944*apar[7])-0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])-0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]-0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(-(0.6123724356957944*apar[7])-0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[16])-0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])-0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]-0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]-0.1767766952966368*apargradH_1[8]-0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]-0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])-0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]-0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]-0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_2[16])-0.1767766952966368*apargradH_2[8]-0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]-0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])+0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]-0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]-0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])-0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]-0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]-0.1767766952966368*apargradH_3[8]-0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]-0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])-0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]-0.1767766952966368*gradHxgradA_3[8]-0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]-0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(-(0.3535533905932737*apardot[7])-0.3535533905932737*apardot[6]-0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]-0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -399,12 +483,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(-(0.3061862178478971*hamil[21])+0.3061862178478971*hamil[16]-0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_1[27])-0.1767766952966368*apargradH_1[22]-0.1767766952966368*apargradH_1[21]-0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]-0.1767766952966368*apargradH_1[14]-0.1767766952966368*apargradH_1[13]-0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]-0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(-(0.1767766952966368*gradHxgradA_1[21])-0.1767766952966368*gradHxgradA_1[14]-0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]-0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]+0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(-(0.1767766952966368*gradHxgradA_2[22])-0.1767766952966368*gradHxgradA_2[20]-0.1767766952966368*gradHxgradA_2[14]-0.1767766952966368*gradHxgradA_2[13]-0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]-0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (-(0.1767766952966368*apargradH_3[27])-0.1767766952966368*apargradH_3[22]-0.1767766952966368*apargradH_3[21]-0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]-0.1767766952966368*apargradH_3[14]-0.1767766952966368*apargradH_3[13]-0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]-0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(-(0.1767766952966368*gradHxgradA_3[21])-0.1767766952966368*gradHxgradA_3[14]-0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]-0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;
@@ -418,12 +502,12 @@ GKYL_CU_DH double gk_collisionless_flux_surfvpar_3x2v_ser_p1(
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[0]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[1]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
   alpha_quad += -((0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)/m_/bmag_quad * 1/q_*dualcurlbhat_quad[2]*((0.8164965809277261*(0.3061862178478971*hamil[4]-1.185854122563142*hamil[32]))/vmap[1]); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2)*dualcurlbhat_quad[0]; 
-  alpha_quad += -bioverJB_quad[0]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdy2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdy2)*dualcurlbhat_quad[1]; 
-  alpha_quad += -bioverJB_quad[1]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdx2*rdz2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[5]+0.6123724356957944*apar[3])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdz2); 
-  alpha_quad += -1.0/m_/bmag_quad * ((0.3535533905932737*apar[7]+0.3535533905932737*apar[6]+0.3535533905932737*apar[5]+0.3535533905932737*apar[4]+0.3535533905932737*apar[3]+0.3535533905932737*apar[2]+0.3535533905932737*apar[1]+0.3535533905932737*apar[0])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[14]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[3])*rdz2)*dualcurlbhat_quad[2]; 
-  alpha_quad += -bioverJB_quad[2]/m_ *((0.6123724356957944*apar[7]+0.6123724356957944*apar[6]+0.6123724356957944*apar[4]+0.6123724356957944*apar[2])*(0.3061862178478971*hamil[21]+0.3061862178478971*hamil[16]+0.3061862178478971*hamil[12]+0.3061862178478971*hamil[7]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[1])*rdx2*rdy2-1.0*(0.6123724356957944*apar[7]+0.6123724356957944*apar[5]+0.6123724356957944*apar[4]+0.6123724356957944*apar[1])*(0.3061862178478971*hamil[16]+0.3061862178478971*hamil[8]+0.3061862178478971*hamil[6]+0.3061862178478971*hamil[2])*rdx2*rdy2); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_1[27]+0.1767766952966368*apargradH_1[22]+0.1767766952966368*apargradH_1[21]+0.1767766952966368*apargradH_1[20]+0.1767766952966368*apargradH_1[16]+0.1767766952966368*apargradH_1[14]+0.1767766952966368*apargradH_1[13]+0.1767766952966368*apargradH_1[12]+0.1767766952966368*apargradH_1[8]+0.1767766952966368*apargradH_1[7]+0.1767766952966368*apargradH_1[6]+0.1767766952966368*apargradH_1[5]+0.1767766952966368*apargradH_1[3]+0.1767766952966368*apargradH_1[2]+0.1767766952966368*apargradH_1[1]+0.1767766952966368*apargradH_1[0])*dualcurlbhat_quad[0]; 
+  alpha_quad += -bioverJB_quad[0]/m_ *(0.1767766952966368*gradHxgradA_1[21]+0.1767766952966368*gradHxgradA_1[14]+0.1767766952966368*gradHxgradA_1[12]+0.1767766952966368*gradHxgradA_1[7]+0.1767766952966368*gradHxgradA_1[6]+0.1767766952966368*gradHxgradA_1[5]+0.1767766952966368*gradHxgradA_1[3]+0.1767766952966368*gradHxgradA_1[2]+0.1767766952966368*gradHxgradA_1[1]+0.1767766952966368*gradHxgradA_1[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_2[16]+0.1767766952966368*apargradH_2[8]+0.1767766952966368*apargradH_2[7]+0.1767766952966368*apargradH_2[6]+0.1767766952966368*apargradH_2[3]+0.1767766952966368*apargradH_2[2]+0.1767766952966368*apargradH_2[1]+0.1767766952966368*apargradH_2[0])*dualcurlbhat_quad[1]; 
+  alpha_quad += -bioverJB_quad[1]/m_ *(0.1767766952966368*gradHxgradA_2[22]+0.1767766952966368*gradHxgradA_2[20]+0.1767766952966368*gradHxgradA_2[14]+0.1767766952966368*gradHxgradA_2[13]+0.1767766952966368*gradHxgradA_2[12]+0.1767766952966368*gradHxgradA_2[8]+0.1767766952966368*gradHxgradA_2[6]+0.1767766952966368*gradHxgradA_2[5]+0.1767766952966368*gradHxgradA_2[3]+0.1767766952966368*gradHxgradA_2[2]+0.1767766952966368*gradHxgradA_2[1]+0.1767766952966368*gradHxgradA_2[0]); 
+  alpha_quad += -1.0/m_/bmag_quad * (0.1767766952966368*apargradH_3[27]+0.1767766952966368*apargradH_3[22]+0.1767766952966368*apargradH_3[21]+0.1767766952966368*apargradH_3[20]+0.1767766952966368*apargradH_3[16]+0.1767766952966368*apargradH_3[14]+0.1767766952966368*apargradH_3[13]+0.1767766952966368*apargradH_3[12]+0.1767766952966368*apargradH_3[8]+0.1767766952966368*apargradH_3[7]+0.1767766952966368*apargradH_3[6]+0.1767766952966368*apargradH_3[5]+0.1767766952966368*apargradH_3[3]+0.1767766952966368*apargradH_3[2]+0.1767766952966368*apargradH_3[1]+0.1767766952966368*apargradH_3[0])*dualcurlbhat_quad[2]; 
+  alpha_quad += -bioverJB_quad[2]/m_ *(0.1767766952966368*gradHxgradA_3[21]+0.1767766952966368*gradHxgradA_3[14]+0.1767766952966368*gradHxgradA_3[12]+0.1767766952966368*gradHxgradA_3[8]+0.1767766952966368*gradHxgradA_3[7]+0.1767766952966368*gradHxgradA_3[5]+0.1767766952966368*gradHxgradA_3[3]+0.1767766952966368*gradHxgradA_3[2]+0.1767766952966368*gradHxgradA_3[1]+0.1767766952966368*gradHxgradA_3[0]); 
   alpha_quad += -q_/m_*(0.3535533905932737*apardot[7]+0.3535533905932737*apardot[6]+0.3535533905932737*apardot[5]+0.3535533905932737*apardot[4]+0.3535533905932737*apardot[3]+0.3535533905932737*apardot[2]+0.3535533905932737*apardot[1]+0.3535533905932737*apardot[0]); 
 
   cfl = fmax(fabs(alpha_quad), fabs(cfl)) ;

From f5b3806f5c1fe07fe7b4e509dac79f53aeb922ea Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 30 Apr 2026 11:12:49 -0700
Subject: [PATCH 159/181] This commit shows the exact same conservation
 properties as in the main branch. It was tested with this version of the tcv
 3x2v regression test. The 2x2v does not conserve well particle but this is
 related to the poisson_perp_bias branch that was merged in.

---
 gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c | 633 ++++++++++++++++++
 .../creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c |   4 -
 .../creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c |   6 +-
 3 files changed, 636 insertions(+), 7 deletions(-)
 create mode 100644 gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
new file mode 100644
index 0000000000..a26038cf30
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
@@ -0,0 +1,633 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  
+  // Geometry and magnetic field.
+  double B_axis;
+  double R0;
+  double Rc;
+  double Bv0;
+
+  // Plasma parameters.
+  double me; double qe;
+  double mi; double qi;
+  double n0; double Te0; double Ti0; 
+
+  // Collisions.
+  double nu_frac;
+
+  // Source parameters.
+  double P_SOL;
+  double S0;
+  double xSource;
+  double lambdaSource;
+
+  // Grid parameters.
+  double Lx; // Domain size in radial direction.
+  double Ly; // Domain size in binormal direction.
+  double Lz; // Domain size along magnetic field.
+  double x_min; double x_max;
+  double y_min; double y_max;
+  double z_min; double z_max;
+  int Nx;
+  int Ny;
+  int Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc; double mu_max_elc;
+  double vpar_max_ion; double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Common source density profiles.
+double sourceDensity(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[2];
+  double sourceFloor = 0.1;
+
+  struct gk_app_ctx *app = ctx;
+  double S0 = app->S0;
+  double lambdaSource = app->lambdaSource;
+  double xSource = app->xSource;
+  double Lz = app->Lz;
+
+  if (x < xSource) {
+    sourceFloor = 0.5;
+  }
+  if (fabs(z) < Lz/4) {
+    return 0.90625*S0*fmax(exp(-0.5*pow((x-xSource)/lambdaSource,2)),sourceFloor);
+  } else {
+    return 1e-10;
+  }
+}
+
+// Common source temperature profile.
+double sourceTemperature(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3 * lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 30*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial density.
+double densityInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double Ls = app->Lz/4;
+  double xSource[3] = {x, y, 0};
+  double effectiveSource = sourceDensity(t, xSource, ctx);
+  double c_ss = sqrt(5/3*sourceTemperature(t, xSource, ctx)/app->mi);
+  double nPeak = 4*sqrt(5)/3/c_ss*Ls*effectiveSource/2;
+  pcg64_random_t rng = gkyl_pcg64_init(0);
+  double perturb = 1e-3*(gkyl_pcg64_rand_double(&rng) - 0.5)*2.0;
+  if (fabs(z) <= Ls) {
+    return nPeak * (1 + sqrt(1-pow(z/Ls,2)))/2 * (1+perturb);
+  } else {
+    return nPeak/2 * (1+perturb);
+  }
+}
+
+// Initial temperature.
+double temperatureInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3*lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 20*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial ion drift speed.
+double driftSpeed(const double * GKYL_RESTRICT xn, void *ctx){
+  double x = xn[0], y = xn[1], z = xn[2];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  double Lz = app->Lz;
+  double mi = app->mi;
+  double Te;
+  if (x < xSource + 3*lambdaSource) {
+    Te = 50*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    Te = 20*GKYL_ELEMENTARY_CHARGE;
+  }
+  double Ls = Lz/4;
+  if (fabs(z) <= Ls) {
+    return z/Ls*sqrt(Te/mi);
+  } else {
+    return (z > 0 ? 1.0 : -1.0)*sqrt(Te/mi);
+  }
+}
+
+// Radial coordinate mapping.
+double Rx(const double *xc, void *ctx)
+{
+  return xc[0];
+}
+
+// Toroidal magnetic field.
+double Bphi(const double *xc, void *ctx)
+{
+  double x = xc[0];
+  struct gk_app_ctx *app = ctx;
+  double B_axis = app->B_axis;
+  double R0 = app->R0;
+  double R = Rx(xc, ctx);
+  return B_axis*R0/R;
+}
+
+// Vertical magnetic field.
+double Bvert(const double *xc, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double Bv0 = app->Bv0;
+  return Bv0;
+}
+
+// Magnetic field magnitude.
+double bmag(const double *xc, void *ctx)
+{
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  return sqrt(pow(Bt,2) + pow(Bv,2));
+}
+
+// Field line pitch.
+double thetax(const double *xc, void *ctx)
+{
+  return asin(Bvert(xc, ctx)/bmag(xc, ctx));
+}
+
+// Parallel coordinate mapping.
+double Zx(const double *xc, void *ctx)
+{
+  double theta = thetax(xc, ctx);
+  return xc[2]*sin(theta);
+}
+
+double phix(const double *xc, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+  struct gk_app_ctx *app = ctx;
+  double Rc = app->Rc;
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+
+  // Original Shi mapping. This mapping does not pass the right hand check.
+  // double theta = asin(Lp/Lt);
+  // return (y/sin(theta) + z*cos(theta))/Rc; // O
+
+  // This mapping passes right hand check but does not conserve particle!
+  // double theta = thetax(xc, ctx);
+  // return (y/sin(theta) + z*cos(theta))/x;
+
+  // Helical sheared mapping. Passes right hand check and conserves particle.
+  double theta = thetax(xc, ctx);
+  return y/Rc + (Bt * z*sin(theta))/(Bv * x); 
+}
+
+// Interface function calls.
+void source_density(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceDensity(t, xn, ctx); }
+void source_temperature(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceTemperature(t, xn, ctx); }
+void density_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = densityInit(t, xn, ctx); }
+void temp_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = temperatureInit(t, xn, ctx); }
+void upar_ion_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = driftSpeed(xn, ctx); }
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{ 
+  // Cartesian formulation of the magnetic field.
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  double phi = phix(xc, ctx);
+  fout[0] = -Bt*sin(phi);
+  fout[1] = Bt*cos(phi);
+  fout[2] = Bv;
+}
+void zero_func(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = 0.0; }
+
+// Geometry evaluation functions for the gk app
+void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+
+  // Map to cylindrical (R, Z, phi) coordinates.
+  double R   = Rx(xc, ctx);
+  double Z   = Zx(xc, ctx);
+  double phi = phix(xc, ctx);
+  // Map to Cartesian (X, Y, Z) coordinates.
+  double X = R*cos(phi);
+  double Y = R*sin(phi);
+
+  xp[0] = X; xp[1] = Y; xp[2] = Z;
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 3, vdim = 2; // Dimensionality.
+
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double mp = GKYL_PROTON_MASS, me = GKYL_ELECTRON_MASS;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+
+  // Plasma parameters. Chosen based on the value of a cubic sline
+  // between the last TS data inside the LCFS and the probe data in
+  // in the far SOL, near R=0.475 m.
+  double AMU = 2.01410177811;
+  double mi = mp*AMU; // Deuterium ions.
+  double Te0 = 40*eV;
+  double Ti0 = 40*eV;
+  double n0 = 7e18*10; // [1/m^3]
+
+  // Geometry and magnetic field.
+  double B_axis = 0.5;
+  double R0 = 0.85;
+  double a0 = 0.5;
+  double Lp = 2.4; // Poloidal length at x0.
+  double Lt = 8.0; // Toroidal length at x0.
+  double Rc = R0 + a0;
+  double B0 = B_axis*R0/Rc;
+
+  double sintheta = Lp/Lt;
+  double Bv0 = B0*sintheta;
+
+  // Source parameters.
+  double P_SOL = 8.1e5;
+  double S0 = 5.7691e23*10; // Multiplied by 10 to increase beta
+  double xSource = Rc - 0.05;
+  double lambdaSource = 0.005;
+
+  // Collisions;
+  double nuFrac = 0.1;
+
+  // Derived parameters.
+  double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
+  double c_s = sqrt(Te0/mi); // Sound speed.
+  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius.
+
+  // Box size.
+  double Lx = 50*rho_s;
+  double Ly = 100*rho_s;
+  double Lz = Lt; // [m]
+
+  double x_min = Rc - Lx/2;
+  double x_max = Rc + Lx/2;
+  double y_min = -Ly/2;
+  double y_max = Ly/2;
+  double z_min = -Lz/2;
+  double z_max = Lz/2;
+
+  // Grid parameters
+  int Nx = 8;
+  int Ny = 4;
+  int Nz = 4;
+  int Nvpar = 4;
+  int Nmu = 2;
+  int poly_order = 1;
+
+  double vpar_max_elc = 4.*vte;
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
+  double vpar_max_ion = 4.*vti;
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
+
+  double t_end = 1.e-6; // End time, should terminate in 43 steps.
+  int num_frames = 1;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*100;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 20; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .B_axis = B_axis,
+    .R0 = R0,
+    .Rc = Rc,
+    .Bv0 = Bv0,
+    .Lx = Lx,
+    .Ly = Ly,
+    .Lz = Lz,
+    .x_min = x_min, .x_max = x_max,
+    .y_min = y_min, .y_max = y_max,
+    .z_min = z_min, .z_max = z_max,
+
+    .me = me, .qe = qe,
+    .mi = mi, .qi = qi,
+    .n0 = n0, .Te0 = Te0, .Ti0 = Ti0,
+  
+    .nu_frac = nuFrac,
+    
+    .P_SOL = P_SOL,
+    .S0 = S0,
+    .xSource = xSource,
+    .lambdaSource = lambdaSource,
+  
+    .Nx = Nx,
+    .Ny = Ny,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .cells = {Nx, Ny, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+    .vpar_max_elc = vpar_max_elc, .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion, .mu_max_ion = mu_max_ion,
+
+    .t_end = t_end, .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+
+int 
+main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // electrons
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = {-ctx.vpar_max_elc, 0.0},
+    .upper = { ctx.vpar_max_elc, ctx.mu_max_elc},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = zero_func,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_ES,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "elc" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Te0,
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+    
+    .time_rate_diagnostics = true,
+  };
+
+  // ions
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = { ctx.vpar_max_ion, ctx.mu_max_ion},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = upar_ion_init,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_ES,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "ion" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Ti0, 
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 2, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 2, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+
+    .time_rate_diagnostics = true,
+  };
+
+  // field
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+
+    .cfl_frac_omegaH = 1.0,
+    .cfl_frac = 0.9,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.y_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.y_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1], cells_x[2] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx,
+    },
+
+    .num_periodic_dir = 1,
+    .periodic_dirs = { 1 },
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .comm = comm,
+      .cuts = { app_args.cuts[0], app_args.cuts[1], app_args.cuts[2] },
+    }
+  };
+
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+  
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+
+  return 0;
+}
\ No newline at end of file
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index 90b093c2e2..6ecf5369b8 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -826,10 +826,6 @@ main(int argc, char **argv)
       .restart_frame = app_args.restart_frame,
       .num_steps = app_args.num_steps,
     },
-    .print_verbosity = {
-      .enabled = true,
-      .frequency = 0.01,
-    }
   };
 
   gkyl_gyrokinetic_run_simulation(&run_inp);
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 80ddb2f5af..f03e2ce195 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -50,7 +50,7 @@ double r_x(double x, double a_mid, double x_inner)
   return x+a_mid-x_inner;
 }
 
-// cubic polynomial fit to TCV PT q profile (more stable for reg test than NT one).
+// cubic polynomial fit to TCV NT q profile (discharge #65130)
 double qprofile(double R) {
   double qfit[4] = {
     497.3420166252413, -1408.736172826569, 1331.4134861681464, -419.00692601227627
@@ -317,7 +317,7 @@ void bc_shift_func_lo(double t, const double *xc, double* GKYL_RESTRICT fout, vo
 
   double r = r_x(x, a_mid, x_inner);
 
-  fout[0] = Cy*( alpha(r, z_min, 0.0, ctx) - alpha(r, z_max, 0.0, ctx) );
+  fout[0] = Cy*( alpha(r, z_min, 0.0, ctx) - alpha(r, z_max, 0.0, ctx) )/2; // Half the shift for stability.
 }
 
 void bc_shift_func_up(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
@@ -333,7 +333,7 @@ void bc_shift_func_up(double t, const double *xc, double* GKYL_RESTRICT fout, vo
 
   double r = r_x(x, a_mid, x_inner);
 
-  fout[0] = -Cy*( alpha(r, z_min, 0.0, ctx) - alpha(r, z_max, 0.0, ctx) );
+  fout[0] = -Cy*( alpha(r, z_min, 0.0, ctx) - alpha(r, z_max, 0.0, ctx) )/2; // Half the shift for stability.
 }
 
 struct gk_app_ctx create_ctx(void)

From 8db0b1c53fef840e616c71541ccd11ffdbf45a8a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 30 Apr 2026 11:47:32 -0700
Subject: [PATCH 160/181] Remove the bias from Apar and Apardot solvers as they
 do not need to be smooth along z and fix a merging bug.

---
 gyrokinetic/apps/gk_field_2x3x.c | 56 +++-----------------------------
 1 file changed, 4 insertions(+), 52 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 8f0c20ba4c..37223b92a6 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -380,54 +380,6 @@ gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const st
   // Do nothing.
 }
 
-static void 
-gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
-  struct timespec wst = gkyl_wall_clock();
-  
-  gkyl_fem_poisson_perp_update_lhs(field->fem_apardot_solver, field->lapWeightAmpere, field->dApartdtSlvr_kSq);
-  gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
-  gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
-
-  field->invert_flr(app, field, field->apardot);
-
-  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
-}
-
-static void 
-gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
-  struct timespec wst = gkyl_wall_clock();
-
-  gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
-  gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
-
-  // Smooth along z.
-  // gk_field_fem_projection_par(app, field, field->apar, field->apar_smooth_aux);
-  // gkyl_array_copy_range(field->apar, field->apar_smooth_aux, &app->local_ext);
-
-  field->invert_flr(app, field, field->apar);
-
-  app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
-}
-
-static void 
-gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field){
-  // Do nothing.
-}
-
-static void
-gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
-{
-  gk_field_accumulate_current_dens_dot(app, field, rhs_in);
-  gk_field_accumulate_ohms_kSq(app, field, f_in);
-  gk_field_ohm_solve(app, field);
-}
-
-static void
-gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct gkyl_array *f_in[],  struct gkyl_array *rhs_in[])
-{
-  // Do nothing.
-}
-
 static void
 gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -674,10 +626,10 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     }
     // FEM solver for Ampere equation (solved at IC only).
     f->fem_apar_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-        &f->ampere_bcs, f->info.bias_line_list, f->lapWeightAmpere, NULL, app->use_gpu);
+        &f->ampere_bcs, 0, f->lapWeightAmpere, NULL, app->use_gpu);
     // FEM solver for Ohm's law (evolves d(Apart)/dt).
     f->fem_apardot_solver = gkyl_fem_poisson_perp_new(&app->local, &app->grid, app->basis,
-      &f->ampere_bcs, f->info.bias_line_list, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
+      &f->ampere_bcs, 0, f->lapWeightAmpere, f->dApartdtSlvr_kSq, app->use_gpu);
 
     // We have to advance the updater once to be able to update the kSq later.
     gkyl_fem_poisson_perp_set_rhs(f->fem_apardot_solver, f->currentDensdot);
@@ -685,8 +637,8 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     
     // FEM smoother for Aparallel.
     f->fem_parproj_ampere_bc = GKYL_FEM_PARPROJ_NONE;
-    f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->basis,
-      f->fem_parproj_ampere_bc, 0, 0, app->use_gpu);
+    f->fem_apar_parproj = gkyl_fem_parproj_new(&app->global, &app->grid, 
+       &app->basis, f->fem_parproj_ampere_bc, 0, 0, 0, app->use_gpu);
 
     f->ampere_solve = gk_field_ampere_solve_enabled;
     f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;

From 9d78ea504d722135780ff95fef261d58c114495d Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 30 Apr 2026 14:49:09 -0700
Subject: [PATCH 161/181] minimize diff with poisson_perp_bias

---
 gyrokinetic/apps/gk_field.c      | 15 +++++----------
 gyrokinetic/apps/gk_field_2x3x.c | 12 ++++++------
 2 files changed, 11 insertions(+), 16 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 84c4562116..3d5ff9c209 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -301,11 +301,12 @@ gk_field_energy_new(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->is_first_energy_write_call = true;
 
   f->calc_energy_func = gk_field_calc_energy_enabled;
-
   f->calc_energy_dt_func = gk_field_calc_energy_dt_none;
   f->calc_apar_energy_dt_func = gk_field_calc_energy_dt_none;
-  if (f->info.time_rate_diagnostics)
+  
+  if (f->info.time_rate_diagnostics) {
     gk_field_time_rate_diags_new(app, f);
+  }
 
   // Factors for ES energy.
   f->es_energy_fac = mkarr(app->use_gpu, (2*(app->cdim/3)+1)*app->basis.num_basis, app->local_ext.volume);
@@ -369,13 +370,6 @@ gk_field_energy_release(const struct gkyl_gyrokinetic_app *app, struct gk_field
   }
 }
 
-// Related to enforcing parallel Vlasov boundary conditions
-void
-gk_field_enforce_parallel_bc_disabled(const gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *finout)
-{
-  // Do nothing.
-}
-
 // Initialize field object.
 struct gk_field* 
 gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
@@ -506,7 +500,8 @@ gk_field_calc_apar_energy_dt(gkyl_gyrokinetic_app *app, const struct gk_field *f
   field->calc_apar_energy_dt_func(app, field, dt, energy_reduced);
 }
 
-void gk_field_accumulate_rho_c_adiabatic(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gk_species *s, struct gkyl_array **bflux)
+void gk_field_accumulate_rho_c_adiabatic(gkyl_gyrokinetic_app *app, struct gk_field *field,
+  struct gk_species *s, struct gkyl_array **bflux)
 {
   // Gyroaverage the density if needed.
   s->gyroaverage(app, s, s->m0.marr, s->m0_gyroavg);
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 37223b92a6..0a26ee77b8 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -332,7 +332,7 @@ gk_field_rhs_poisson_perp_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field
   field->invert_flr(app, field, field->phi_smooth);
 }
 
-static void 
+static void
 gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   struct timespec wst = gkyl_wall_clock();
   
@@ -589,12 +589,12 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   }
 
   // Potential smoothing (in z) updater
-    enum gkyl_fem_parproj_bc_type fem_parproj_bc = GKYL_FEM_PARPROJ_NONE;
-    for (int d=0; d<app->num_periodic_dir; ++d)
-      if (app->periodic_dirs[d] == app->cdim-1) fem_parproj_bc = GKYL_FEM_PARPROJ_PERIODIC;
+  enum gkyl_fem_parproj_bc_type fem_parproj_bc = GKYL_FEM_PARPROJ_NONE;
+  for (int d=0; d<app->num_periodic_dir; ++d)
+    if (app->periodic_dirs[d] == app->cdim-1) fem_parproj_bc = GKYL_FEM_PARPROJ_PERIODIC;
 
-    f->fem_parproj = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
-      fem_parproj_bc, 0, 0, 0, app->use_gpu);
+  f->fem_parproj = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
+    fem_parproj_bc, 0, 0, 0, app->use_gpu);
 
   f->fem_projection_par_rho_func = gk_field_fem_projection_par;
   f->fem_projection_par_phi_func = gk_field_fem_projection_par;

From c4a9de5d3a1317b88257eb354e62da6638dd9e09 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 1 May 2026 15:08:54 -0700
Subject: [PATCH 162/181] cosmetics

---
 gyrokinetic/apps/gyrokinetic.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index b0be35869d..43c8381898 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1266,7 +1266,6 @@ gkyl_gyrokinetic_app_calc_field_energy(gkyl_gyrokinetic_app* app, double tm)
   }
 }
 
-
 void
 gkyl_gyrokinetic_app_write_field_energy(gkyl_gyrokinetic_app* app)
 {

From 31b08aaacb062b7e0e9e447eaee59d1de0ca8609 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 6 May 2026 12:17:57 -0400
Subject: [PATCH 163/181] rename the surface flux solver em_star to complete_em
 and reset the collisionless priv.h file since the EM and ES surface flux
 kernels are merged now.

---
 gyrokinetic/apps/gk_species_collisionless.c   |   6 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |   2 +-
 .../zero/gkyl_gk_collisionless_flux_priv.h    | 375 ++++++++----------
 3 files changed, 164 insertions(+), 219 deletions(-)

diff --git a/gyrokinetic/apps/gk_species_collisionless.c b/gyrokinetic/apps/gk_species_collisionless.c
index d07f9c254e..2c78a9754f 100644
--- a/gyrokinetic/apps/gk_species_collisionless.c
+++ b/gyrokinetic/apps/gk_species_collisionless.c
@@ -28,7 +28,7 @@ gk_species_collisionless_flux_em_enabled(gkyl_gyrokinetic_app *app, struct gk_sp
   struct gk_collisionless *gkcls, const struct gkyl_array *fin)
 {
   // Compute the surface expansion of the phase space flux for ES + Apar contributions.
-  gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_em_star_op, 
+  gkyl_gk_collisionless_flux_surf(gkcls->surf_flux_em_complete_op, 
     &app->local, &species->local, &app->local_ext, &species->local_ext, 
     species->gyro_phi, species->gyro_apar, species->gyro_apardot, fin, gkcls->flux_surf, species->cflrate);
 }
@@ -202,7 +202,7 @@ gk_species_collisionless_init(struct gkyl_gyrokinetic_app *app, struct gk_specie
     if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) {
       // Set up ES + Apar contributions to flux and solver.
       complete_em = true;
-      gkcls->surf_flux_em_star_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
+      gkcls->surf_flux_em_complete_op = gkyl_gk_collisionless_flux_new(&gks->grid, &app->basis, &gks->basis, 
         gks->info.charge, gks->info.mass, gkcls->collisionless_id, gkcls->no_by, complete_em, app->gk_geom, 
         app->dg_geom, app->gk_dg_geom, gks->vel_map, bctype_conf, app->use_gpu);
       gkcls->slvr_em_complete = gkyl_dg_updater_gyrokinetic_new(&gks->grid, &app->basis, &gks->basis, 
@@ -255,7 +255,7 @@ gk_species_collisionless_release(const struct gkyl_gyrokinetic_app *app, const s
     gkyl_dg_updater_gyrokinetic_release(gkcls->slvr);
 
     if (gkcls->collisionless_id == GKYL_GK_COLLISIONLESS_EM) {
-      gkyl_gk_collisionless_flux_release(gkcls->surf_flux_em_star_op);
+      gkyl_gk_collisionless_flux_release(gkcls->surf_flux_em_complete_op);
       gkyl_dg_updater_gyrokinetic_release(gkcls->slvr_em_complete);
     }
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 85010558f0..f8a468b650 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -285,7 +285,7 @@ struct gk_collisionless {
       struct gkyl_array *flux_surf; // Array for surface phase space flux
       struct gkyl_array *flux_surf_ho; // Host array for surface phase space flux
       struct gkyl_gk_collisionless_flux *surf_flux_op; // Collisionless fluxes.
-      struct gkyl_gk_collisionless_flux *surf_flux_em_star_op; // EM collisionless fluxes without Apardot contribution.
+      struct gkyl_gk_collisionless_flux *surf_flux_em_complete_op; // EM collisionless fluxes without Apardot contribution.
       gkyl_dg_updater_gyrokinetic *slvr; // Collisionless solver.
       gkyl_dg_updater_gyrokinetic *slvr_em_complete; // EM without Apardot contribution.
 
diff --git a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
index c9e42d4c2e..d01adb8cb4 100644
--- a/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
+++ b/gyrokinetic/zero/gkyl_gk_collisionless_flux_priv.h
@@ -36,10 +36,7 @@ static struct { int vdim[3]; } cv_index[] = {
 
 // for use in kernel tables
 typedef struct { gk_collisionless_flux_surf_t kernels[3]; } gkyl_gk_collisionless_flux_surf_kern_list;
-typedef struct { gkyl_gk_collisionless_flux_surf_kern_list kernels_list[4]; } gkyl_gk_collisionless_flux_surf_kern_table;
-
 typedef struct { gk_collisionless_flux_surfvpar_t kernels[3]; } gkyl_gk_collisionless_flux_surfvpar_kern_list;
-typedef struct { gkyl_gk_collisionless_flux_surfvpar_kern_list kernels_list[4]; } gkyl_gk_collisionless_flux_surfvpar_kern_table;
 
 struct gkyl_gk_collisionless_flux {
   struct gkyl_rect_grid phase_grid; // Phase space grid for cell spacing and cell center
@@ -50,9 +47,7 @@ struct gkyl_gk_collisionless_flux {
   gk_collisionless_flux_surf_t flux_surf_edge_up[GKYL_MAX_CDIM]; // kernel for computing surface expansion of phase space flux.
                                                         // at upper configuration space edge
   gk_collisionless_flux_surfvpar_t flux_surfvpar[1]; // kernel for computing surface expansion of phase space flux alpha
-  
   double charge, mass;
-  bool is_em; // Whether it is electromagnetic.
   const struct gk_geometry *gk_geom; // Pointer to geometry struct.
   const struct gkyl_dg_geom *dg_geom; // Pointer to vol dg geometry struct.
   const struct gkyl_gk_dg_geom *gk_dg_geom; // Pointer to vol gk dg geometry struct.
@@ -63,83 +58,69 @@ struct gkyl_gk_collisionless_flux {
 };
 
 //
-// Electrostatic serendipity surface kernels.
+// Serendipity surface kernels.
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_edge_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_surfvpar_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_surfvpar_kernels[] = {
+  { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
 
 //
@@ -148,68 +129,56 @@ static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels = {
-  .kernels_list= {
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-    },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux flux edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 
@@ -218,171 +187,147 @@ static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flu
 //
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_edge_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in vpar (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surfvpar_kern_table ser_gk_collisionless_flux_no_by_surfvpar_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surfvpar_kern_list ser_gk_collisionless_flux_no_by_surfvpar_kernels[] = {
+  { NULL, gk_collisionless_flux_surfvpar_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_surfvpar_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_surfvpar_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_surfvpar_3x2v_ser_p1, NULL }, // 3
 };
+
 //
 // Kernels used at multiblock boundaries.
 //
 
 // Gyrokinetic phase space flux alpha surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_multib_boundary_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in x (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels = {
-  .kernels_list = {
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
-    { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[] = {
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x1v_ser_p1, NULL }, // 0
+  { NULL, gk_collisionless_flux_multib_boundary_edge_surfx_1x2v_ser_p1, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfx_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in y (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_2x2v_ser_p1, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfy_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
 // Gyrokinetic phase space flux alpha edge surface expansions in z (Serendipity kernels)
 GKYL_CU_D
-static const gkyl_gk_collisionless_flux_surf_kern_table ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels = {
-  .kernels_list = {
-    { NULL, NULL, NULL }, // 0
-    { NULL, NULL, NULL }, // 1
-    { NULL, NULL, NULL }, // 2
-    { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
-  },
+static const gkyl_gk_collisionless_flux_surf_kern_list ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[] = {
+  { NULL, NULL, NULL }, // 0
+  { NULL, NULL, NULL }, // 1
+  { NULL, NULL, NULL }, // 2
+  { NULL, gk_collisionless_flux_no_by_multib_boundary_edge_surfz_3x2v_ser_p1, NULL }, // 3
 };
 
+
 GKYL_CU_D
 static gk_collisionless_flux_surf_t
 choose_gk_collisionless_flux_surf_conf_kern(int dir, int cdim, int vdim, int poly_order, enum gkyl_gyrokinetic_bc_type bc)
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -394,21 +339,21 @@ choose_gk_collisionless_flux_edge_surf_conf_kern(int dir, int cdim, int vdim, in
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -418,7 +363,7 @@ GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
 choose_gk_collisionless_flux_surf_vpar_kern(int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_surfvpar_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 GKYL_CU_D
@@ -427,21 +372,21 @@ choose_gk_collisionless_flux_no_by_surf_conf_kern(int dir, int cdim, int vdim, i
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)                                       
-      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -453,21 +398,21 @@ choose_gk_collisionless_flux_no_by_edge_surf_conf_kern(int dir, int cdim, int vd
 {
   if (bc == GKYL_BC_GK_SKIP) {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_multib_boundary_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
   else {
     if (dir == 0)
-      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfx_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 1)
-      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfy_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else if (dir == 2)
-      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+      return ser_gk_collisionless_flux_no_by_edge_surfz_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
     else
       return NULL;
   }
@@ -477,7 +422,7 @@ GKYL_CU_D
 static gk_collisionless_flux_surfvpar_t
 choose_gk_collisionless_flux_no_by_surf_vpar_kern(int cdim, int vdim, int poly_order)
 {
-  return ser_gk_collisionless_flux_no_by_surfvpar_kernels.kernels_list[cv_index[cdim].vdim[vdim]].kernels[poly_order];
+  return ser_gk_collisionless_flux_no_by_surfvpar_kernels[cv_index[cdim].vdim[vdim]].kernels[poly_order];
 }
 
 #ifdef GKYL_HAVE_CUDA
@@ -502,4 +447,4 @@ void gkyl_gk_collisionless_flux_surf_cu(struct gkyl_gk_collisionless_flux *up,
   const struct gkyl_range *conf_ext_range, const struct gkyl_range *phase_ext_range, 
   const struct gkyl_array *phi, const struct gkyl_array *apar, const struct gkyl_array *apardot, 
   const struct gkyl_array* fin, struct gkyl_array* flux_surf, struct gkyl_array* cflrate);
-#endif
+#endif
\ No newline at end of file

From 56acd04e5cf527bf18350c59ebd6060b38bf9390 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 6 May 2026 14:44:59 -0400
Subject: [PATCH 164/181] add standard naming of regression test

---
 gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c | 2 +-
 gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c | 2 +-
 gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c | 4 ++--
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
index 7893e230c4..8e5aeddfb2 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_1x2v_p1.c
@@ -393,7 +393,6 @@ int main(int argc, char **argv)
 
   // GK app
   struct gkyl_gk app_inp = {
-    .name = "gk_em_alfven_1x2v_p1",
     .cfl_frac = 1.0,
     .cfl_frac_omegaH = 1.0,
 
@@ -427,6 +426,7 @@ int main(int argc, char **argv)
     },
   };
 
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
     .time_stepping = {
diff --git a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
index 2e35daa53d..53c9268d12 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_2x2v_p1.c
@@ -388,7 +388,6 @@ int main(int argc, char **argv)
 
   // GK app
   struct gkyl_gk app_inp = {
-    .name = "gk_em_alfven_2x2v_p1",
     .cfl_frac = 1.0,
     .cfl_frac_omegaH = 1.0,
 
@@ -421,6 +420,7 @@ int main(int argc, char **argv)
     },
   };
 
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
     .time_stepping = {
diff --git a/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
index b22a61c190..4e03f28e75 100644
--- a/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_em_alfven_3x2v_p1.c
@@ -398,7 +398,6 @@ int main(int argc, char **argv)
 
   // GK app
   struct gkyl_gk app_inp = {
-    .name = "gk_em_alfven_3x2v_p1",
     .cfl_frac = 1.0,
     .cfl_frac_omegaH = 1.0,
 
@@ -430,7 +429,8 @@ int main(int argc, char **argv)
       .comm = comm,
     },
   };
-
+  
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
     .time_stepping = {

From ec901ae981517cb4884e830ee23f541b068023d7 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sun, 17 May 2026 14:24:10 -0400
Subject: [PATCH 165/181] Add the helical EM 2x2v regression test, this passes
 the particle conservation check. The helical EM 3x2v case is failing at
 conserving particles as soon as some EM activity is triggered regardless if
 it is induction related or fluctuation itself.

---
 gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c | 638 ++++++++++++++++++
 1 file changed, 638 insertions(+)
 create mode 100644 gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c

diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
new file mode 100644
index 0000000000..9339022279
--- /dev/null
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
@@ -0,0 +1,638 @@
+#include <math.h>
+#include <stdio.h>
+#include <time.h>
+
+#include <gkyl_alloc.h>
+#include <gkyl_const.h>
+#include <gkyl_eqn_type.h>
+#include <gkyl_fem_poisson_bctype.h>
+#include <gkyl_gyrokinetic.h>
+#include <gkyl_gyrokinetic_run.h>
+#include <gkyl_math.h>
+
+#include <rt_arg_parse.h>
+
+// Define the context of the simulation. This is basically all the globals
+struct gk_app_ctx {
+  int cdim, vdim; // Dimensionality.
+  
+  // Geometry and magnetic field.
+  double B_axis;
+  double R0;
+  double Rc;
+  double Bv0;
+
+  // Plasma parameters.
+  double me; double qe;
+  double mi; double qi;
+  double n0; double Te0; double Ti0; 
+
+  // Collisions.
+  double nu_frac;
+
+  // Source parameters.
+  double P_SOL;
+  double S0;
+  double xSource;
+  double lambdaSource;
+
+  // Grid parameters.
+  double Lx; // Domain size in radial direction.
+  double Lz; // Domain size along magnetic field.
+  double x_min; double x_max;
+  double z_min; double z_max;
+  int Nx;
+  int Nz;
+  int Nvpar;
+  int Nmu;
+  int cells[GKYL_MAX_DIM]; // Number of cells in all directions.
+  int poly_order;
+  double vpar_max_elc; double mu_max_elc;
+  double vpar_max_ion; double mu_max_ion;
+
+  double t_end; // End time.
+  int num_frames; // Number of output frames.
+  double write_phase_freq; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num; // Number of integrated diagnostics computations (=INT_MAX for every step).
+  double dt_failure_tol; // Minimum allowable fraction of initial time-step.
+  int num_failures_max; // Maximum allowable number of consecutive small time-steps.
+};
+
+// Common source density profiles.
+double sourceDensity(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  double sourceFloor = 0.1;
+
+  struct gk_app_ctx *app = ctx;
+  double S0 = app->S0;
+  double lambdaSource = app->lambdaSource;
+  double xSource = app->xSource;
+  double Lz = app->Lz;
+
+  if (x < xSource) {
+    sourceFloor = 0.5;
+  }
+  if (fabs(z) < Lz/4) {
+    return 0.90625*S0*fmax(exp(-0.5*pow((x-xSource)/lambdaSource,2)),sourceFloor);
+  } else {
+    return 1e-10;
+  }
+}
+
+// Common source temperature profile.
+double sourceTemperature(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3 * lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 30*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial density.
+double densityInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  struct gk_app_ctx *app = ctx;
+  double Ls = app->Lz/4;
+  double xSource[2] = {x, 0};
+  double effectiveSource = sourceDensity(t, xSource, ctx);
+  double c_ss = sqrt(5/3*sourceTemperature(t, xSource, ctx)/app->mi);
+  double nPeak = 4*sqrt(5)/3/c_ss*Ls*effectiveSource/2;
+  pcg64_random_t rng = gkyl_pcg64_init(0);
+  double perturb = 1e-3*(gkyl_pcg64_rand_double(&rng) - 0.5)*2.0;
+  if (fabs(z) <= Ls) {
+    return nPeak * (1 + sqrt(1-pow(z/Ls,2)))/2 * (1+perturb);
+  } else {
+    return nPeak/2 * (1+perturb);
+  }
+}
+
+// Initial temperature.
+double temperatureInit(double t, const double * GKYL_RESTRICT xn, void *ctx)
+{
+  double x = xn[0], z = xn[1];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  if (x < xSource + 3*lambdaSource) {
+    return 80*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    return 20*GKYL_ELEMENTARY_CHARGE;
+  }
+}
+
+// Initial ion drift speed.
+double driftSpeed(const double * GKYL_RESTRICT xn, void *ctx){
+  double x = xn[0], z = xn[1];
+  struct gk_app_ctx *app = ctx;
+  double xSource = app->xSource;
+  double lambdaSource = app->lambdaSource;
+  double Lz = app->Lz;
+  double mi = app->mi;
+  double Te;
+  if (x < xSource + 3*lambdaSource) {
+    Te = 50*GKYL_ELEMENTARY_CHARGE;
+  } else {
+    Te = 20*GKYL_ELEMENTARY_CHARGE;
+  }
+  double Ls = Lz/4;
+  if (fabs(z) <= Ls) {
+    return z/Ls*sqrt(Te/mi);
+  } else {
+    return (z > 0 ? 1.0 : -1.0)*sqrt(Te/mi);
+  }
+}
+
+void
+diffusion_D_func(double t, const double* GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void* ctx)
+{
+  struct sheath_ctx *app = ctx;
+
+  fout[0] = 0.5; // Diffusivity [m^2/s].
+}
+
+// Radial coordinate mapping.
+double Rx(const double *xc, void *ctx)
+{
+  return xc[0];
+}
+
+// Toroidal magnetic field.
+double Bphi(const double *xc, void *ctx)
+{
+  double x = xc[0];
+  struct gk_app_ctx *app = ctx;
+  double B_axis = app->B_axis;
+  double R0 = app->R0;
+  double R = Rx(xc, ctx);
+  return B_axis*R0/R;
+}
+
+// Vertical magnetic field.
+double Bvert(const double *xc, void *ctx)
+{
+  struct gk_app_ctx *app = ctx;
+  double Bv0 = app->Bv0;
+  return Bv0;
+}
+
+// Magnetic field magnitude.
+double bmag(const double *xc, void *ctx)
+{
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  return sqrt(pow(Bt,2) + pow(Bv,2));
+}
+
+// Field line pitch.
+double thetax(const double *xc, void *ctx)
+{
+  return asin(Bvert(xc, ctx)/bmag(xc, ctx));
+}
+
+// Parallel coordinate mapping.
+double Zx(const double *xc, void *ctx)
+{
+  double theta = thetax(xc, ctx);
+  return xc[2]*sin(theta);
+}
+
+double phix(const double *xc, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+  struct gk_app_ctx *app = ctx;
+  double Rc = app->Rc;
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  double theta = thetax(xc, ctx);
+
+  return y/Rc + (Bt * z*sin(theta))/(Bv * x); 
+}
+
+// Interface function calls.
+void source_density(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceDensity(t, xn, ctx); }
+void source_temperature(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = sourceTemperature(t, xn, ctx); }
+void density_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = densityInit(t, xn, ctx); }
+void temp_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = temperatureInit(t, xn, ctx); }
+void upar_ion_init(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = driftSpeed(xn, ctx); }
+void bfield_func(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{ 
+  // Cartesian formulation of the magnetic field.
+  double Bt = Bphi(xc, ctx);
+  double Bv = Bvert(xc, ctx);
+  double phi = phix(xc, ctx);
+  fout[0] = -Bt*sin(phi);
+  fout[1] = Bt*cos(phi);
+  fout[2] = Bv;
+}
+void zero_func(double t, const double * GKYL_RESTRICT xn, double* GKYL_RESTRICT fout, void *ctx)
+{ fout[0] = 0.0; }
+
+// Geometry evaluation functions for the gk app
+void mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
+{
+  double x = xc[0], y = xc[1], z = xc[2];
+
+  // Map to cylindrical (R, Z, phi) coordinates.
+  double R   = Rx(xc, ctx);
+  double Z   = Zx(xc, ctx);
+  double phi = phix(xc, ctx);
+  // Map to Cartesian (X, Y, Z) coordinates.
+  double X = R*cos(phi);
+  double Y = R*sin(phi);
+
+  xp[0] = X; xp[1] = Y; xp[2] = Z;
+}
+
+struct gk_app_ctx
+create_ctx(void)
+{
+  int cdim = 2, vdim = 2; // Dimensionality.
+
+  // Universal constant parameters.
+  double eps0 = GKYL_EPSILON0, eV = GKYL_ELEMENTARY_CHARGE;
+  double mp = GKYL_PROTON_MASS, me = GKYL_ELECTRON_MASS;
+  double qi = eV; // ion charge
+  double qe = -eV; // electron charge
+
+  // Plasma parameters. Chosen based on the value of a cubic sline
+  // between the last TS data inside the LCFS and the probe data in
+  // in the far SOL, near R=0.475 m.
+  double AMU = 2.01410177811;
+  double mi = mp*AMU; // Deuterium ions.
+  double Te0 = 40*eV;
+  double Ti0 = 40*eV;
+  double n0 = 7e18*10; // [1/m^3]
+
+  // Geometry and magnetic field.
+  double B_axis = 0.5;
+  double R0 = 0.85;
+  double a0 = 0.5;
+  double Lp = 2.4; // Poloidal length at x0.
+  double Lt = 8.0; // Toroidal length at x0.
+  double Rc = R0 + a0;
+  double B0 = B_axis*R0/Rc;
+
+  double sintheta = Lp/Lt;
+  double Bv0 = B0*sintheta;
+
+  // Source parameters.
+  double P_SOL = 8.1e5;
+  double S0 = 5.7691e23*10; // Multiplied by 10 to increase beta
+  double xSource = Rc - 0.05;
+  double lambdaSource = 0.005;
+
+  // Collisions;
+  double nuFrac = 0.1;
+
+  // Derived parameters.
+  double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
+  double c_s = sqrt(Te0/mi); // Sound speed.
+  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
+  double rho_s = c_s/omega_ci; // Ion sound gyroradius.
+
+  // Box size.
+  double Lx = 50*rho_s;
+  double Lz = Lt; // [m]
+
+  double x_min = Rc - Lx/2;
+  double x_max = Rc + Lx/2;
+  double z_min = -Lz/2;
+  double z_max = Lz/2;
+
+  // Grid parameters
+  int Nx = 8;
+  int Nz = 4;
+  int Nvpar = 4;
+  int Nmu = 2;
+  int poly_order = 1;
+
+  double vpar_max_elc = 4.*vte;
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
+  double vpar_max_ion = 4.*vti;
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
+
+  double t_end = 1.e-6; // End time, should terminate in 43 steps.
+  int num_frames = 1;
+  double write_phase_freq = 1.0; // Frequency of writing phase-space diagnostics (as a fraction of num_frames).
+  int int_diag_calc_num = num_frames*100;
+  double dt_failure_tol = 1.0e-4; // Minimum allowable fraction of initial time-step.
+  int num_failures_max = 20; // Maximum allowable number of consecutive small time-steps.
+
+  struct gk_app_ctx ctx = {
+    .cdim = cdim,
+    .vdim = vdim,
+    .B_axis = B_axis,
+    .R0 = R0,
+    .Rc = Rc,
+    .Bv0 = Bv0,
+    .Lx = Lx,
+    .Lz = Lz,
+    .x_min = x_min, .x_max = x_max,
+    .z_min = z_min, .z_max = z_max,
+
+    .me = me, .qe = qe,
+    .mi = mi, .qi = qi,
+    .n0 = n0, .Te0 = Te0, .Ti0 = Ti0,
+  
+    .nu_frac = nuFrac,
+    
+    .P_SOL = P_SOL,
+    .S0 = S0,
+    .xSource = xSource,
+    .lambdaSource = lambdaSource,
+  
+    .Nx = Nx,
+    .Nz = Nz,
+    .Nvpar = Nvpar,
+    .Nmu = Nmu,
+    .cells = {Nx, Nz, Nvpar, Nmu},
+    .poly_order = poly_order,
+    .vpar_max_elc = vpar_max_elc, .mu_max_elc = mu_max_elc,
+    .vpar_max_ion = vpar_max_ion, .mu_max_ion = mu_max_ion,
+
+    .t_end = t_end, .num_frames = num_frames,
+    .write_phase_freq = write_phase_freq,
+    .int_diag_calc_num = int_diag_calc_num,
+    .dt_failure_tol = dt_failure_tol,
+    .num_failures_max = num_failures_max,
+  };
+  return ctx;
+}
+
+
+int 
+main(int argc, char **argv)
+{
+  struct gkyl_app_args app_args = parse_app_args(argc, argv);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi) MPI_Init(&argc, &argv);
+#endif
+
+  if (app_args.trace_mem) {
+    gkyl_cu_dev_mem_debug_set(true);
+    gkyl_mem_debug_set(true);
+  }
+
+  struct gk_app_ctx ctx = create_ctx(); // Context for init functions.
+
+  int cells_x[ctx.cdim], cells_v[ctx.vdim];
+  for (int d=0; d<ctx.cdim; d++)
+    cells_x[d] = APP_ARGS_CHOOSE(app_args.xcells[d], ctx.cells[d]);
+  for (int d=0; d<ctx.vdim; d++)
+    cells_v[d] = APP_ARGS_CHOOSE(app_args.vcells[d], ctx.cells[ctx.cdim+d]);
+
+  // Construct communicator for use in app.
+  struct gkyl_comm *comm = gkyl_gyrokinetic_comms_new(app_args.use_mpi, app_args.use_gpu, stderr);
+
+  // electrons
+  struct gkyl_gyrokinetic_species elc = {
+    .name = "elc",
+    .charge = ctx.qe, .mass = ctx.me,
+    .vdim = ctx.vdim,
+    .lower = {-ctx.vpar_max_elc, 0.0},
+    .upper = { ctx.vpar_max_elc, ctx.mu_max_elc},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = zero_func,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .anomalous_diffusion = {
+      .anomalous_diff_id = GKYL_GK_ANOMALOUS_DIFF_D,
+      .D_profile = diffusion_D_func,
+      .D_profile_ctx = &ctx,
+      .write_diagnostics = true,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "elc" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Te0,
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+    
+    .time_rate_diagnostics = true,
+  };
+
+  // ions
+  struct gkyl_gyrokinetic_species ion = {
+    .name = "ion",
+    .charge = ctx.qi, .mass = ctx.mi,
+    .vdim = ctx.vdim,
+    .lower = { -ctx.vpar_max_ion, 0.0},
+    .upper = { ctx.vpar_max_ion, ctx.mu_max_ion},
+    .cells = { cells_v[0], cells_v[1] },
+    .polarization_density = ctx.n0,
+
+    .projection = {
+      .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+      .ctx_density = &ctx,
+      .ctx_upar = &ctx,
+      .ctx_temp = &ctx,
+      .density = density_init,
+      .upar = upar_ion_init,
+      .temp = temp_init,
+    },
+
+    .collisionless = {
+      .type = GKYL_GK_COLLISIONLESS_EM,
+    },
+
+    .anomalous_diffusion = {
+      .anomalous_diff_id = GKYL_GK_ANOMALOUS_DIFF_D,
+      .D_profile = diffusion_D_func,
+      .D_profile_ctx = &ctx,
+      .write_diagnostics = true,
+    },
+
+    .collisions =  {
+      .collision_id = GKYL_LBO_COLLISIONS,
+      .num_cross_collisions = 1,
+      .collide_with = { "ion" },
+      .den_ref = ctx.n0,
+      .temp_ref = ctx.Ti0, 
+      .nu_frac = ctx.nu_frac,
+    },
+
+    .source = {
+      .source_id = GKYL_PROJ_SOURCE,
+      .num_sources = 1,
+      .projection[0] = {
+        .proj_id = GKYL_PROJ_MAXWELLIAN_PRIM,
+        .ctx_density = &ctx,
+        .ctx_upar = &ctx,
+        .ctx_temp = &ctx,
+        .density = source_density,
+        .upar = zero_func,
+        .temp = source_temperature,
+      },
+      .diagnostics = {
+        .num_integrated_diag_moments = 1,
+        .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+      },
+    },
+
+    .bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_ZERO_FLUX },
+      { .dir = 1, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+      { .dir = 1, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_SPECIES_SHEATH },
+    },
+
+    .num_diag_moments = 9,
+    .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN, GKYL_F_MOMENT_BIMAXWELLIAN, 
+      GKYL_F_MOMENT_M0, GKYL_F_MOMENT_M1, GKYL_F_MOMENT_M2PAR, GKYL_F_MOMENT_M2PERP, 
+      GKYL_F_MOMENT_M2, GKYL_F_MOMENT_M3PAR, GKYL_F_MOMENT_M3PERP},
+
+    .num_integrated_diag_moments = 1,
+    .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+
+    .boundary_flux_diagnostics = {
+      .num_diag_moments = 1,
+      .diag_moments = {GKYL_F_MOMENT_HAMILTONIAN},
+      .num_integrated_diag_moments = 1,
+      .integrated_diag_moments = { GKYL_F_MOMENT_HAMILTONIAN },
+    },
+
+    .time_rate_diagnostics = true,
+  };
+
+  // field
+  struct gkyl_gyrokinetic_field field = {
+    .poisson_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .mu0 = GKYL_MU0,
+    .time_rate_diagnostics = true,
+  };
+
+  // GK app
+  struct gkyl_gk app_inp = {
+
+    .cfl_frac_omegaH = 1.0,
+    .cfl_frac = 1.0,
+
+    .cdim = ctx.cdim,
+    .lower = { ctx.x_min, ctx.z_min },
+    .upper = { ctx.x_max, ctx.z_max },
+    .cells = { cells_x[0], cells_x[1] },
+    .poly_order = ctx.poly_order,
+    .basis_type = app_args.basis_type,
+
+    .geometry = {
+      .geometry_id = GKYL_GEOMETRY_MAPC2P,
+      .mapc2p = mapc2p, // mapping of computational to physical space
+      .c2p_ctx = &ctx,
+      .bfield_func = bfield_func, // magnetic field
+      .bfield_ctx = &ctx,
+    },
+
+    .num_species = 2,
+    .species = { elc, ion },
+    .field = field,
+
+    .parallelism = {
+      .use_gpu = app_args.use_gpu,
+      .comm = comm,
+      .cuts = { app_args.cuts[0], app_args.cuts[1] },
+    }
+  };
+
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
+  struct gkyl_gyrokinetic_run_inp run_inp = {
+    .app_inp = app_inp,
+    .time_stepping = {
+      .t_end = ctx.t_end,
+      .num_frames = ctx.num_frames,
+      .write_phase_freq = ctx.write_phase_freq,
+      .int_diag_calc_num = ctx.int_diag_calc_num,
+      .dt_failure_tol = ctx.dt_failure_tol,
+      .num_failures_max = ctx.num_failures_max,
+      .is_restart = app_args.is_restart,
+      .restart_frame = app_args.restart_frame,
+      .num_steps = app_args.num_steps,
+    },
+  };
+
+  gkyl_gyrokinetic_run_simulation(&run_inp);
+  
+  gkyl_gyrokinetic_comms_release(comm);
+
+#ifdef GKYL_HAVE_MPI
+  if (app_args.use_mpi)
+    MPI_Finalize();
+#endif
+
+  return 0;
+}
\ No newline at end of file

From 2054437b1e2ac6099ac3607d2ce5bd04f69d5e64 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sun, 17 May 2026 15:23:46 -0400
Subject: [PATCH 166/181] ensure coherent naming in the helical 3x2v tests and
 activate EM by default. Both aren't conserving particles with EM for now...

---
 gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c | 50 +++++++++++-------
 .../creg/rt_gk_helical_zvert_3x2v_p1.c        | 51 ++++++++++---------
 2 files changed, 59 insertions(+), 42 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
index a26038cf30..a605105045 100644
--- a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
@@ -18,9 +18,10 @@ struct gk_app_ctx {
   
   // Geometry and magnetic field.
   double B_axis;
+  double R_axis;
   double R0;
-  double Rc;
   double Bv0;
+  int n;
 
   // Plasma parameters.
   double me; double qe;
@@ -164,9 +165,9 @@ double Bphi(const double *xc, void *ctx)
   double x = xc[0];
   struct gk_app_ctx *app = ctx;
   double B_axis = app->B_axis;
-  double R0 = app->R0;
+  double R_axis = app->R_axis;
   double R = Rx(xc, ctx);
-  return B_axis*R0/R;
+  return B_axis*R_axis/R;
 }
 
 // Vertical magnetic field.
@@ -174,11 +175,14 @@ double Bvert(const double *xc, void *ctx)
 {
   struct gk_app_ctx *app = ctx;
   double Bv0 = app->Bv0;
-  return Bv0;
+  int n = app->n;
+  double R0 = app->R0;
+  double R = Rx(xc, ctx);
+  return Bv0 * pow(R/R0, n);
 }
 
 // Magnetic field magnitude.
-double bmag(const double *xc, void *ctx)
+double Bmag(const double *xc, void *ctx)
 {
   double Bt = Bphi(xc, ctx);
   double Bv = Bvert(xc, ctx);
@@ -188,7 +192,7 @@ double bmag(const double *xc, void *ctx)
 // Field line pitch.
 double thetax(const double *xc, void *ctx)
 {
-  return asin(Bvert(xc, ctx)/bmag(xc, ctx));
+  return asin(Bvert(xc, ctx)/Bmag(xc, ctx));
 }
 
 // Parallel coordinate mapping.
@@ -202,21 +206,21 @@ double phix(const double *xc, void *ctx)
 {
   double x = xc[0], y = xc[1], z = xc[2];
   struct gk_app_ctx *app = ctx;
-  double Rc = app->Rc;
+  double R_axis = app->R_axis;
   double Bt = Bphi(xc, ctx);
   double Bv = Bvert(xc, ctx);
 
   // Original Shi mapping. This mapping does not pass the right hand check.
   // double theta = asin(Lp/Lt);
-  // return (y/sin(theta) + z*cos(theta))/Rc; // O
+  // return (y/sin(theta) + z*cos(theta))/R0; // O
 
   // This mapping passes right hand check but does not conserve particle!
   // double theta = thetax(xc, ctx);
   // return (y/sin(theta) + z*cos(theta))/x;
 
-  // Helical sheared mapping. Passes right hand check and conserves particle.
+  // Helical sheared mapping. Passes right hand check and conserves particle (ES).
   double theta = thetax(xc, ctx);
-  return y/Rc + (Bt * z*sin(theta))/(Bv * x); 
+  return y/R_axis + (Bt * z*sin(theta))/(Bv * x); 
 }
 
 // Interface function calls.
@@ -281,12 +285,14 @@ create_ctx(void)
 
   // Geometry and magnetic field.
   double B_axis = 0.5;
-  double R0 = 0.85;
+  double R_axis = 0.85;
   double a0 = 0.5;
   double Lp = 2.4; // Poloidal length at x0.
   double Lt = 8.0; // Toroidal length at x0.
-  double Rc = R0 + a0;
-  double B0 = B_axis*R0/Rc;
+  int shear = -2;
+  double R0 = R_axis + a0;
+  double B0 = B_axis*R_axis/R0;
+  int n = shear + 2;
 
   double sintheta = Lp/Lt;
   double Bv0 = B0*sintheta;
@@ -294,7 +300,7 @@ create_ctx(void)
   // Source parameters.
   double P_SOL = 8.1e5;
   double S0 = 5.7691e23*10; // Multiplied by 10 to increase beta
-  double xSource = Rc - 0.05;
+  double xSource = R0 - 0.05;
   double lambdaSource = 0.005;
 
   // Collisions;
@@ -311,8 +317,8 @@ create_ctx(void)
   double Ly = 100*rho_s;
   double Lz = Lt; // [m]
 
-  double x_min = Rc - Lx/2;
-  double x_max = Rc + Lx/2;
+  double x_min = R0 - Lx/2;
+  double x_max = R0 + Lx/2;
   double y_min = -Ly/2;
   double y_max = Ly/2;
   double z_min = -Lz/2;
@@ -342,9 +348,10 @@ create_ctx(void)
     .cdim = cdim,
     .vdim = vdim,
     .B_axis = B_axis,
+    .R_axis = R_axis,
     .R0 = R0,
-    .Rc = Rc,
     .Bv0 = Bv0,
+    .n = n,
     .Lx = Lx,
     .Ly = Ly,
     .Lz = Lz,
@@ -429,7 +436,7 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES,
+      .type = GKYL_GK_COLLISIONLESS_EM,
     },
 
     .collisions =  {
@@ -505,7 +512,7 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES,
+      .type = GKYL_GK_COLLISIONLESS_EM,
     },
 
     .collisions =  {
@@ -566,6 +573,11 @@ main(int argc, char **argv)
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
     },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
   };
 
diff --git a/gyrokinetic/creg/rt_gk_helical_zvert_3x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zvert_3x2v_p1.c
index b5a364a3f8..c6d306fa15 100644
--- a/gyrokinetic/creg/rt_gk_helical_zvert_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zvert_3x2v_p1.c
@@ -21,11 +21,12 @@ struct gk_app_ctx {
   int cdim, vdim; // Dimensionality.
   
   // Geometry and magnetic field.
-  double R0;
+  double R_axis;
   double a0;
-  double B0;
+  double B_axis;
   double Bvx0;
   double x0;
+  double R0;
   double H;
   int n; // Exponent for vertical magnetic field profile.
 
@@ -175,22 +176,20 @@ double Bphi(const double *xc, void *ctx)
 {
   double x = xc[0];
   struct gk_app_ctx *app = ctx;
-  double B0 = app->B0;
-  double R0 = app->R0;
-
+  double B_axis = app->B_axis;
+  double R_axis = app->R_axis;
   double R = Rx(xc, ctx);
-  return B0*R0/R;
+  return B_axis*R_axis/R;
 }
 
 double Bvert(const double *xc, void *ctx)
 {
   struct gk_app_ctx *app = ctx;
   double Bvx0 = app->Bvx0;
-  double x0 = app->x0;
   int n = app->n;
+  double R0 = app->R0;
   double R = Rx(xc, ctx);
-  
-  return Bvx0 * pow(R/x0, n);
+  return Bvx0 * pow(R/R0, n);
 }
 
 double Bmag(const double *xc, void *ctx)
@@ -205,11 +204,11 @@ double phix(const double *xc, void *ctx)
 {
   double x = xc[0], y = xc[1], z = xc[2];
   struct gk_app_ctx *app = ctx;
-  double R0 = app->R0;
+  double R_axis = app->R_axis;
   double Lz = app->Lz;
   double Bt = Bphi(xc, ctx);
   double Bv = Bvert(xc, ctx);
-  return y/R0 + (Bt * z)/(Bv * x);
+  return y/R_axis + (Bt * z)/(Bv * x);
 }
 
 double qprofile(const double *xc, void *ctx)
@@ -283,18 +282,19 @@ create_ctx(void)
   double n0 = 7e18*10; // [1/m^3]
 
   // Geometry and magnetic field.
-  double B0 = 0.5;
-  double R0 = 0.85;
+  double B_axis = 0.5;
+  double R_axis = 0.85;
   double a0 = 0.5;
   double H = 2.4; // Poloidal length (used to get the field line pitch).
   double Lcx0 = 8.0; // Connection length in the middle of the domain.
   int shear = -2;
 
-  double x0 = R0 + a0;
+  double x0 = R_axis + a0;
+  double R0 = x0;
   
   const double vec0[3] = {x0, 0.0, 0.0};
-  double Bc = Bphi(vec0, &(struct gk_app_ctx){.B0=B0, .R0=R0});
-  double Bvx0 = H * Bc / Lcx0;
+  double B0 = Bphi(vec0, &(struct gk_app_ctx){.B_axis=B_axis, .R_axis=R_axis});
+  double Bvx0 = H * B0 / Lcx0;
   double n = shear + 2;
 
   // Source parameters.
@@ -310,7 +310,7 @@ create_ctx(void)
   // Derived parameters.
   double vte = sqrt(Te0/me), vti = sqrt(Ti0/mi); // Thermal speeds.
   double c_s = sqrt(Te0/mi); // Sound speed.
-  double omega_ci = fabs(qi*B0/mi); // Ion cyclotron frequency.
+  double omega_ci = fabs(qi*B_axis/mi); // Ion cyclotron frequency.
   double rho_s = c_s/omega_ci; // Ion sound gyroradius.
 
   // Box size.
@@ -334,9 +334,9 @@ create_ctx(void)
   int poly_order = 1;
 
   double vpar_max_elc = 4.*vte;
-  double mu_max_elc = 12*me*pow(vte,2)/(2*B0);
+  double mu_max_elc = 12*me*pow(vte,2)/(2*B_axis);
   double vpar_max_ion = 4.*vti;
-  double mu_max_ion = 12*mi*pow(vti,2)/(2*B0);
+  double mu_max_ion = 12*mi*pow(vti,2)/(2*B_axis);
 
   double t_end = 1.e-6; // End time, should terminate in 43 steps.
   int num_frames = 1;
@@ -349,8 +349,9 @@ create_ctx(void)
     .cdim = cdim,
     .vdim = vdim,
 
-    .B0 = B0,
+    .B_axis = B_axis,
     .Bvx0 = Bvx0,
+    .R_axis = R_axis,
     .R0 = R0,
     .a0 = a0,
     .H = H,
@@ -443,7 +444,7 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES,
+      .type = GKYL_GK_COLLISIONLESS_EM,
     },
 
     .collisions =  {
@@ -519,7 +520,7 @@ main(int argc, char **argv)
     },
 
     .collisionless = {
-      .type = GKYL_GK_COLLISIONLESS_ES,
+      .type = GKYL_GK_COLLISIONLESS_EM,
     },
 
     .collisions =  {
@@ -576,11 +577,15 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
     },
+    .ampere_bcs = {
+      { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+      { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
+    },
+    .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
   };
 

From f32ad1e87536ca0f4186aacb44ae70b56d6c7f63 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 18 May 2026 11:08:10 -0400
Subject: [PATCH 167/181] improve comment

---
 core/zero/gkyl_eqn_type.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/core/zero/gkyl_eqn_type.h b/core/zero/gkyl_eqn_type.h
index 099650bf79..d6ff10a75e 100644
--- a/core/zero/gkyl_eqn_type.h
+++ b/core/zero/gkyl_eqn_type.h
@@ -41,7 +41,7 @@ enum gkyl_gkfield_id {
   GKYL_GK_FIELD_ES = 4, // Electrostatic field.
   GKYL_GK_FIELD_ES_IWL = 5, // Electromagnetic field with inner-wall limited BCs.
   GKYL_GK_FIELD_EM = 6, // To force electromagnetic field solve (even if no species is EM).
-  GKYL_GK_FIELD_EM_IWL = 7, // As above but for IWL.
+  GKYL_GK_FIELD_EM_IWL = 7, // Electromagnetic field with inner-wall limited BCs, even if no species is EM.
 };
 
 // Identifiers for specific field object types.

From 389152313e64aed0ca054c53d0eb264ed33d7a92 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Fri, 22 May 2026 11:21:42 -0700
Subject: [PATCH 168/181] add an array to store the gyroaveraged m1 moment for
 possibly FLR effects in EM

---
 gyrokinetic/apps/gk_field.c              | 12 ++++--------
 gyrokinetic/apps/gk_species.c            | 10 ++++++----
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  1 +
 3 files changed, 11 insertions(+), 12 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index a70998f785..bce365b4e4 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -283,10 +283,6 @@ gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, st
 {
   // Apar^{n+1} = Apar^{n} + dt*dApar/dt
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
-
-  // Smooth along z.
-  // gk_field_fem_projection_par(app, field, field->apar, field->apar_smooth_aux);
-  // gkyl_array_copy_range(field->apar, field->apar_smooth_aux, &app->local_ext);
 }
 
 static void
@@ -606,7 +602,8 @@ gk_field_accumulate_current_dens(gkyl_gyrokinetic_app *app, struct gk_field *fie
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
     gk_species_moment_calc(&s->m1, s->local, app->local, fin[i]);
-    gkyl_array_accumulate_range(field->currentDens, s->info.charge, s->m1.marr, &app->local);
+    s->gyroaverage(app, s, s->m1.marr, s->m1_gyroavg);
+    gkyl_array_accumulate_range(field->currentDens, s->info.charge, s->m1_gyroavg, &app->local);
   } 
   app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -619,10 +616,9 @@ gk_field_accumulate_current_dens_dot(gkyl_gyrokinetic_app *app, struct gk_field
   gkyl_array_clear(field->currentDensdot, 0.0);
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
-
     gk_species_moment_calc(&s->m1, s->local, app->local, rhs_in[i]);
-
-    gkyl_array_accumulate_range(field->currentDensdot, s->info.charge, s->m1.marr, &app->local);
+    s->gyroaverage(app, s, s->m1.marr, s->m1_gyroavg);
+    gkyl_array_accumulate_range(field->currentDensdot, s->info.charge, s->m1_gyroavg, &app->local);
   } 
   app->stat.field_apar_rhs_tm += gkyl_time_diff_now_sec(wst);
 }
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index b875004e38..e308842b1e 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -1469,6 +1469,8 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
 
   // Allocate data for density (for charge density or upar calculation).
   gk_species_moment_init(app, gks, &gks->m0, GKYL_F_MOMENT_M0, false);
+  // To compute current density for Ampere's law and current dot for Ohm's law.
+  gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
 
   if (gks->info.flr.type) {
     // Create operator needed for FLR effects.
@@ -1477,6 +1479,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gks->gyroaverage = gk_species_gyroaverage_enabled;
     // Gyroaveraged M0 and phi.
     gks->m0_gyroavg = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+    gks->m1_gyroavg = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
     gks->gyro_phi = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
     double gyroradius_bmag = gks->info.flr.bmag ? gks->info.flr.bmag : app->bmag_ref;
@@ -1519,6 +1522,7 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
   else {
     gks->gyroaverage = gk_species_gyroaverage_disabled;
     gks->m0_gyroavg = gkyl_array_acquire(gks->m0.marr);
+    gks->m1_gyroavg = gkyl_array_acquire(gks->m1.marr);
     gks->gyro_phi = gkyl_array_acquire(app->field->phi_smooth);
   }
 
@@ -1530,9 +1534,6 @@ gk_species_init(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app *app, st
     gks->gyro_apar = gkyl_array_acquire(app->field->apar_curr);
   gks->gyro_apardot = gkyl_array_acquire(app->field->apardot);
 
-  // To compute current density for Ampere's law and current dot for Ohm's law.
-  gk_species_moment_init(app, gks, &gks->m1, GKYL_F_MOMENT_M1, false);
-
   // Initialize the collisionless solver.
   gks->collisionless = (struct gk_collisionless) { };
   gk_species_collisionless_init(app, gks, &gks->collisionless);
@@ -1963,6 +1964,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *gks
 
   // Release moment data.
   gk_species_moment_release(app, &gks->m0);
+  gk_species_moment_release(app, &gks->m1);
   for (int i=0; i<gks->info.num_diag_moments; ++i) {
     gk_species_moment_release(app, &gks->moms[i]);
   }
@@ -1994,6 +1996,7 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *gks
   gk_species_lte_release(app, &gks->lte);
 
   gkyl_array_release(gks->m0_gyroavg);
+  gkyl_array_release(gks->m1_gyroavg);
   gkyl_array_release(gks->gyro_phi);
   if (gks->info.flr.type) {
     gkyl_array_release(gks->flr_rhoSqD2);
@@ -2003,7 +2006,6 @@ gk_species_release(const gkyl_gyrokinetic_app* app, const struct gk_species *gks
 
   gkyl_array_release(gks->gyro_apar);
   gkyl_array_release(gks->gyro_apardot);
-  gk_species_moment_release(app, &gks->m1);
 
   gks->release_func(app, gks);
 }
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index f8a468b650..9655ab232d 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1101,6 +1101,7 @@ struct gk_species {
 
   // Quantities used for FLR model:
   struct gkyl_array *m0_gyroavg; // Gyroaveraged particle density.
+  struct gkyl_array *m1_gyroavg; // Gyroaveraged particle flow.
   struct gkyl_array *flr_rhoSqD2; // Laplacian weight in FLR operator.
   struct gkyl_array *flr_kSq; // Field multiplying phi in FLR operator.
   struct gkyl_deflated_fem_poisson *flr_op; // Helmholtz solver to invert FLR operator.

From dbfab35b7d696eb51fcc07d36ed99bd4043c0653 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Sat, 30 May 2026 14:30:58 -0700
Subject: [PATCH 169/181] implement a method to remove the flux surface
 average. For now it is only available for Apardot but one may be interested
 to use it for phi if we decide to implement the adiabatic electron model.

---
 gyrokinetic/apps/gk_field_2x3x.c         | 69 ++++++++++++++++++++++++
 gyrokinetic/apps/gkyl_gyrokinetic.h      |  3 +-
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h |  9 ++++
 3 files changed, 80 insertions(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index a4e0509e3e..541adda1c8 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -7,6 +7,7 @@
 #include <gkyl_gk_field_priv.h>
 #include <gkyl_array_rio_priv.h>
 #include <gkyl_comm_io.h>
+#include <gkyl_array_average.h>
 
 #include <assert.h>
 #include <float.h>
@@ -343,6 +344,8 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
 
   field->invert_flr(app, field, field->apardot);
 
+  field->remove_em_zonal(app, field, field->apardot);
+
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
@@ -381,6 +384,22 @@ gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const st
   // Do nothing.
 }
 
+static void
+gk_field_remove_em_zonal_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *field_array)
+{
+  gkyl_array_average_advance(field->fs_avg_op, field_array, field->fs_avg);
+  // Hack the conf to phase space dg op to do the 1x substraction over the entire conf space.
+  gkyl_dg_mul_conf_phase_op_accumulate_range( &field->fs_avg_basis, &app->basis, 
+    field_array, -1.0, field->fs_avg, field->fs_avg_conf_one, &field->fs_avg_range, &app->local);
+}
+
+static void
+gk_field_em_zonal_component_none(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *field_array)
+{
+  // Do nothing.
+}
+
+
 static void
 gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -408,6 +427,16 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
     }
+    if (f->remove_em_zonal) {
+     gkyl_array_average_release(f->fs_avg_op);
+     gkyl_array_release(f->fs_avg);
+     gkyl_array_release(f->fs_avg_conf_one);
+     if (app->use_gpu) {
+      gkyl_cu_free(f->fs_avg_subdir);
+     } else {
+      gkyl_free(f->fs_avg_subdir);
+     }
+    }
   }
 
   if (app->use_gpu) {
@@ -603,6 +632,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Setup EM solvers.
   f->ampere_solve = gk_field_ampere_solve_none;
   f->em_rhs_func = gk_field_em_rhs_none;
+  f->remove_em_zonal = gk_field_em_zonal_component_none;
   if (f->is_em) {
     // Translate input file BCs into Ampere BCs.
     for (int d=0; d<app->cdim-1; d++) {
@@ -643,6 +673,45 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
 
     f->ampere_solve = gk_field_ampere_solve_enabled;
     f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
+
+    if (f->info.remove_em_zonal) {
+      f->remove_em_zonal = gk_field_remove_em_zonal_enabled;
+      // define the reduced range and basis for averaging along x only
+      struct gkyl_rect_grid grid_x;
+      gkyl_rect_grid_init(&grid_x, 1, &app->grid.lower[0], &app->grid.upper[0], &app->grid.cells[0]);
+      int ghost_x[] = {1};
+      gkyl_create_grid_ranges(&grid_x, ghost_x, &f->fs_avg_range_ext, &f->fs_avg_range);
+      gkyl_cart_modal_serendip(&f->fs_avg_basis, 1, app->basis.poly_order);
+      // create and run the array average updater to average y and z
+      // Not that in 2x, it will only average over z.
+      int avg_dim_yz[] = {0,1,1};
+      struct gkyl_array_average_inp inp_avg_xyz_to_x = {
+        .grid = &app->grid,
+        .basis = app->basis,
+        .basis_avg = f->fs_avg_basis,
+        .local = &app->local,
+        .local_avg = &f->fs_avg_range,
+        .local_avg_ext = &f->fs_avg_range_ext,
+        .weight = app->gk_geom->geo_int.jacobgeo,
+        .avg_dim = avg_dim_yz,
+        .use_gpu = app->use_gpu
+      };
+      int fs_avg_subdir[GKYL_MAX_CDIM];
+      fs_avg_subdir[0] = 0; // Average along x only, so subdir is just 0.
+      if (app->use_gpu) {
+        f->fs_avg_subdir = gkyl_cu_malloc(GKYL_MAX_CDIM*sizeof(int));
+        gkyl_cu_memcpy(f->fs_avg_subdir, fs_avg_subdir, GKYL_MAX_CDIM*sizeof(int), GKYL_CU_MEMCPY_H2D);
+      } else {
+        f->fs_avg_subdir = gkyl_malloc(GKYL_MAX_CDIM*sizeof(int));
+        for (int i=0; i<GKYL_MAX_CDIM; i++)
+          f->fs_avg_subdir[i] = fs_avg_subdir[i];
+      }
+      f->fs_avg_op = gkyl_array_average_new(&inp_avg_xyz_to_x);
+      f->fs_avg = mkarr(app->use_gpu, f->fs_avg_basis.num_basis, f->fs_avg_range_ext.volume);
+      f->fs_avg_conf_one = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+      double dg_norm = pow(sqrt(2.0), app->basis.ndim);
+      gkyl_array_shiftc_range(f->fs_avg_conf_one, dg_norm, 0, &app->local);
+    }
   }
 
   // Updater for field energy calculation.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 6b92ed448d..82aa484e29 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -496,7 +496,6 @@ struct gkyl_gyrokinetic_neut_species {
 struct gkyl_gyrokinetic_field {
   enum gkyl_gkfield_id gkfield_id;
   bool is_static; // =true field does not change in time.
-  bool is_apar_static; // =true Apar at initial time is used for all time steps.
   bool zero_init_field; // =true doesn't compute the initial field.
   bool calc_init_apar; // Whether to calculate the initial Apar from the initial condition of the distribution function.
 
@@ -511,6 +510,8 @@ struct gkyl_gyrokinetic_field {
   // parameters for EMGK
   struct gkyl_gyrokinetic_bc ampere_bcs[2*GKYL_MAX_CDIM];
   double mu0; // Magnetic permeability of free space.
+  bool remove_em_zonal; // Whether to remove zonal component.
+  bool is_apar_static; // =true Apar at initial time is used for all time steps.
 
   bool time_rate_diagnostics; // Writes the time rate of change of field energy.
 
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 9655ab232d..8de3a4a261 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1343,6 +1343,15 @@ struct gk_field {
   gkyl_dynvec integ_apar_energy_dot; // d/dt of integrated EM energy components (separate from electrostatic energy for debugging purposes)
   bool is_first_apar_energy_dot_write_call; // flag for d(energy)/dt dynvec written first time
 
+  void (*remove_em_zonal)(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *phi); // Function to remove zonal component.
+  struct gkyl_array_average *fs_avg_op; // Updater for flux surface averaging.
+  struct gkyl_array *fs_avg; // Array for storing flux-surface averaged quantities.
+  struct gkyl_array *fs_avg_conf_one; // Array of ones in configuration space for flux-surface averaging.
+  struct gkyl_range fs_avg_range; // Range for flux-surface average arrays.
+  struct gkyl_basis fs_avg_basis; // Basis for flux-surface average arrays.
+  struct gkyl_range fs_avg_range_ext; // Range for flux-surface average arrays.
+  int *fs_avg_subdir; // Subscript for flux-surface average direction.
+
   bool has_phi_wall_lo; // flag to indicate there is biased wall potential on lower wall
   bool phi_wall_lo_evolve; // flag to indicate biased wall potential on lower wall is time dependent
   struct gkyl_array *phi_wall_lo; // biased wall potential on lower wall

From 3def11f1443e185f07cbb324665dd940ba0bc8c8 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 10 Jun 2026 15:51:31 -0700
Subject: [PATCH 170/181] add a sanity check where we also solve ampere and
 output it to compare with the stepped version. Also fix a merge bug.

---
 gyrokinetic/apps/gk_field.c              | 10 +++++-----
 gyrokinetic/apps/gk_field_1x.c           | 17 +++++++++++------
 gyrokinetic/apps/gk_field_2x3x.c         | 18 +++++++++++-------
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 10 ++++++----
 gyrokinetic/apps/gyrokinetic.c           | 19 +++++++++++++++++--
 5 files changed, 50 insertions(+), 24 deletions(-)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index bce365b4e4..38f333c295 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -434,9 +434,9 @@ gk_field_new(struct gkyl_gk *gk, struct gkyl_gyrokinetic_app *app)
 
   f->info = gk->field;
 
-  f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD_ES;
+  f->gkfield_id = f->info.gkfield_id ? f->info.gkfield_id : GKYL_GK_FIELD;
   
-  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM || f->info.gkfield_id == GKYL_GK_FIELD_EM_IWL;
+  f->is_em = f->info.gkfield_id == GKYL_GK_FIELD_EM;
   // Ensure that if any species is electromagnetic, the field is electromagnetic.
   for (int i=0; i<app->num_species; ++i) {
     struct gk_species *s = &app->species[i];
@@ -507,12 +507,12 @@ gk_field_em_rhs(gkyl_gyrokinetic_app *app, struct gk_field *field, const struct
   app->stat.field_tm += gkyl_time_diff_now_sec(wst);
 }
 
-void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field)
+void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out)
 {
   struct timespec wst = gkyl_wall_clock();
-  field->ampere_solve(app, field);
+  field->ampere_solve(app, field, out);
   // Smooth Apar after solving Ampere's law.
-  gk_field_fem_projection_par(app, field, field->apar, field->apar);
+  gk_field_fem_projection_par(app, field, out, out);
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index a2ce21e041..88e8a06a8a 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -20,7 +20,7 @@ gk_field_rhs_phi_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field)
 }
 
 static void 
-gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   struct timespec wst = gkyl_wall_clock();
 
   // Compute the LHS factor (= k_perp^2/mu_0 + sum_s q_s^2 n_s/m_s)
@@ -30,7 +30,7 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
   gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
 
   // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )
-  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apardot, 0, field->currentDensdot, 
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, out, 0, field->currentDensdot, 
     0, field->dApartdtSlvr_lhs_factor, &app->local);
   
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
@@ -38,18 +38,18 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
 }
 
 static void 
-gk_field_ampere_solve_1x_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ampere_solve_1x_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   struct timespec wst = gkyl_wall_clock();
 
   // Weak division method Apar = sum_s q_s int dv vpar F_s / (k_perp^2/mu_0)
-  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, field->apar, 0, field->currentDens, 
+  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, out, 0, field->currentDens, 
     0, field->lapWeightAmpere, &app->local);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
 static void 
-gk_field_ampere_solve_1x_none(gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ampere_solve_1x_none(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   // Do nothing.
 }
 
@@ -58,7 +58,7 @@ gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const
 {
   gk_field_accumulate_current_dens_dot(app, field, rhs_in);
   gk_field_accumulate_ohms_kSq(app, field, f_in);
-  gk_field_ohm_solve_1x(app, field);
+  gk_field_ohm_solve_1x(app, field, field->apardot);
 }
 
 static void
@@ -79,6 +79,7 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->apar1);
   gkyl_array_release(f->aparnew);
   gkyl_array_release(f->apardot);
+  gkyl_array_release(f->amperesol);
 
   if (f->is_em) {
     gkyl_array_release(f->currentDens);
@@ -91,6 +92,7 @@ gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     if (app->use_gpu) {
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
+      gkyl_array_release(f->amperesol_host);
     }
   }
 
@@ -123,15 +125,18 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->amperesol = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
   // Allocate additional arrays for EM case.
   if (f->is_em) {
     
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
+    f->amperesol_host = f->amperesol;
     if (app->use_gpu) {
       f->apar_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
       f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+      f->amperesol_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
     }
 
     f->currentDens = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 57ae1881e0..a61d3a654b 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -479,12 +479,12 @@ gk_field_rhs_poisson_perp_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field
 }
 
 static void
-gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   struct timespec wst = gkyl_wall_clock();
   
   gkyl_fem_poisson_perp_update_lhs(field->fem_apardot_solver, field->lapWeightAmpere, field->dApartdtSlvr_kSq);
   gkyl_fem_poisson_perp_set_rhs(field->fem_apardot_solver, field->currentDensdot);
-  gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, field->apardot);
+  gkyl_fem_poisson_perp_solve(field->fem_apardot_solver, out);
 
   field->invert_flr(app, field, field->apardot);
 
@@ -494,23 +494,23 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field){
 }
 
 static void 
-gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ampere_solve_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   struct timespec wst = gkyl_wall_clock();
 
   gkyl_fem_poisson_perp_set_rhs(field->fem_apar_solver, field->currentDens);
-  gkyl_fem_poisson_perp_solve(field->fem_apar_solver, field->apar);
+  gkyl_fem_poisson_perp_solve(field->fem_apar_solver, out);
 
   // Smooth along z.
   // gk_field_fem_projection_par(app, field, field->apar, field->apar_smooth_aux);
   // gkyl_array_copy_range(field->apar, field->apar_smooth_aux, &app->local_ext);
 
-  field->invert_flr(app, field, field->apar);
+  field->invert_flr(app, field, out);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
 
 static void 
-gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field){
+gk_field_ampere_solve_none(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out){
   // Do nothing.
 }
 
@@ -519,7 +519,7 @@ gk_field_em_rhs_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, const
 {
   gk_field_accumulate_current_dens_dot(app, field, rhs_in);
   gk_field_accumulate_ohms_kSq(app, field, f_in);
-  gk_field_ohm_solve(app, field);
+  gk_field_ohm_solve(app, field, field->apardot);
 }
 
 static void
@@ -570,6 +570,7 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
     if (app->use_gpu) {
       gkyl_array_release(f->apar_host);
       gkyl_array_release(f->apardot_host);
+      gkyl_array_release(f->amperesol_host);
     }
     if (f->remove_em_zonal) {
      gkyl_array_average_release(f->fs_avg_op);
@@ -650,14 +651,17 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->apar1 = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->aparnew = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
   f->apardot = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
+  f->amperesol = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
 
   // Setup electromagnetic variables if needed.
   if (f->is_em) {
     f->apar_host = f->apar;
     f->apardot_host = f->apardot;
+    f->amperesol_host = f->amperesol;
     if (app->use_gpu) {
       f->apar_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
       f->apardot_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
+      f->amperesol_host = mkarr(false, app->basis.num_basis, app->local_ext.volume);
     }
 
     f->apar_smooth_aux = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e227f829ee..46eb127b9c 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1346,6 +1346,8 @@ struct gk_field {
       struct gkyl_array *apar_host; // Host copy for use IO.
       struct gkyl_array *apardot; // Array for d(A_parallel)/dt (solved through Ohm's law).
       struct gkyl_array *apardot_host; // Host copy for use IO.
+      struct gkyl_array *amperesol; // Array for Ampere's law solution.
+      struct gkyl_array *amperesol_host; // Host copy for use IO.
       struct gkyl_array *currentDens; // Current density.
       struct gkyl_array *currentDens_global; // Current density.
       struct gkyl_array *currentDensdot; // Time derivative of current density.
@@ -1444,8 +1446,8 @@ struct gk_field {
     const struct gkyl_array *fin[]);
   void (*accumulate_current_dot) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, 
     struct gkyl_array *rhs_in[]);
-  void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
-  void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field);
+  void (*ampere_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out);
+  void (*ohm_solve) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out);
   void (*step_apar) (struct gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array* out, double a, const struct gkyl_array* inp);
   void (*em_combine_func) (struct gkyl_array *out, double c1, const struct gkyl_array *arr1, double c2, const struct gkyl_array *arr2,const struct gkyl_range *rng);
   void (*em_copy_func) (struct gkyl_array *out, const struct gkyl_array *inp, const struct gkyl_range *range);
@@ -4277,9 +4279,9 @@ gk_field_accumulate_ohms_kSq(gkyl_gyrokinetic_app *app, struct gk_field *field,
  * 
  * @param app gyrokinetic app object.
  * @param field Pointer to field.
- * @param em Output field.
+ * @param out Output array. (apar)
  */
-void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field);
+void gk_field_calc_apar_ic(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *out);
 
 /**
  * Step the parallel component of the magnetic vector potential, apar, forward in time.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 051d69f4ff..300f8dca8f 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -968,7 +968,7 @@ gkyl_gyrokinetic_app_apply_ic(gkyl_gyrokinetic_app* app, double t0)
       // It benign because this will be overwritten by the first RHS calls.
       if (app->field->is_em) {
         gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
-        gk_field_calc_apar_ic(app, app->field);
+        gk_field_calc_apar_ic(app, app->field, app->field->apar);
         for (int i=0; i<app->num_species; ++i) {
           struct gk_species *gk_s = &app->species[i];
           gk_species_rhs_em_complete(app, gk_s, distf[i], distfdot[i], bflux[i]);
@@ -1286,10 +1286,18 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
 
     if (app->field->is_em) {
+      // Solve ampere to output it and compare with stepped apar.
+      struct gkyl_array *distf[app->num_species];
+      for (int i=0; i<app->num_species; ++i) {
+        distf[i] = app->species[i].f;
+      }
+      gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
+      gk_field_calc_apar_ic(app, app->field, app->field->amperesol);
       // Copy data from device to host before writing it out.
       if (app->use_gpu) {
         gkyl_array_copy(app->field->apar_host, app->field->apar);
         gkyl_array_copy(app->field->apardot_host, app->field->apardot);
+        gkyl_array_copy(app->field->amperesol_host, app->field->amperesol);
       }
       const char *fmt_apar = "%s-apar_%d.gkyl";
       int sz_apar = gkyl_calc_strlen(fmt_apar, app->name, frame);
@@ -1304,6 +1312,13 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
       snprintf(fileNm_apardot, sizeof fileNm_apardot, fmt_apardot, app->name, frame);
 
       gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm_apardot);
+
+      const char *fmt_amperesol = "%s-amperesol_%d.gkyl";
+      int sz_amperesol = gkyl_calc_strlen(fmt_amperesol, app->name, frame);
+      char fileNm_amperesol[sz_amperesol+1]; // ensures no buffer overflow
+      snprintf(fileNm_amperesol, sizeof fileNm_amperesol, fmt_amperesol, app->name, frame);
+
+      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->amperesol_host, fileNm_amperesol);
     }
 
     gkyl_msgpack_data_release(mt);
@@ -3246,7 +3261,7 @@ gkyl_gyrokinetic_app_read_from_frame(gkyl_gyrokinetic_app *app, int frame)
         if (app->field->calc_init_apar) {
           // Compute Apar.
           gk_field_accumulate_current_dens(app, app->field, (const struct gkyl_array **) distf);
-          gk_field_calc_apar_ic(app, app->field);
+          gk_field_calc_apar_ic(app, app->field, app->field->apar);
           // We also compute Apardot here to output the first frame.
           for (int i=0; i<app->num_species; ++i) {
             struct gk_species *gk_s = &app->species[i];

From 73a61958a7de5b8dbcd9e4c3d76d2d4cb88a2b8d Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 10 Jun 2026 15:55:39 -0700
Subject: [PATCH 171/181] remove "Electromagnetic Inner wall limited" entry
 from gk_field_type enum

---
 gyrokinetic/apps/gyrokinetic_lw.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/gyrokinetic/apps/gyrokinetic_lw.c b/gyrokinetic/apps/gyrokinetic_lw.c
index 1c8f2e5bd6..c71119be62 100644
--- a/gyrokinetic/apps/gyrokinetic_lw.c
+++ b/gyrokinetic/apps/gyrokinetic_lw.c
@@ -69,7 +69,6 @@ static const struct gkyl_str_int_pair gk_field_type[] = {
   { "Boltzmann", GKYL_GK_FIELD_BOLTZMANN },
   { "Adiabatic", GKYL_GK_FIELD_ADIABATIC },
   { "Electromagnetic", GKYL_GK_FIELD_EM },
-  { "Electromagnetic Inner wall limited", GKYL_GK_FIELD_EM_IWL },
   { 0, 0 }
 };
 

From 06d9f6e16443e3a37f53c0b2967d528329f1e23b Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 11 Jun 2026 09:36:30 -0400
Subject: [PATCH 172/181] fix some confusion between remove zonal function and
 boolean

---
 gyrokinetic/apps/gk_field_2x3x.c         | 8 ++++----
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h | 2 +-
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index a61d3a654b..3fbc3f5128 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -488,7 +488,7 @@ gk_field_ohm_solve(struct gkyl_gyrokinetic_app *app, struct gk_field *field, str
 
   field->invert_flr(app, field, field->apardot);
 
-  field->remove_em_zonal(app, field, field->apardot);
+  field->remove_em_zonal_func(app, field, field->apardot);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
 }
@@ -572,7 +572,7 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
       gkyl_array_release(f->apardot_host);
       gkyl_array_release(f->amperesol_host);
     }
-    if (f->remove_em_zonal) {
+    if (f->info.remove_em_zonal) {
      gkyl_array_average_release(f->fs_avg_op);
      gkyl_array_release(f->fs_avg);
      gkyl_array_release(f->fs_avg_conf_one);
@@ -793,7 +793,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   // Setup EM solvers.
   f->ampere_solve = gk_field_ampere_solve_none;
   f->em_rhs_func = gk_field_em_rhs_none;
-  f->remove_em_zonal = gk_field_em_zonal_component_none;
+  f->remove_em_zonal_func = gk_field_em_zonal_component_none;
   if (f->is_em) {
     // Translate input file BCs into Ampere BCs.
     for (int d=0; d<app->cdim-1; d++) {
@@ -836,7 +836,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
     f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
 
     if (f->info.remove_em_zonal) {
-      f->remove_em_zonal = gk_field_remove_em_zonal_enabled;
+      f->remove_em_zonal_func = gk_field_remove_em_zonal_enabled;
       // define the reduced range and basis for averaging along x only
       struct gkyl_rect_grid grid_x;
       gkyl_rect_grid_init(&grid_x, 1, &app->grid.lower[0], &app->grid.upper[0], &app->grid.cells[0]);
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 46eb127b9c..4f0ed4f2ae 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1402,7 +1402,7 @@ struct gk_field {
   gkyl_dynvec integ_apar_energy_dot; // d/dt of integrated EM energy components (separate from electrostatic energy for debugging purposes)
   bool is_first_apar_energy_dot_write_call; // flag for d(energy)/dt dynvec written first time
 
-  void (*remove_em_zonal)(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *phi); // Function to remove zonal component.
+  void (*remove_em_zonal_func)(gkyl_gyrokinetic_app *app, struct gk_field *field, struct gkyl_array *phi); // Function to remove zonal component.
   struct gkyl_array_average *fs_avg_op; // Updater for flux surface averaging.
   struct gkyl_array *fs_avg; // Array for storing flux-surface averaged quantities.
   struct gkyl_array *fs_avg_conf_one; // Array of ones in configuration space for flux-surface averaging.

From b2b779d6914c362136a40929d40f776a18296971 Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 11 Jun 2026 08:31:23 -0700
Subject: [PATCH 173/181] add a new option to smooth Aparallel along z after
 stepping it. A new function pointer either points to a none func or connect
 to fem_projection_par_phi_func. This is then used on `out` in the apar
 stepper in gk_field.c. I guess this way allows to fully use any twist or
 other special BCs since it uses the phi infra. Tests soon. This is valgrind
 clean btw

---
 gyrokinetic/apps/gk_field.c                   |  3 +++
 gyrokinetic/apps/gk_field_2x3x.c              | 12 ++++++++++++
 gyrokinetic/apps/gkyl_gyrokinetic.h           |  1 +
 gyrokinetic/apps/gkyl_gyrokinetic_priv.h      |  2 ++
 gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c |  2 ++
 gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c |  2 ++
 6 files changed, 22 insertions(+)

diff --git a/gyrokinetic/apps/gk_field.c b/gyrokinetic/apps/gk_field.c
index 38f333c295..1d7faec4b7 100644
--- a/gyrokinetic/apps/gk_field.c
+++ b/gyrokinetic/apps/gk_field.c
@@ -283,6 +283,9 @@ gk_field_step_apar_enabled(gkyl_gyrokinetic_app *app, struct gk_field *field, st
 {
   // Apar^{n+1} = Apar^{n} + dt*dApar/dt
   gkyl_array_accumulate(gkyl_array_scale(out, dt), 1.0, inp);
+
+  // Smooth Apar along z.
+  field->fem_projection_par_apar_func(app, field, out, out);
 }
 
 static void
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 3fbc3f5128..e085cb0813 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -82,6 +82,13 @@ gk_field_3x_write_twistshift(struct gkyl_gyrokinetic_app *app, struct gk_field *
   }
 }
 
+static void
+gk_field_fem_projection_par_none(gkyl_gyrokinetic_app *app, struct gk_field *field,
+  struct gkyl_array *arr_dg, struct gkyl_array *arr_fem)
+{
+  // Do nothing.
+}
+
 static void
 gk_field_fem_projection_par_rho_ts_2x(gkyl_gyrokinetic_app *app, struct gk_field *field,
   struct gkyl_array *arr_dg, struct gkyl_array *arr_fem)
@@ -554,6 +561,7 @@ gk_field_fem_release_2x3x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
   gkyl_array_release(f->phi_smooth);
   gkyl_array_release(f->apar);
   gkyl_array_release(f->apardot);
+  gkyl_array_release(f->amperesol);
   gkyl_array_release(f->apar_curr);
   gkyl_array_release(f->apar1);
   gkyl_array_release(f->aparnew);
@@ -794,6 +802,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   f->ampere_solve = gk_field_ampere_solve_none;
   f->em_rhs_func = gk_field_em_rhs_none;
   f->remove_em_zonal_func = gk_field_em_zonal_component_none;
+  f->fem_projection_par_apar_func = gk_field_fem_projection_par_none;
   if (f->is_em) {
     // Translate input file BCs into Ampere BCs.
     for (int d=0; d<app->cdim-1; d++) {
@@ -873,6 +882,9 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       double dg_norm = pow(sqrt(2.0), app->basis.ndim);
       gkyl_array_shiftc_range(f->fs_avg_conf_one, dg_norm, 0, &app->local);
     }
+    if (f->info.smooth_apar_z) {
+      f->fem_projection_par_apar_func = f->fem_projection_par_phi_func;
+    }
   }
 
   // Updater for field energy calculation.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 1b132c6255..cbabaeeada 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -557,6 +557,7 @@ struct gkyl_gyrokinetic_field {
   struct gkyl_gyrokinetic_bc ampere_bcs[2*GKYL_MAX_CDIM];
   double mu0; // Magnetic permeability of free space.
   bool remove_em_zonal; // Whether to remove zonal component.
+  bool smooth_apar_z; // Whether to apply a smoother in the z direction for Ampere stepping in EMGK.
   bool is_apar_static; // =true Apar at initial time is used for all time steps.
 
   bool time_rate_diagnostics; // Writes the time rate of change of field energy.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index 4f0ed4f2ae..f7a59347b1 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -1437,6 +1437,8 @@ struct gk_field {
     struct gkyl_array *arr_dg, struct gkyl_array *arr_fem);
   void (*fem_projection_par_phi_func)(gkyl_gyrokinetic_app *app, struct gk_field *field,
     struct gkyl_array *arr_dg, struct gkyl_array *arr_fem);
+  void (*fem_projection_par_apar_func)(gkyl_gyrokinetic_app *app, struct gk_field *field,
+    struct gkyl_array *arr_dg, struct gkyl_array *arr_fem);
   void (*twistshift_func) (struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
 
   // Pointer to function for electromagnetic field solve.
diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
index 9339022279..8c4faf5199 100644
--- a/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
@@ -575,6 +575,8 @@ main(int argc, char **argv)
     },
     .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
+    .remove_em_zonal = false,
+    .smooth_apar_z = false,
   };
 
   // GK app
diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
index a605105045..d796911b8a 100644
--- a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
@@ -579,6 +579,8 @@ main(int argc, char **argv)
     },
     .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
+    .smooth_apar_z = false,
+    .remove_em_zonal = false,
   };
 
   // GK app

From 876113f8ca98ef2934f4c19f7a444f2eb4fc757a Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 18 Jun 2026 10:22:03 -0400
Subject: [PATCH 174/181] remove gk_field_id from the table since this is now
 decided by the collisionless type

---
 gyrokinetic/creg/rt_gk_cbc_2x2v_p1.c                  | 1 -
 gyrokinetic/creg/rt_gk_cbc_3x2v_p1.c                  | 1 -
 gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c              | 1 -
 gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c              | 1 -
 gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c              | 1 -
 gyrokinetic/creg/rt_gk_ltx_iwl_num_miller_3x2v_p1.c   | 1 -
 gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c | 1 -
 gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c | 1 -
 8 files changed, 8 deletions(-)

diff --git a/gyrokinetic/creg/rt_gk_cbc_2x2v_p1.c b/gyrokinetic/creg/rt_gk_cbc_2x2v_p1.c
index b49d37b153..3c1fe567d4 100644
--- a/gyrokinetic/creg/rt_gk_cbc_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_cbc_2x2v_p1.c
@@ -834,7 +834,6 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_cbc_3x2v_p1.c b/gyrokinetic/creg/rt_gk_cbc_3x2v_p1.c
index 2dcfcb6175..7de15edf6e 100644
--- a/gyrokinetic/creg/rt_gk_cbc_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_cbc_3x2v_p1.c
@@ -856,7 +856,6 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
index 22edb63f91..ce10bf047d 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_2x2v_p1.c
@@ -743,7 +743,6 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
index 5ac1995229..714b73f7a2 100644
--- a/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_d3d_iwl_3x2v_p1.c
@@ -841,7 +841,6 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {ctx.side_wall_bias} },
diff --git a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
index ef503fd615..7cf2944b6e 100644
--- a/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_ltx_iwl_2x2v_p1.c
@@ -438,7 +438,6 @@ int main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_ltx_iwl_num_miller_3x2v_p1.c b/gyrokinetic/creg/rt_gk_ltx_iwl_num_miller_3x2v_p1.c
index 8ddb4c9d5f..6a345c14c3 100644
--- a/gyrokinetic/creg/rt_gk_ltx_iwl_num_miller_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_ltx_iwl_num_miller_3x2v_p1.c
@@ -418,7 +418,6 @@ int main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
       { .dir = 0, .edge = GKYL_UPPER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0}, },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
index 50ba3641f7..048c293363 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_2x2v_p1.c
@@ -769,7 +769,6 @@ main(int argc, char **argv)
 
   // Field.
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 60f6a5ae7a..626368922c 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -808,7 +808,6 @@ main(int argc, char **argv)
 
   // field
   struct gkyl_gyrokinetic_field field = {
-    .gkfield_id = GKYL_GK_FIELD_ES,
     .polarization_bmag = ctx.Bref,
     .poisson_bcs = {
       { .dir = 0, .edge = GKYL_LOWER_EDGE, .type = GKYL_BC_GK_FIELD_DIRICHLET, .value = {0.0} },

From c6401fd9aa0570fd9e5d950145a9d0c54125d5dd Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 18 Jun 2026 10:28:43 -0400
Subject: [PATCH 175/181] set the fem_projection_par_apar_func to none in the
 1x em solver

---
 gyrokinetic/apps/gk_field_1x.c | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index 88e8a06a8a..fab85d8947 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -67,6 +67,13 @@ gk_field_em_rhs_none(gkyl_gyrokinetic_app *app, struct gk_field *field, const st
   // Do nothing.
 }
 
+static void
+gk_field_fem_projection_par_none(gkyl_gyrokinetic_app *app, struct gk_field *field,
+  struct gkyl_array *arr_dg, struct gkyl_array *arr_fem)
+{
+  // Do nothing.
+}
+
 static void
 gk_field_fem_release_1x(const gkyl_gyrokinetic_app *app, struct gk_field *f)
 {
@@ -173,6 +180,7 @@ gk_field_fem_new_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
   if (f->is_em) {
     f->em_rhs_func = f->info.is_apar_static ? gk_field_em_rhs_none : gk_field_em_rhs_enabled;
     f->ampere_solve = gk_field_ampere_solve_1x_enabled;
+    f->fem_projection_par_apar_func = gk_field_fem_projection_par_none;
   } else {
     f->em_rhs_func = gk_field_em_rhs_none;
     f->ampere_solve = gk_field_ampere_solve_1x_none;

From ebb992e27f2e53c00f12a80ef8cef207374f75f4 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 18 Jun 2026 10:29:41 -0400
Subject: [PATCH 176/181] GKYL_FIELD_ES does not exist anymore as this is
 decided through the collisionless term

---
 gyrokinetic/apps/gk_multib_field.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_multib_field.c b/gyrokinetic/apps/gk_multib_field.c
index 384da3fd15..a250e2d6e1 100644
--- a/gyrokinetic/apps/gk_multib_field.c
+++ b/gyrokinetic/apps/gk_multib_field.c
@@ -649,7 +649,7 @@ gk_multib_field_new(const struct gkyl_gyrokinetic_multib *mbinp, struct gkyl_gyr
   struct gk_multib_field *mbf = gkyl_malloc(sizeof(struct gk_multib_field));
 
   mbf->info = mbinp->field;
-  mbf->gkfield_id = mbf->info.gkfield_id? mbf->info.gkfield_id : GKYL_GK_FIELD_ES;
+  mbf->gkfield_id = mbf->info.gkfield_id? mbf->info.gkfield_id : GKYL_GK_FIELD;
   mbf->num_local_blocks = mbapp->num_local_blocks;
   mbf->cdim = mbapp->block_topo->ndim;
   mbf->half_domain = mbf->info.half_domain ? mbf->info.half_domain : false;

From 9289c8674d0395c2bc07b5a8d7c3b39303f5ebb3 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Thu, 18 Jun 2026 10:30:09 -0400
Subject: [PATCH 177/181] add output of the solution of the ampere's law and
 unify the description writing in a static routine.

---
 gyrokinetic/apps/gyrokinetic.c | 57 +++++++++++++++++++++-------------
 1 file changed, 36 insertions(+), 21 deletions(-)

diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 8ada173625..f2cfbb2b2e 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1617,6 +1617,26 @@ gkyl_gyrokinetic_app_write_geometry(gkyl_gyrokinetic_app* app, struct gkyl_gk_ge
 //
 // ............. Field outputs ............... //
 // 
+static void write_field_with_metadata(struct gkyl_gyrokinetic_app *app, int frame, const char *field_suffix, 
+  const char *description, struct gkyl_array *field_host) 
+{
+    struct gkyl_msgpack_map_elem custom_meta[] = {
+        { .key = "Description", .elem_type = GKYL_MP_STRING, .cval = description }
+    };
+    int io_meta_len[] = { app->io_meta_grid_len, app->gk_geom->io_meta_basic_len, 1 };
+    const struct gkyl_msgpack_map_elem* io_meta[] = { app->io_meta_grid, app->gk_geom->io_meta_basic, custom_meta };
+    
+    struct gkyl_msgpack_data *mt_data = gkyl_msgpack_create_union(
+        sizeof(io_meta_len) / sizeof(int), io_meta_len, io_meta
+    );
+    const char *fmt = "%s-%s_%d.gkyl";
+    int sz = gkyl_calc_strlen(fmt, app->name, field_suffix, frame);
+    char fileNm[sz + 1];
+    snprintf(fileNm, sizeof(fileNm), fmt, app->name, field_suffix, frame);
+    gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt_data, field_host, fileNm);
+    gkyl_msgpack_data_release(mt_data);
+}
+
 void
 gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame)
 {
@@ -1627,9 +1647,13 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
       gkyl_array_copy(app->field->phi_host, app->field->phi_smooth);
     }
 
-    // Package metadata.
+    // Update metadata for the fields being written out.
     gkyl_msgpack_map_elem_set_double(app->io_meta_grid_len, app->io_meta_grid, "time", tm);
     gkyl_msgpack_map_elem_set_uint(app->io_meta_grid_len, app->io_meta_grid, "frame", frame);
+
+    write_field_with_metadata(app, frame, "field","Electrostatic potential.", app->field->phi_host);
+
+    // Package metadata.
     struct gkyl_msgpack_map_elem io_meta_phi[] = {
       { .key = "Description", .elem_type = GKYL_MP_STRING, .cval = "Electrostatic potential." }
     };
@@ -1643,6 +1667,7 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
     snprintf(fileNm, sizeof fileNm, fmt, app->name, frame);
 
     gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->phi_host, fileNm);
+    gkyl_msgpack_data_release(mt);
 
     if (app->field->is_em) {
       // Solve ampere to output it and compare with stepped apar.
@@ -1658,29 +1683,19 @@ gkyl_gyrokinetic_app_write_field(gkyl_gyrokinetic_app* app, double tm, int frame
         gkyl_array_copy(app->field->apardot_host, app->field->apardot);
         gkyl_array_copy(app->field->amperesol_host, app->field->amperesol);
       }
-      const char *fmt_apar = "%s-apar_%d.gkyl";
-      int sz_apar = gkyl_calc_strlen(fmt_apar, app->name, frame);
-      char fileNm_apar[sz_apar+1]; // ensures no buffer overflow
-      snprintf(fileNm_apar, sizeof fileNm_apar, fmt_apar, app->name, frame);
-
-      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apar_host, fileNm_apar);
-
-      const char *fmt_apardot = "%s-apardot_%d.gkyl";
-      int sz_apardot = gkyl_calc_strlen(fmt_apardot, app->name, frame);
-      char fileNm_apardot[sz_apardot+1]; // ensures no buffer overflow
-      snprintf(fileNm_apardot, sizeof fileNm_apardot, fmt_apardot, app->name, frame);
 
-      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->apardot_host, fileNm_apardot);
+      write_field_with_metadata(app, frame, "apar", 
+        "Stepped parallel component of the magnetic vector potential.", 
+        app->field->apar_host);
 
-      const char *fmt_amperesol = "%s-amperesol_%d.gkyl";
-      int sz_amperesol = gkyl_calc_strlen(fmt_amperesol, app->name, frame);
-      char fileNm_amperesol[sz_amperesol+1]; // ensures no buffer overflow
-      snprintf(fileNm_amperesol, sizeof fileNm_amperesol, fmt_amperesol, app->name, frame);
+      write_field_with_metadata(app, frame, "apardot", 
+        "Time derivative of the parallel component of the magnetic vector potential obtained with Ohm's law.", 
+        app->field->apardot_host);
 
-      gkyl_comm_array_write(app->comm, &app->grid, &app->local, mt, app->field->amperesol_host, fileNm_amperesol);
-    }
-
-    gkyl_msgpack_data_release(mt);
+      write_field_with_metadata(app, frame, "amperesol", 
+        "Solution of the Ampere's law.", 
+        app->field->amperesol_host);
+      }
 
     app->stat.field_io_tm += gkyl_time_diff_now_sec(wtm);
     app->stat.n_field_io += 1;

From 121ba48954895b2971b46a45dae2280d37bc4e0e Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Mon, 29 Jun 2026 18:42:16 -0400
Subject: [PATCH 178/181] some merge fix

---
 gyrokinetic/apps/gk_field_1x.c | 4 ++--
 gyrokinetic/apps/gyrokinetic.c | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_1x.c b/gyrokinetic/apps/gk_field_1x.c
index fab85d8947..d5bb6be72b 100644
--- a/gyrokinetic/apps/gk_field_1x.c
+++ b/gyrokinetic/apps/gk_field_1x.c
@@ -30,7 +30,7 @@ gk_field_ohm_solve_1x(struct gkyl_gyrokinetic_app *app, struct gk_field *field,
   gkyl_array_accumulate_range(field->dApartdtSlvr_lhs_factor, 1.0, field->lapWeightAmpere, &app->local);
 
   // Weak division method dApar/dt = sum_s q_s int dv vpar d/dt(F_s) / ( (k_perp^2/mu_0 + sum_s q_s^2/m_s int dv F_s) )
-  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, out, 0, field->currentDensdot, 
+  gkyl_dg_div_op_range(field->div_mem, &app->basis, 0, out, 0, field->currentDensdot,
     0, field->dApartdtSlvr_lhs_factor, &app->local);
   
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
@@ -42,7 +42,7 @@ gk_field_ampere_solve_1x_enabled(gkyl_gyrokinetic_app *app, struct gk_field *fie
   struct timespec wst = gkyl_wall_clock();
 
   // Weak division method Apar = sum_s q_s int dv vpar F_s / (k_perp^2/mu_0)
-  gkyl_dg_div_op_range(field->div_mem, app->basis, 0, out, 0, field->currentDens, 
+  gkyl_dg_div_op_range(field->div_mem, &app->basis, 0, out, 0, field->currentDens,
     0, field->lapWeightAmpere, &app->local);
 
   app->stat.field_apar_solve_tm += gkyl_time_diff_now_sec(wst);
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 4b529b5bd8..6ec58ec2f5 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -1623,8 +1623,8 @@ static void write_field_with_metadata(struct gkyl_gyrokinetic_app *app, int fram
     struct gkyl_msgpack_map_elem custom_meta[] = {
         { .key = "Description", .elem_type = GKYL_MP_STRING, .cval = description }
     };
-    int io_meta_len[] = { app->io_meta_grid_len, app->gk_geom->io_meta_basic_len, 1 };
-    const struct gkyl_msgpack_map_elem* io_meta[] = { app->io_meta_grid, app->gk_geom->io_meta_basic, custom_meta };
+    int io_meta_len[] = { app->io_meta_dg_len, app->gk_geom->io_meta_basic_len, 1 };
+    const struct gkyl_msgpack_map_elem* io_meta[] = { app->io_meta_dg, app->gk_geom->io_meta_basic, custom_meta };
     
     struct gkyl_msgpack_data *mt_data = gkyl_msgpack_create_union(
         sizeof(io_meta_len) / sizeof(int), io_meta_len, io_meta

From c5db4a6233351e34dcd36d7a126a2d95c2973046 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 2 Sep 2026 11:55:11 -0400
Subject: [PATCH 179/181] merge fix

---
 gyrokinetic/apps/gk_field_2x3x.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index ee6810d150..4ab5aa18a0 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -813,7 +813,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
         for (int i=0; i<GKYL_MAX_CDIM; i++)
           f->fs_avg_subdir[i] = fs_avg_subdir[i];
       }
-      f->fs_avg_op = gkyl_array_average_new(&inp_avg_xyz_to_x);
+      f->fs_avg_op = gkyl_array_average_inew(&inp_avg_xyz_to_x);
       f->fs_avg = mkarr(app->use_gpu, f->fs_avg_basis.num_basis, f->fs_avg_range_ext.volume);
       f->fs_avg_conf_one = mkarr(app->use_gpu, app->basis.num_basis, app->local_ext.volume);
       double dg_norm = pow(sqrt(2.0), app->basis.ndim);

From 36905bb177fdba48b5f6c898b0e6a29fa9fa7bc7 Mon Sep 17 00:00:00 2001
From: antoinehoff <antoine-hoffmann@hotmail.com>
Date: Wed, 2 Sep 2026 11:55:23 -0400
Subject: [PATCH 180/181] Make the dg gk unit test electromagnetic

---
 gyrokinetic/unit/ctest_dg_gyrokinetic.c         | 2 +-
 gyrokinetic/unit/ctest_dg_gyrokinetic_kern_tm.c | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/gyrokinetic/unit/ctest_dg_gyrokinetic.c b/gyrokinetic/unit/ctest_dg_gyrokinetic.c
index 7186e34050..43d5567993 100644
--- a/gyrokinetic/unit/ctest_dg_gyrokinetic.c
+++ b/gyrokinetic/unit/ctest_dg_gyrokinetic.c
@@ -110,7 +110,7 @@ test_dg_gyrokinetic()
     phaseRange, phaseRange_ext, velLocal, velLocal_ext, false);
 
   struct gkyl_dg_eqn* eqn = gkyl_dg_gyrokinetic_new(&confBasis, &basis, &confRange, &phaseRange, 
-    charge, mass, 0, gk_geom, gvm, false);
+    charge, mass, GKYL_GK_COLLISIONLESS_EM, false, false, gk_geom, gvm, false);
 
   TEST_CHECK( eqn->num_equations == 1 );
 
diff --git a/gyrokinetic/unit/ctest_dg_gyrokinetic_kern_tm.c b/gyrokinetic/unit/ctest_dg_gyrokinetic_kern_tm.c
index 9ab3173e12..faf097b510 100644
--- a/gyrokinetic/unit/ctest_dg_gyrokinetic_kern_tm.c
+++ b/gyrokinetic/unit/ctest_dg_gyrokinetic_kern_tm.c
@@ -131,7 +131,7 @@ test_3x2v_p1(bool use_gpu)
 
   struct gkyl_dg_updater_gyrokinetic* up;
   up = gkyl_dg_updater_gyrokinetic_new(&phaseGrid, &confBasis, &basis, &confRange, &phaseRange,
-    is_zero_flux, 1.0, 1.0, GKYL_GK_COLLISIONLESS_ES, gk_geom, gvm, &aux, use_gpu);
+    is_zero_flux, 1.0, 1.0, GKYL_GK_COLLISIONLESS_EM, false, false, gk_geom, gvm, &aux, use_gpu);
 
   // initialize arrays
   struct gkyl_array *fin, *rhs, *cflrate;

From 509304c508d2a3152565b23c2de9c6b23fa6836a Mon Sep 17 00:00:00 2001
From: Antoinehoff <antoine-hoffmann@hotmail.com>
Date: Tue, 8 Sep 2026 10:36:53 -0400
Subject: [PATCH 181/181] We now always apply Apar smoothing, `smooth_apar_z`
 option is removed.

---
 gyrokinetic/apps/gk_field_2x3x.c              | 4 +---
 gyrokinetic/apps/gkyl_gyrokinetic.h           | 1 -
 gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c | 1 -
 gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c | 1 -
 4 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index 4ab5aa18a0..f3f40bda7a 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -819,9 +819,7 @@ gk_field_fem_new_2x3x(struct gkyl_gyrokinetic_app *app, struct gk_field *f)
       double dg_norm = pow(sqrt(2.0), app->basis.ndim);
       gkyl_array_shiftc_range(f->fs_avg_conf_one, dg_norm, 0, &app->local);
     }
-    if (f->info.smooth_apar_z) {
-      f->fem_projection_par_apar_func = f->fem_projection_par_phi_func;
-    }
+    f->fem_projection_par_apar_func = f->fem_projection_par_phi_func;
   }
 
   // Updater for field energy calculation.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 320dd22936..dfae3b6f86 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -568,7 +568,6 @@ struct gkyl_gyrokinetic_field {
   struct gkyl_gyrokinetic_bc ampere_bcs[2*GKYL_MAX_CDIM];
   double mu0; // Magnetic permeability of free space.
   bool remove_em_zonal; // Whether to remove zonal component.
-  bool smooth_apar_z; // Whether to apply a smoother in the z direction for Ampere stepping in EMGK.
   bool is_apar_static; // =true Apar at initial time is used for all time steps.
 
   bool time_rate_diagnostics; // Writes the time rate of change of field energy.
diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
index 8c4faf5199..0feac34d61 100644
--- a/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_2x2v_p1.c
@@ -576,7 +576,6 @@ main(int argc, char **argv)
     .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
     .remove_em_zonal = false,
-    .smooth_apar_z = false,
   };
 
   // GK app
diff --git a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
index d796911b8a..461174d282 100644
--- a/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_helical_zpar_3x2v_p1.c
@@ -579,7 +579,6 @@ main(int argc, char **argv)
     },
     .mu0 = GKYL_MU0,
     .time_rate_diagnostics = true,
-    .smooth_apar_z = false,
     .remove_em_zonal = false,
   };